![Algebraic Expansions 13
Fig. 4 Adapting two algebraic surfaces into enclosed volumes (Dana Kummerlöw (left) and
Christopher Jarchow (right))
surfaces into enclosures through various operations like for example section with a
cuboid or deforming the surface until it becomes a volume (Fig.4).
In a fourth step, experimental architectures are generated by synthesizing the
knowledge and know-how acquired in the first three steps (Fig.5-7). The resulting
building designs are furthermore situated in urban contexts. While it can be argued
that the extra-ordinary shapes of algebraic surfaces by definition have difficulty be-
coming part of any urban context, we argue that human settlements have always
contained special buildings that have often been the most radical expression of what
was possible at any given time. Those special buildings have also played impor-
tant roles in the social life of communities, attracting visitors and inspiring social
and cultural exchange. The building designs which incorporate the unprecedented
shapes of algebraic surfaces can therefore play important roles in human commu-
nities, providing spatial focus points and inspiring new forms of social exchange.
Additionally, the polyoptical qualities of such shapes [see above] means that they
can relate differently to the more and more diversified urban fabrics of todays cities.
The last step consists of printing the designs in 3D (Fig.8). While we use the
technology to print only models of the designs, it is rapidly progressing to print
larger and larger objects, the largest at the moment exceeding telephone box size.
While it is as a matter of course not satisfactory to see building construction as a
matter of simply printing large objects of a uniform material, for us in our project
the printability of the shapes is proof of concept enough insofar that unprecedented,
new and never seen or touched objects are transported from the intellectual world of
mathematics into a tangible physical reality.
5 Function Inspired by Form?
The steps we take in the experimental design project changes the common design
procedure of Form follows function to Form inspires function or even Function fol-
lows form. At first, this may be seen as a severe restriction of designers capabilities,
restraining their options to a corset defined by a given algebraic surface. Yet, we](https://image.slidesharecdn.com/1246481-250518172131-70717bd2/85/Computational-Design-Modelling-Proceedings-Of-The-Design-Modelling-Symposium-Berlin-2011-1st-Edition-Robert-Aish-Auth-31-320.jpg)
![Tools and Design Strategies to Study Rib Growth
Chris Bardt, Michal Dziedziniewicz, and Joy Ko
1 Introduction
Ever since Viollet-le-Duc the 19th century engineer and architect proposed “natural”
structures borne out of ideal forms of specific materials, engineers and architects
alike have been interested in the notion of an organic approach to form and structure
[7]. Functionalism, the idea that form is a resultant of forces and needs, was core to
the modernist project but became overly deterministic and untenable for architecture
[1]. The course of much of the latter part of the 20th century history was one of
the separation of engineering (calculation) and architecture (organization) into two
exclusive realms uneasily brought together, with one or the other taking the lead
in the generation of form [4]. In the architectural design process, calculation of
structural performance customarily entered late in the design process when the form
was already largely realized.
Computation, now the widely accepted lingua franca of many fields that archi-
tecture touches, has played a central role in rekindling interest amongst architects to
rejoin calculation and organization as a critical step in creating truly performative
forms. Current interests in architecture such as biomimicry, genetic algorithms, and
emergence through agent-based methods allude to an organic process; they reflect
a desire to bring the architectural process closer to one in which structure and form
are interdependent. The rapid pace of development and adoption by the architec-
ture community of various experimental software and workflow models – such as
the traer-physics library for Processing or the Grasshopper plugins Kangaroo and
Geometry Gym–are telltale signs that the computer is no longer seen by architects
as merely a mechanism for representation divorced from physical conditions. Al-
ready, structural performance is part of the design process because of a traditionally
close dialog between architects and structural engineers. Still, the challenge inher-
ent to the creation of a truly generative computational tool for architectural design
Chris Bardt · Michal Dziedziniewicz · Joy Ko
Department of Architecture, Rhode Island School of Design, Providence, Rhode Island](https://image.slidesharecdn.com/1246481-250518172131-70717bd2/85/Computational-Design-Modelling-Proceedings-Of-The-Design-Modelling-Symposium-Berlin-2011-1st-Edition-Robert-Aish-Auth-35-320.jpg)
![20 C. Bardt, M. Dziedziniewicz, and J. Ko
these supports are modeled within ABAQUS requiring no change to the ABAQUS
script within a given run. Meshing is done using a tetrahedral meshing to handle
forms that are not constrained to a predeterminedgrid. This is done via a specification
of a seeding of the boundary, which in turn is a function of the seed number (an
average node-vertex to node-vertex distance). By fixing the seed number we fix the
nodes on the surface and hence, obtain a consistent set of vertices throughout a run.
For a design objective of least square deflection of the plate, these plate vertices are
further identified by looking at the coordinates of each vertex of the instance created
and matching the vertices in the sheet with corresponding field outputs. By using
ABAQUS, there is the advantage of an extensive material library which is constantly
expanding through such additions like the Granta material selection plugin.
3 Case Study: A Design Experiment to Model Rib Growth
3.1 Historical Significance of Rib Forms
The relation of ribs to surface form has intrigued architects and engineers for hun-
dreds of years. The early medieval masons developed ribs based on drawn arcs of
circles, and the vaults spanning these ribs were distorted and uneven irregular sur-
faces “stretched” to fit between the splayed rib structures [9]. The ribs served as the
structure, to a large extent, carrying the vaults. The 16th century development of
sophisticated drawing systems allowed masons to control the stonecutting of vaults
to such an extent that the vaults became shell structures and the ribs a reinforcing
lattice work – in effect reversing the structural role of vaults and ribs from the early
Gothic period [6].
Historically, there has been a fundamental ambiguity between rib and surface.
Which comes first – the form of the rib or the the surface which is being rein-
forced by the rib? In the 20th century, rib and surface research was conducted by a
new breed of designer, the architect-engineer such as Nervi, Maillart, Dieste, Can-
dela. Their research took the form of experimental long span structures such as
thin shells, ribbed shells, and lamella structures often using the new technology
of reinforced concrete. These experiments were limited to statically determinate
structures, geometries optimized for given parameters. Any kind of experimenta-
tion that went beyond these structures proved difficult, an example being Frank
Lloyd Wrights tapered, dendriform, mushroom columns which were subject to a
combination of tensile, coplanar and non axial loads. The local building commit-
tee refused to approve the column for construction until its performance had been
empirically demonstrated [8].
In recent decades, the problem of generating optimal patterns of reinforcement in
plate and shell structures – topology optimization – has been studied intensively by
the mathematical and engineering communities. Some notable precedents have in-
formed our work, including Bendsoe and Kikuchi’s work [2] which spawned studies
of a large range of loading conditions, optimality and efficiency criteria and hybrid
materials (many detailed in [3]) that utilize the homogenization method–a powerful](https://image.slidesharecdn.com/1246481-250518172131-70717bd2/85/Computational-Design-Modelling-Proceedings-Of-The-Design-Modelling-Symposium-Berlin-2011-1st-Edition-Robert-Aish-Auth-38-320.jpg)
![Tools and Design Strategies to Study Rib Growth 21
tool in variational calculus–which results in solutions that are density distributions
of material. For practical concerns of buildability and formwork, we looked to tech-
niques that produced distinct pattern of reinforcements. In [5], Ding and Yamazaki
proposed a technique based on the adaptive growth rule of branching systems using
a design criterion of maximum global stiffness, which has the benefit of producing
distinct patterns. While it seems quite general to a number of support and load-
ing conditions, only typical support and loading conditions on a square plate were
implemented.
3.2 Creating the Methodological Framework for an Experiment
The integrated tool and workflow is designed as a sandbox in which experiments
to test intuition-led strategies can be conducted with relative ease. In devising this
initial experiment, a number of assumptions were made. The surface that we con-
sider in this experiment is a square plate with uniform thickness and a single cir-
cular column of support. The ribs are uniform in cross-section and of fixed length.
The surface and ribs are made of the same isotropic elastic material and form a
monolithic ribbed surface. The boundary conditions applied are total encastre for
the support allowing displacement of the ribbed surface. Since the surface here is a
plate, we can consider a design objective of least square deflection of the surface.
The set of mesh nodes on the plate, N , stays constant through a given run so we can
define deflection in the least-squares sense by
Σi∈N Δz2
i , where Δzi is the vertical
deflection of the ith node relative to the height of the plate above the support. The
growth strategy used here is based on a “greedy algorithm” approach where at each
step in the iteration, the choice that minimizes the squared deflection amongst all
local possibilities is taken. This growth strategy comprises the following rules:
• Growth initializes at the position of the support, which we call the origin.
• An active growth point is either the end of a connected set of ribs emanating from
the origin or the origin itself.
• At each active growth point, there are k equivariant possible directions of growth.
At all active growth points other than the origin, the length of the rib grown at
each step is a fixed length l. The length of a rib emanating from the origin is
length r +l, where r is the radius of the circular support.
• A finite elements analysis for the whole structure is carried out at each growth
point for each direction of growth, and rib growth occurs at the point and direc-
tion that minimizes the least squared deflection amongst all local possibilities.
• When the rib hits the boundary of the plate, the rib is cut short and the point of
intersection with the boundary becomes an active growth point.
This initial experiment is intended to be interactive with the user so no a priori
stopping condition is given other than the number of steps that the user specifies, or
when the ribs at all active points grows back onto itself. Fig. 2. illustrates the rules
governing this growth strategy.](https://image.slidesharecdn.com/1246481-250518172131-70717bd2/85/Computational-Design-Modelling-Proceedings-Of-The-Design-Modelling-Symposium-Berlin-2011-1st-Edition-Robert-Aish-Auth-39-320.jpg)
![Free Shape Optimal Design of Structures
Kai-Uwe Bletzinger
Abstract. Actual trends in numerical shape optimal design of structures deal with
handling of very large dimensions of design space. The goal is to allowing as much
design freedom as possible while considerably reducing the modeling effort. As a
consequence, several technical problems have to be solved to get procedures which
are robust, easy to use and which can handle many design parameters efficiently.
The paper briefly discusses several of the most important aspects in this context and
presents many illustrative examples which show typical applications for the design
of light weight shell and membrane structures.
1 Introduction
Shape optimal design is a classical field of structural optimization. Applied to the
design of free form shells and membranes or, more generally, light weight structures,
it is of big importance in architecture, civil engineering or various applications of
industrial metallic or composite shells as e.g. in automotive or aerospace industries
[1, 2, 3]. In the “old” days of the pre-computer age optimal shapes had been found
by experiments such as inverted hanging models or soap film experiments. Still,
those shapes are of great importance for practical design as they define structures
of minimal amount of bending which, in turn, are as stiff as possible. As a conse-
quence, “stiffness” is one of the most important design criteria one can think of. The
methods discussed in the sequel refer to this design criterion in various ways.
A standard approach of optimal shape design is to discretize the structure and to
use geometrical discretization parameters as design variables, e.g. nodal coordinates.
As optimization is a mathematical inverse problem it exhibits typical pathological
properties which in particular become obvious or even dominant if the number of
design parameters becomes large. In particular, one has to deal with questions like
Kai-Uwe Bletzinger
Lehrstuhl für Statik, Technische Universität München, Germany](https://image.slidesharecdn.com/1246481-250518172131-70717bd2/85/Computational-Design-Modelling-Proceedings-Of-The-Design-Modelling-Symposium-Berlin-2011-1st-Edition-Robert-Aish-Auth-43-320.jpg)
![28 K.-U. Bletzinger
3 Direct Filtering of Numerical Models
Numerical form finding techniques allow the direct approach of filtering the de-
sign noise. As an example, consider a circular plate as shown in Fig.2 which
is discretized by finite shell elements. The nodal positions of the finite element
nodes shall be found such that the stiffness of the structure is maximized. With-
out any additional treatment numerical optimization procedures suggest a highly
crinkled shape. Obviously, the simulation resolves the physics of the random stiff-
ening pattern similar to the paper experiment. The smallest crinkles are defined
by the possible resolution of the finite element mesh. Finer meshes allow even
higher frequencies. Additionally, high frequent crinkles result in extreme element
distortions which come together with additional artificial, non-physically stiff ele-
ment behavior which is known as “locking”. That means that filtering play a dou-
ble role (i) to prevent non-physical artifacts by controlling mesh distortion and
(ii) to help to identify the preferred optimal shape within the infinity of the de-
sign space. For the plate in Fig.2 a coarse low pass filter has been applied. It
is a simple hat function of rotational symmetry with a base length of the size
of the plate diameter. Consequently, the dome is identified as optimal structure
which is well known from the inverted hanging model experiment. It appears that
the type of filter (e.g. hat, cubic spline or Gauss distribution) is of minor impor-
tance in contrast to the size of the filter basis which directly controls the minimum
size of stiffening “crinkles”. The filter size is a very effective as well as efficient
control for exploring the design space as it is shown in the following examples
[1, 2, 3, 4].
4 CAGD Based Parameterization Techniques and Structural
Shape Optimization
The industrial state of the art in structural optimization is characterized by the com-
bined application of CAGD methods (Computer Aided Geometric Design), finite
element analysis, and non-linear programming. The idea is to define the degrees
of freedom for shape optimization and form finding by some few but character-
istic control parameters of the CAGD model. The choice of a CAGD model is
indeed identical to an implicit pre-selection of a design filter which directly af-
fects the result. As most often a CAGD model is quite complex, modifications
are cumbersome and it is difficult to explore the design space by adjusting the
implicit design filter. Often architects and engineers are not totally aware about
that and miss alternatives. Still, however, the remaining design space might be
large enough and the limitations might be accepted. The most actual trend is
defined by the Isogeometric Analysis, where NURBS shape functions are used
for both, the design modeling as well as the structural analysis [5, 6, 7, 8, 9].](https://image.slidesharecdn.com/1246481-250518172131-70717bd2/85/Computational-Design-Modelling-Proceedings-Of-The-Design-Modelling-Symposium-Berlin-2011-1st-Edition-Robert-Aish-Auth-46-320.jpg)
![Free Shape Optimal Design of Structures 29
As a consequence, design models must be analysis suitable which create new chal-
lenges for the CAGD community regarding geometrical compatibility and treating
trimmed surfaces. T-splines have been suggested as remedy [10, 11].
5 Minimal Surfaces
The form finding of tensile structures is defined by the equilibrium of external and
internal pre-stress forces. The choice of pre-stresses of surface and edge cables is
the “filter” applied to screen the design space. As the shape is uniquely defined
by the equilibrium of forces and stresses there is no material related term in the
equations. Consequently, nodes of the discretization mesh can float freely on the
surface because surface strains are not inducing elastic stresses relevant for the form
finding process. Additional regularization of the method is necessary for procedural
reasons not as means to explore the design space. In contrast to the most of the
available methods the Updated Reference Strategy (URS) is consistently derived
from continuum mechanics [12, 13]. Therefore, it appears to be very robust and can
easily be applied for all kind of applications, for membranes as well as cables and
their combinations. It can be interpreted as a generalization of the well-known force
density method [14].
6 Illustrative Examples
6.1 Pre-stressed Surfaces
These examples, Fig.3 and Fig.4, present the direct application of URS for the de-
sign of pre-stressed surfaces due to isotropic (minimal surfaces) and anisotropic
surface stresses. Note, that even ideal minimal surfaces can easily be determined
which is a challenge for many available structural form finding methods. The im-
plemented procedure is able to treat form finding under additional effects as there
are additional surface loads (e.g. pressure), interior edge cables (needs additional
formulation of constraints on cable length) and consideration of stiffening members
in bending and compression (kind of tensegrity structures). For further information
refer to www.membranes24.com.
6.2 Norwegian Pavilion at EXPO 2010, Shanghai
This example shows the application of the URS technique in architecture and civil
engineering for the form finding of the roof for the Norwegian pavilion at the EXPO
2010 in Shanghai, Fig.5, [15].](https://image.slidesharecdn.com/1246481-250518172131-70717bd2/85/Computational-Design-Modelling-Proceedings-Of-The-Design-Modelling-Symposium-Berlin-2011-1st-Edition-Robert-Aish-Auth-47-320.jpg)
![32 K.-U. Bletzinger
Fig. 7 Optimal bead design of initially plane sheet
Fig. 8 Bead optimization of a thin metal sheet for the automotive industry
6.4 Shape Optimization of a Wind Turbine Blade
The shape of a wind turbine blade is optimized for two cases, Fig.9 to Fig.11: To
maximize stiffness for given mass and to minimize mass for defined stiffness. The
pressure distribution has been determined from a CFD simulation is applied to a
linear elastic structural model for shape optimization as a preliminary design study.
The next steps will consider a complete non-linear structural model in a fully cou-
pled FSI-environment for shape optimization. More than 9.000 shape variables have
been used. Again, note, the smooth shape although small design filters have been
used to prevent numerical noise. The initial shape has been generated from a Rhino
3D c
model which also can be used for a isogeometric analysis for the fully cou-
pled, transient analysis of the blade in a numerical wind tunnel [7, 8, 9]. The latter
study has been done in a joint work together with Yuri Bazilevs at University of
California at San Diego [16].](https://image.slidesharecdn.com/1246481-250518172131-70717bd2/85/Computational-Design-Modelling-Proceedings-Of-The-Design-Modelling-Symposium-Berlin-2011-1st-Edition-Robert-Aish-Auth-50-320.jpg)
![trend indicated by the majority of the isobars, without reproducing any
exceptional shapes.
Write out a careful description of the average form, dimensions
[measured by a scale of miles or of latitude degrees (70 miles = 1 degree
about)] and gradients of these areas of low pressure, noting any tendency to
elongate in a particular direction; any portions of the composite where the
gradients are especially strong, weak, etc.
B. Anticyclones.—This investigation is carried out in precisely the same
manner as the preceding one, except that anticyclones (highs) are now
studied instead of cyclones. The isobars may be traced off as far away from
the center as the 30.20-inch line in most cases. When, however, the pressure
at the center is exceptionally high, it will not be necessary to trace off lower
isobars than those for 30.30, or 30.40, or sometimes 30.50 inches.
Loomis’s Results as to Form and Dimensions of Cyclones and
Anticyclones.—One of the leading American meteorologists, Loomis, who
was for many years a professor in Yale University, made an extended study of
the form and dimensions of areas of low and high pressure as they appear on
our daily weather maps. In the cases of areas of low pressure which he
examined, the average form of the areas was elliptical, the longer diameter
being nearly twice as long as the shorter (to be exact the ratio was 1.94 : 1).
The average direction of the longer diameter he found to be about NE. (N.
36° E.), and the length of the longer diameter often 1600 miles. In the case
of areas of high pressure, Loomis also found an elliptical form predominating;
the longer diameter being about twice as long as the shorter (ratio 1.91 : 1),
and the direction of trend about NE. (N. 44° E.). These characteristics hold, in
general, for the cyclonic and anticyclonic areas of Europe also. The cyclones
of the tropics differ considerably from those of temperate latitudes in being
nearly circular in form.](https://image.slidesharecdn.com/1246481-250518172131-70717bd2/85/Computational-Design-Modelling-Proceedings-Of-The-Design-Modelling-Symposium-Berlin-2011-1st-Edition-Robert-Aish-Auth-70-320.jpg)
![your wind arrows so that the composite shall properly represent winds in all
parts of the cyclonic area.
Deduce a general rule for the circulation and velocity of the wind in a
cyclonic area, as shown on your tracing, and write it out.
B. Anticyclones.—This exercise is done in precisely the same way as the
preceding one, except that anticyclones and their winds are studied instead of
cyclones.
Deduce a general rule for the circulation and velocity of the wind in an
anticyclonic area, as shown on your tracing, and write it out.
The control of the wind circulation by areas of low and high
pressure is one of the most important laws in meteorology. Buys-Ballot, a
Dutch meteorologist, first called attention to the importance of this law in
Europe, and it has ever since been known by his name. Buys-Ballot’s Law is
generally stated as follows: Stand with your back to the wind, and the
barometer will be lower on your left hand than on your right.[4] This
statement, as will be seen, covers both cyclonic and anticyclonic systems. The
circulations shown on your tracings hold everywhere in the Northern
Hemisphere, not only around the areas of low and high pressure seen on the
United States weather maps, but around those which are found in Europe and
Asia, and over the oceans as well. Mention has already been made, in the
chapter on isobars (VII), of the occurrence of immense cyclonic and
anticyclonic areas, covering the greater portion of a continent or an ocean,
and lasting for months at a time. These great cyclones and anticyclones have
the same systems of winds around them that the smaller areas, with similar
characteristics, have on our weather maps. A further extension of what has
just been learned will show that if in any region there comes a change from
low pressure to high pressure, or vice versa, the system of winds in that
region will also change. Many such changes of pressures and winds actually
occur in different parts of the world, and are of great importance in controlling
the climate. The best-known and the most-marked of all these changes occurs
in the case of India. During the winter, an anticyclonic area of high pressure is
central over the continent of Asia. The winds blow out from it on all sides,
thus causing general northeasterly winds over the greater portion of India.
These winds are prevailingly dry and clear, and the weather during the time
they blow is fine. India then has its dry season. As the summer comes on, the
pressure over Asia changes, becoming low; a cyclonic area replaces the winter
anticyclone, and inflowing winds take the place of the outflowing ones of the
winter. The summer winds cross India from a general southwesterly direction,](https://image.slidesharecdn.com/1246481-250518172131-70717bd2/85/Computational-Design-Modelling-Proceedings-Of-The-Design-Modelling-Symposium-Berlin-2011-1st-Edition-Robert-Aish-Auth-72-320.jpg)
![come from over the ocean, and are moist and rainy. India then has its rainy
season. These seasonal winds are known as Monsoons, a name derived from
the Arabic and meaning seasonal.
[4] In the Northern Hemisphere.
Fig. 48.
The accompanying figure (Fig. 48) is taken from the Pilot Chart of the
North Atlantic Ocean, published by the Hydrographic Office of the United
States Navy for the use of seamen. It shows the wind circulation around the
center of a cyclone which is moving northward along the Atlantic Coast of the
United States. The long arrow indicates the path of movement; the shorter
arrows indicate the directions of the winds. By means of such a diagram as
this a captain is able to calculate, with a considerable degree of accuracy, the
position of the center of the cyclone, and can often avoid the violent winds
near that center by sailing away from it, or by “lying to,” as it is called, and
waiting until the center passes by him at a safe distance. These cyclones
which come up the eastern coast of the United States at certain seasons are
usually violent, and often do considerable damage to shipping. The Weather
Bureau gives all the warning possible of the coming of these hurricanes, as
they are called, by displaying hurricane signals along the coast, and by issuing
telegraphic warnings to newspapers. In this way ship captains, knowing of the
approach of gales dangerous to navigation, may keep their vessels in port
until all danger is past. Millions of dollars’ worth of property and hundreds of
lives have thus been saved.](https://image.slidesharecdn.com/1246481-250518172131-70717bd2/85/Computational-Design-Modelling-Proceedings-Of-The-Design-Modelling-Symposium-Berlin-2011-1st-Edition-Robert-Aish-Auth-73-320.jpg)
![Sums Total
Cases Total
Means Mean
Enter the temperature at 8 A.M. on the first day of the month in a column
of the table under the proper wind direction. Thus, if the wind is NE., and the
temperature 42°, enter 42 in the second column of the table. Repeat the
observation for the same station, and for all the other days of the month,
recording the temperatures in each case in their appropriate columns in the
table. Omit all cases in which the wind is light, because winds of low velocities
are apt to be considerably affected by local influences. When the observations
for the whole month have been entered in the table, add up all the
temperatures in each column (sums). Find the mean temperature (means)
observed with each wind direction by dividing the sums by the number of
observations in each column (cases). Add all the sums together; divide by the
total number of cases, and the result will be the mean temperature[5] for the
month at the station. The general effect of the different wind directions upon
the temperature is shown by a comparison of the means derived from each
column with the mean for the month.
[5] Derived from the 8 A.M. observations. This does not give the true
mean temperature.
Fig. 49.](https://image.slidesharecdn.com/1246481-250518172131-70717bd2/85/Computational-Design-Modelling-Proceedings-Of-The-Design-Modelling-Symposium-Berlin-2011-1st-Edition-Robert-Aish-Auth-76-320.jpg)
Computational Design Modelling Proceedings Of The Design Modelling Symposium Berlin 2011 1st Edition Robert Aish Auth
- 1. Computational Design Modelling Proceedings Of The Design Modelling Symposium Berlin 2011 1st Edition Robert Aish Auth download https://ebookbell.com/product/computational-design-modelling- proceedings-of-the-design-modelling-symposium-berlin-2011-1st- edition-robert-aish-auth-2492962 Explore and download more ebooks at ebookbell.com
- 5. Christoph Gengnagel, Axel Kilian, Norbert Palz, and Fabian Scheurer (Eds.) Computational Design Modelling Proceedings of the Design Modelling Symposium Berlin 2011 ABC
- 6. Editors Prof. Dr. Christoph Gengnagel Universität der Künste Berlin Hardenbergstraße 33 10623 Berlin, Germany E-mail: gengnagel@udk-berlin.de Prof. Axel Kilian PhD Princeton University Princeton NJ 08544 USA Prof. Dipl.-Ing. Norbert Palz Universität der Künste Berlin UDK Hardenbergstraße 33 10623 Berlin, Gemany E-mail: n.palz@udk-berlin.de Fabian Scheurer designtoproduction GmbH Seestraße 78 Erlenbach/Zurich, Switzerland ISBN 978-3-642-23434-7 e-ISBN 978-3-642-23435-4 DOI 10.1007/978-3-642-23435-4 Library of Congress Control Number: 2011935739 c 2011 Springer-Verlag Berlin Heidelberg This work is subject to copyright. All rights are reserved, whether the whole or part of the mate- rial is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Dupli- cation of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer. Violations are liable to prosecution under the German Copyright Law. The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. Typeset Cover Design: Scientific Publishing Services Pvt. Ltd., Chennai, India. Printed on acid-free paper 9 8 7 6 5 4 3 2 1 springer.com
- 7. Foreword Now in its third edition, the Design Modelling Symposium Berlin constitutes a platform for dialogue on experimental practice and research within the field of com- putationally informed architectural design. Contemporary architectural production employs an increasing number of com- putational tools that undergo continuous proliferation of functions and expand their role within the design process. CAD/CAM technologies have matured into appli- cations with increasingly user-friendly programme structures and an efficient ex- change between various analytical tools. Computational geometry enables the de- sign and manufacturing of complex surface configurations, a capacity beyond the repertoire of analog architectural practices constrained by the limitations of de- scriptive geometry. CAD/CAM technologies have been used successfully to achieve novel architectural expression by enabling digital geometry to drive digital fabri- cation processes. These innovations that have changed the work flow and design approach of a wide range of architectural practices and within academia. Yet in parallel to these advances, limitations have become apparent. In many cases the relationship between design idea and computational tool seems reversed. The resulting buildings appear as reductionist materialization of the possibilities of software that shaped them. Only few examples exist where computational tools are used to develop design solutions for complex building programs within a moderate budget, yet driven by a rich conceptual approach that ventures beyond established theoretical paradigms of computational practice. On the basis of these observations, a critical evaluation of the relationships be- tween tool, conceptual model and final materialization appears necessary and valu- able. The promise of an increased role of computational processes in the design of architecture lies in the manifold solutions that exceed human calculative capacities. A good example is the integration of Finite Element Method (FEM) based analysis procedures and generative form finding methods. However, these processes depend strongly on boundary conditions induced in the problem setup defined by the archi- tect or engineer. Each optimization—be it structural or environmental—therefore can only produce a result within the realm of the abstracted (computational) model, and in no way represents a final solution for the real world or even an indication for
- 8. VI Foreword changing the design conceptually. The complexity of the interconnected and often conflicting information required to shape a building—be it explicitly describable or not—remains a challenge for contemporary computational processes. A future architectural practice needs to cultivate a critical awareness of such limitations in order to develop successful future strategies. The critical dialogue that we envision and encourage at the Design Modelling Symposium Berlin 2011 should be achieved by a collective contemplation of these current approaches and their entwined technological developments. We would like to promote discussion on future strategies for a reasonable and innovative imple- mentation of digital potentials guided by both responsibility towards processes and the consequences they initiate. The fact that the discipline of architecture has in re- cent decades turned towards a scientific modus operandi—a process that leads to a communally orchestrated establishment of a rich, reflected and globally shared reference body in accordance with the protocols of science—should prove advan- tageous for a dialogue on the relationship between computational tool, concept and practice. This scientific turn in architecture has manifested itself in hundreds of pa- pers, case studies, doctoral research and peer-reviewed publications. This research covers manifold fields and include—among other topics—design theory, digital fab- rication, computational form finding, geometry and pedagogy. The constructive at- mosphere of the last Design Modelling Symposium and comparable events has cre- ated a community characterized by openness, scientific rigor and curiosity. It is fair to assume that in the coming years a proliferation, specification and broader appli- cation of the investigated concepts and tools will take place in building practice, potentially altering the availability and distribution of these research findings. This editorial preface is the result of a shared perspective on the core qualities that we consider necessary for a constructive investigation of the actual and future challenges of computational design and architectural practice. These qualities are centered on a practice of scientific verifiability, shared availability of knowledge and a continuous and constructive reflective monitoring of the manifold develop- ments. We have therefore chosen to identify four areas that are specifically relevant to the field of computational design, fabrication and architectural practice. The brief statements that follow address the conceptual view on the thinking models that were introduced in the fields of architecture and engineering; portray their boundary con- ditions in regard to a realization on site; and give an outlook on future changes of functional and structural tectonics within building components. Models of Design in Computation Models are at the Core of Scientific Thinking Design and even more so computational design relies heavily on abstraction and models of thought. The challenge of any abstraction is the invention of a construct that can stand for the actual phenomena with a good enough approximation to al- low for making accurate predictions about the future solely based on the abstract
- 9. Foreword VII model. This is the core of science and reasoning and so essential to our culture that it is hard to single it out. The formation of new models may start out with a mental model which is fluid and fluctuating, shaped by thoughts, dismissed and resurrected as needed. Defining a more stable, externalized and rigorous model requires sub- stantially more effort. Translating it into a computational model requires an addi- tional level of rigor as it can be operated independently of its creator and be reused essentially as a black box process without further scrutiny by an unaware user. Merging Model Rigor and Design Process Creating new models is difficult and hence the tendency is to work with existing models of thought. In computation this is even more likely due to the reusability of algorithms in the form of code. This path of least resistance has led to a limited set of computational models for design being used over and over again. Therefore a key motivation for holding an international conference on design modeling is to enable the survey and discussion of different approaches to conceptual models and the translation of ideas into novel computational models. A second motivation is to encourage the often substantial research investment to develop new and better fitting computational models for design. The notion of an overall model here is not limited to a 3D geometric data set but refers rather to the holistic, abstract representation of the overall design process including the role of humans in the process. Abstract models for the design process have concrete consequences in the design results. It is therefore not a question of design philosophy but, as we push for more interdisci- plinary design work to take place, a question of how the underlying model defines the outcome. Therefore it is a core responsibility of the field to push forward with more integrated models of design, to test their capability to deal with real world complexity, and to evaluate their potential for improving design results. From Analysis to Simulation From Analysis of Known Problems to Simulation of New Scenarios From a historic perspective the use of computers in structural engineering began much earlier and under different starting conditions than in the practice of architec- ture. Crucial for a more holistic deployment of the computer was the development of hardware in the 1980s, which allowed the computer to become an everyday tool for structural engineers already in the 1990s. Contrary to the developments in ar- chitecture computing in structural engineering was used as a tool for the analysis of structures. Only later its use as tool to speed up and rationalize design representa- tions followed. Exemptions were the design and execution of tensile constructs such as cable net and membrane roofs or the mostly in compression shell structures. In these areas lie the beginnings of the use of computers as a design tool for form finding in com- bination with structural analysis. The form finding of these load bearing systems is
- 10. VIII Foreword based on the search for a membrane geometry, which represents equilibrium of ten- sile forces in the surface given the geometric edge and support conditions, as well as possible external loads. This inverse question is based on the assumption of a prescribed state of tension in a yet unknown geometry, is independent of deforma- tions and therefore does not require any material definition. The first form finding methods such as the force density method use the possible numerical simplifica- tion that follow form this definition. Today, the constantly increasing computational performance of the hardware and the continued improvement of FEM allow for the combination of form finding under consideration of the materiality in direct com- bination with structural analysis. Through these steps a change is taking place in structural design and construction development from analysis to simulation. Computational Design as Experiment Computational design becomes an experiment which investigates the structural be- havior of increasingly complex systems. Most important are the possibilities of in- vestigating the interplay between a system’s elements with external forces. The first crucial step of a simulation is always the definition of the model. While for a long time the foundation of the design process was adapting the structure to be designed to known static based models, today the process begins with the definition of a model that is fine tuned to the task at hand. Modeling the problem requires a new creativity on the part of the engineer as well as knowledge that involves, besides the numeric basics, a substantial amount of craft. Here material and assembly knowl- edge are essential. The possibilities of increasingly complex simulations open up the question as to what extent we are capable of realizing the simulation outcomes in physical structures. Therefore a goal could be to use the new simulation possibil- ities of complex interdependencies to arrive at simple technical solutions that stand out for their multi-functional behavior. This New Low Tech design is characterized by the use of multifunctional, robust, material- and energy-efficient constructions, based on the use of high complexity computational experiments and a deep under- standing of materials and jointing technology. Computational Controlled Fabrication in Architecture Architecture Is Built from Heterogeneous Components The sheer size of buildings makes it practically impossible to fabricate a building as one homogeneous structure. There will always be building components that have to be assembled and connected in one way or another. In order to efficiently create large structures, the components have to reach a certain size, or the cost of assembly will become the main factor in the budget. On top of that the multitude of different functions a building has to fulfill requires a multitude of different building materials. Since they all have their spe- cific properties and most likely different fabrication technologies, designing and
- 11. Foreword IX fabricating building components thus requires specialist knowledge from a multi- tude of domains—usually not found in one single place or brain. The integration of various functions into polyvalent components may reduce the number of differ- ent component types but increases the complexity and the embedded knowledge of each type while at the same time eliminating clear interfaces between different trades. Thus the integration of all required know-how through close cooperation of all involved parties becomes indispensible, also for handling the responsibility and risks of the process. Digital Fabrication Means Pre-Fabrication Apart from very few exceptions (e.g. robots for the rather monofunctional task of brick laying or the robotic high-rise-building factories that never really made it outside of Japan), digital fabrication equipment is too large, costly and delicate to move it to site and to build components directly at their final location. Thus, digi- tal fabrication almost always means pre-fabrication of building components in the controlled environment of the fabricator’s workshop, shipping them to the site and assembling them like a big puzzle. That adds a number of challenges, mainly for just-in-time procurement, production and logistics that have to be carefully dealt with before the actual building process can start. The planning effort has to be moved almost completely to the front of the process, since finding mistakes during the as- sembly on-site and far away from the fabrication facilities can become catastrophic in terms of budget and design intent. Digital Fabrication Needs Precise Descriptions Computers are deterministic machines and need correct input to deliver correct out- put. That also holds true for the controllers of CNC-fabrication machines. Every drilling, milling, bending, planning, glueing or cutting operation a machine has to execute must be unambiguously defined in the digital model that is fed into the ma- chine, down to last screw hole. In general it is not sufficient to create a 3D-model of the component to be produced, because aside from simple 2D-cutting or 3D-printing operations, the translation of geometric description into the machining sequence of a multi-axis CNC-machine, maybe involving several tool-changes during the process, is far from a linear problem. So, to come up with a working fabrication model for a complex component requires the full set of production knowledge for the specific machinery used. Digital Fabrication Is First and Foremost a Question of the Process The technology for digital fabrication is widely available today. The challenge now is to understand how those machines can be integrated into the existing processes of building and how this might change the traditional way to design in order to
- 12. X Foreword exploit the full capabilities of the fabrication equipment. On the other hand, through a deeper understanding of the current technology, we will be able to better identify shortcomings and specific needs of the building sector and (re-) direct the develop- ment of future technologies to better fit the requirements of the architectural process. Rapid Manufacturing in Architecture Fabrication of Material and Structural Heterogeneity Rapid manufacturing has proliferated in the past years due to an improvement of additive fabrication (AF) processes in regard to mechanical properties, greater ma- terial diversity and scale of the producible artifacts. In architecture AF can exceed prior representative applications and progress towards the fabrication of functioning components of high complexity of structure and material composition. First signs indicate such a potential implementation through research conducted by several pri- vate and academic institutions on additively fabricated building-scale parts. Techno- logical progress is accompanied by recent standardization efforts of AF processes and material quality through academic institutions and industry that can promote utilization of AF components within the building sector. Yet additive fabrication of functional building parts requires a phase of wider experimental investigation to be conducted in the coming years. An interesting seg- ment of contemporary AF research is hereby not only investigating the production possibilities of specialized parts but also the calibration of the material itself with regard to its structural performance and composition control. The benefit of this research lies in an achievable congruence between technological development and design activity once the AF processes are suited for architectural applications. The envisioned digitally driven calibration and construction of novel structures and formations hereby alters the historical dialogue on material, structural and for- mal coherency. The conceptual approach between construction typology and ma- terial use that persisted architectural history until now is about to change again. The question in the future will not be centered on a best fitting structural solution for a given material with more or less known properties that drove the thinking of Viollet-le-Duc and others, but a reverse process that tailors a custom material with gradual and non-repetitive characteristics to a chosen form and performance. Towards a New Building Tectonic The achievable control over structure, material, and form opens up a design potential that is a direct descendant of the core properties of the fabrication tectonic and can give birth to novel building components. On a constructive level a merging of mul- tiple building functions into a singular component appears achievable. The timeline of assembly that is usually coordinated from the erecting of a primary load-bearing structure downwards and shapes the appearance of the buildings around us can po- tentially blend multiple building functions in a new construction component whose
- 13. Foreword XI dimensions are then based on building chamber sizes of the manufacturing technol- ogy. Formal complexity and ease of assembly through new joinery systems can so be achieved. The designed structural morphology could be guided by shape- and topology optimization procedures and by that integrate a material saving building practice in the load-bearing core of the project. This rethinking of architectural, structural and material practice holds many promises and a manifold of technologi- cal challenges that will take decades to be overcome. The impression that a wide range of functionalities can be tuned and optimized might be misleading in context of potentially opposing optimization goals that have to be synchronized. Beside such restricting aspects research in these areas is of great interest since it holds a manifold of possible innovations for the design and con- struction process within architecture and may lead to the rewriting of the historical discussion on the relation between matter and form. The following collection of papers presented at the Design Modelling Sympo- sium Berlin 2011 is a cross section through current cutting edge research in the field. Some of the papers respond to the challenges and questions formulated above, others open up new discourses departing from the topics outlined here. Most im- portantly, all authors succeed in challenging our current understanding of the field through the rigor of the presented work. In doing so, they foster advances in archi- tecture and engineering as well as the discourse that creates the conceptual basis of our disciplines. Christoph Gengnagel, University of the Arts, Berlin Axel Kilian, Princeton University, Princeton Norbert Palz, University of the Arts, Berlin Fabian Scheurer, designtoproduction, Zurich
- 15. Contents Foreword . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . V Christoph Gengnagel, Axel Kilian, Norbert Palz, Fabian Scheurer Concept, Tool and Design Strategies DesignScript: Origins, Explanation, Illustration . . . . . . . . . . . . . . . . . . . . 1 Robert Aish Algebraic Expansions: Broadening the Scope of Architectural Design through Algebraic Surfaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 Günter Barczik, Daniel Lordick, Oliver Labs Tools and Design Strategies to Study Rib Growth . . . . . . . . . . . . . . . . . . . . 17 Chris Bardt, Michal Dziedziniewicz, Joy Ko Free Shape Optimal Design of Structures . . . . . . . . . . . . . . . . . . . . . . . . . . 25 Kai-Uwe Bletzinger NetworkedDesign, Next Generation Infrastructure for Design Modelling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 Jeroen Coenders Digital Technologies for Evolutionary Construction . . . . . . . . . . . . . . . . . . 47 Jan Knippers Combinatorial Architecture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 Enrique Sobejano Codes in the Clouds Observing New Design Strategies. . . . . . . . . . . . . . . . 63 Liss C. Werner
- 16. XIV Contents Modeling, Simulation and Optimization Methodological Research Integration of Behaviour-Based Computational and Physical Models: Design Computation and Materialisation of Morphologically Complex Tension-Active Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 Sean Ahlquist, Achim Menges Synthetic Images on Real Surfaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79 Marc Alexa Modelling Hyperboloid Sound Scattering: The Challenge of Simulating, Fabricating and Measuring . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89 Jane Burry, Daniel Davis, Brady Peters, Phil Ayres, John Klein, Alexander Pena de Leon, Mark Burry Integration of FEM, NURBS and Genetic Algorithms in Free-Form Grid Shell Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97 Milos Dimcic, Jan Knippers SOFT.SPACE_Analog and Digital Approaches to Membrane Architecture on the Example of Corner Solutions . . . . . . . . . . . . . . . . . . . . 105 Günther H. Filz Performance Based Interactive Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . 115 Odysseas Georgiou On the Materiality and Structural Behaviour of Highly-Elastic Gridshell Structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123 Elisa Lafuente Hernández, Christoph Gengnagel, Stefan Sechelmann, Thilo Rörig Parametric Design and Construction Optimization of a Freeform Roof Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137 Johan Kure, Thiru Manickam, Kemo Usto, Kenn Clausen, Duoli Chen, Alberto Pugnale Curved Bridge Design. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145 Lorenz Lachauer, Toni Kotnik Linear Folded (Parallel) Stripe(s) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153 Rupert Maleczek The Potential of Scripting Interfaces for Form and Performance Systemic Co-design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161 Julien Nembrini, Steffen Samberger, André Sternitzke, Guillaume Labelle
- 17. Contents XV Building and Plant Simulation Strategies for the Design of Energy Efficient Districts. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171 Christoph Nytsch-Geusen, Jörg Huber, Manuel Ljubijankic New Design and Fabrication Methods for Freeform Stone Vaults Based on Ruled Surfaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181 Matthias Rippmann, Philippe Block Design and Optimization of Orthogonally Intersecting Planar Surfaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191 Yuliy Schwartzburg, Mark Pauly Modelling the Invisible . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 201 Achim Benjamin Späth Applied Research Ornate Screens – Digital Fabrication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 209 Daniel Baerlecken, Judith Reitz, Arne Künstler, Martin Manegold The Railway Station “Stuttgart 21: Structural Modelling and Fabrication of Double Curved Concrete Surfaces . . . . . . . . . . . . . . . . . . . . 217 Lucio Blandini, Albert Schuster, Werner Sobek Performative Surfaces: Computational Form Finding Processes for the Inclusion of Detail in the Surface Condition . . . . . . . . . . . . . . . . . . . . . 225 Matias del Campo, Sandra Manninger ICD/ITKE Research Pavilion: A Case Study of Multi-disciplinary Collaborative Computational Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 239 Moritz Fleischmann, Achim Menges Metropol Parasol - Digital Timber Design . . . . . . . . . . . . . . . . . . . . . . . . . . 249 Jan-Peter Koppitz, Gregory Quinn, Volker Schmid, Anja Thurik Performative Architectural Morphology: Finger-Joined Plate Structures Integrating Robotic Manufacturing, Biological Principles and Location-Specific Requirements. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 259 Oliver Krieg, Karola Dierichs, Steffen Reichert, Tobias Schwinn, Achim Menges A Technique for the Conditional Detailing of Grid-Shell Structures: Using Cellular Automata’s as Decision Making Engines in Large Parametric Model Assemblies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 267 Alexander Peña de Leon, Dennis Shelden Parameterization and Welding of a Knotbox . . . . . . . . . . . . . . . . . . . . . . . . 275 Daniel Lordick
- 18. XVI Contents Viscous Affiliation - A Concrete Structure . . . . . . . . . . . . . . . . . . . . . . . . . . 283 Martin Oberascher, Alexander Matl, Christoph Brandstätter Dynamic Double Curvature Mould System . . . . . . . . . . . . . . . . . . . . . . . . . 291 Christian Raun, Mathias K. Kristensen, Poul Henning Kirkegaard More Is Arbitrary: Music Pavilion for the Salzburg . . . . . . . . . . . . . . . . . 301 Kristina Schinegger, Stefan Rutzinger Design Environments for Material Performance . . . . . . . . . . . . . . . . . . . . . 309 Martin Tamke, Mark Burry, Phil Ayres, Jane Burry, Mette Ramsgaard Thomsen Educational Projects Faserstrom Pavilion: Charm of the Suboptimal . . . . . . . . . . . . . . . . . . . . . 319 Mathis Baumann, Clemens Klein, Thomas Pearce, Leo Stuckardt Rhizome - Parametric Design Inspired by Root Based Linking Structures. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 327 Reiner Beelitz, Julius Blencke, Stefan Liczkowski, Andreas Woyke Kinetic Pavilion: Extendible and Adaptable Architecture . . . . . . . . . . . . . 335 Corneel Cannaerts Author Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 341
- 19. DesignScript: Origins, Explanation, Illustration Robert Aish “A programming language that doesn’t change the way you think is not worth learning” —Alan Perlis, ‘Epigrams in Programming’ Abstract. DesignScript, as the name suggests, is positioned at the intersection of design and programming. DesignScript can be viewed as part of the continuing tra- dition of the development of parametric and associative modeling tools for advanced architectural design and building engineering. Much of the thought processes that contribute to the effective use of DesignScript builds on the tradition of paramet- ric design and associative modeling that is already widely distributed amongst the creative members of the architectural and engineering communities. Many of the ex- isting parametric and associative modelling tools also support conventional scripting via connections to existing programming languages. The originality of DesignScript is that associative and parametric modeling is integrated with conventionalscripting. Indeed, the definition of the associative and parametric model is recorded directly in DesignScript. But it is not what DesignScript does which is important, more what a designer can do with DesignScript. It is this change in the way you think that makes DesignScript worth learning. 1 Introduction DesignScript is intended to be: • a production modeling tool: to provide an efficient way for pragmatic designers to generate and evaluate complex geometric design models • a fully-fledged programming language: as expected by expert programmers. • a pedagogic tool: to help pragmatic design professions make the transition to competent programmer by the progressive acquisition of programming concepts and practice applied to design. Robert Aish Director of Software Development, Autodesk
- 20. 2 R. Aish Essentially there are three themes interwoven here: • The programming language theme: DesignScript as a programming language • The design process theme: The use of DesignScript as a design toolset • The pedagogic theme: using DesignScript as a way of learning how to design and to program. 2 Programming Language From the perspective of a programming language, we might describe DesignScript as an associative language, which maintains a graph of dependencies between vari- ables. In DesignScript these variables can represent numeric values or geometric entities, or other application constructs, including those defined by the user. The execution of a DesignScript program is effectively a change-propagation mecha- nism using this graph of variables. This change-propagation also functions as the update mechanism similar to that found in a conventional CAD application. How- ever, unlike other CAD update mechanisms or associative and parametric modeling systems, in DesignScript this mechanism is exposed to the user and is completely programmable.Figure 1 illustrates the important differences between a conventional imperative language and an associative language such as DesignScript, while Fig- ure 2 shows how a program statement in DesignScript can also be interpreted as natural language. Each term in the statement has an equivalent natural language interpretation so that whole statement can be understood by its natural language equivalent. So a concise but somewhat complex description of DesignScript might be as a domain-specific, end-user, multi-paradigm, host-independent, extensible program- ming language (Fig. 3), as follows: 1. Domain-specific. DesignScript is intended to support the generation of geomet- ric design models and therefore provides special constructs to assist in the repre- sentation of geometric models. More generally: A domain specific language may remove certain general purpose functionality and instead adds domain specific functionality as first class features of the language. 2. End-user. DesignScript is intended to be used by experienced designers with a wide range of programming skill, ranging from non-programmers(who might in- directly program via interactive direct manipulation), to novice non-professional (end-user) programmers, and to experienced designers who have substantial ex- pertise in programing. More generally: An end user language adds simplifying syntax to the language, while reducing some of restriction often associated with general purpose languages (intended for experienced programmers). 3. Multi-paradigm. DesignScript integrates a number of different programming paradigms into a single language (including object-oriented, functional and as- sociative paradigms) and introduces some additional programming concepts
- 21. DesignScript: Origins, Explanation, Illustration 3 Fig. 1 Comparing Imperative and Associative interpretation of the same program statements. It is this change in the way you think that makes DesignScript worth learning. Fig. 2 Giving a natural language interpretation to a DesignScript statement Fig. 3 How DesignScript differs from a regular general purpose programming language
- 22. 4 R. Aish that are relevant to the domain of generative design. More generally: A multi- paradigm language combines different programming styles into a single language and allows the user to select which paradigms or combination of paradigms are appropriate. (See Fig. 4 ) 4. Host-independent. DesignScript is intended to support the generation of geo- metric models and is therefore designed to be hosted within different CAD ap- plications and access different geometric, engineering analysis and simulation libraries. For example, a DesignScript variable (based on specific class) may maintain a correspondence with a geometric entity in AutoCAD and simulta- neously with entities within engineering analysis applications such as Ecotect and Robot. 5. Extensible. DesignScript can be extended by the user, by the addition of func- tions and classes. Fig. 4 The evolutionary tree for DesignScript (showing its precursors). DesignScript is a multi-paradigm language embracing imperative, objected oriented, functional and declarative programming concepts. 3 Design Process DesignScript is intended to support a computational approach to design which is accessible to designers who initially may be unfamiliar with this way of designing. Conventionally, computer-based design applications enabled the designer to create models which represent finished designs. The intention in developing DesignScript is to move beyond the representation of finished designs, and instead to support the designer to develop his own geometric and logical framework within which many different alternative design solutions can be easily generated and evaluated.
- 23. DesignScript: Origins, Explanation, Illustration 5 The development of DesignScript assumes that the designer wants to adopt this more exploratory approach to design and that he appreciates that this may involve some re-factoring of the design process so as to include a more explicit externaliza- tion of particular aspects of design thinking, for example: • Explicitly identifying the key variables that drive the design. • Building the geometric and logical dependencies between these driver variables and the constructive geometry: potentially these dependencies can be complex long chains. • Defining appropriate performance measures that can describe the resulting de- sign solutions. • Exercising the complete model (by changing the design drivers and observing changes in the geometry and resulting performance measures) to explore more appropriate solutions. • Changing the geometric and logical dependencies in order to explore more alter- natives. 4 Pedagogic Perspective From a pedagogic perspective, DesignScript is designed around the concept of a learning curve and supports a very gradual approach to learning programming (Fig. 5): Fig. 5 DesignScript as conceived as a composite learning curve spanning different types of modelling and programming 1. For modelling by direct manipulation, the designer immediately obtains some interesting result for the modelling effort he makes, yet to change or refine or increase the complexity of the model may require an exhaustive amount of addi- tional effort. Therefore the perceptive designer may search for a way to overcome the limitations of direct manipulation.
- 24. 6 R. Aish 2. For Associative or parametric modelling, the designer may have to initially make some more effort to create the first associative model (than he did with reg- ular modelling). Although the initial results may be unimpressive, he is investing in an associative model with higher semantic value. Because of this investment in design logic the designers ability to change and refine that model becomes com- paratively easy (compared to non-associative modelling). The designer is not just investing his time and effort, but also has to learn new skills: in particular how to think associatively. However, the perceptive designer may recognise that some types of design logic are difficult to express in an associative modelling system, therefore the perceptive designer may search for a way to overcome the limita- tions of associative modelling. 3. With scripting and programming, considerable time and effort may be ex- pended apparently without much evidence of success. Nothing works until it all works, but then the complexity of the model and the ability to re-generate the model with radically different design logic appears more powerful than what can be achieved with associative modelling. We can summarise this as: • Learning by doing, for example, by interactive modelling • Learning by observing the correspondence between the DesignScript notation and geometry, for example, by comparing the geometric model with the graph based symbolic model and with the DesignScript notation displayed in the IDE) The following example illustrates the use of DesignScript. The design problem is to model a wave roof, based on a complex wave formation. The first step is to recog- nise that we should not attempt to directly model the wave formations with regular modelling tools. Instead we should recall that most complex wave forms can be con- structed as the aggregate effect of simpler waves combined with related harmonic waves. In this case, the geometry is constructed by using a series of low and high frequency sine waves running orthogonally in the X and Y direction (Fig 6). The amplitude and number of peaks in the waves are controlled by root parameters. The X, Y and Z coordinates of the 2D field of points is defined by combining these sine waves (Fig 7). The number of peaks can be varied (Fig 8). The X, Y and base Z coordinates of the points can be derived from points in the UV parametric space of a surface, thereby giving the effect that the wave geometry is draped (and offset) from an underlying surface (Fig 9). Finally, the control vertices of the underlying surface can be modified giving the effect that the underlying surface is controlling the wave roof (Fig 10). This presents the exactly the combination of direct modelling, associative mod- elling and scripting suggested in the learning curve in Fig. 5. It is not just the model (or the computation of the model) which is spanning this different approaches. It is the thought processes of the designer which is combining these different ways of thinking.
- 25. DesignScript: Origins, Explanation, Illustration 7 Fig. 6 High and Low frequency waves in the X and Y directions Fig. 7 The resulting wave roof is created by aggregating these orthogonal waves Fig. 8 The number of peaks can be varied
- 26. 8 R. Aish Fig. 9 Draping (and offsetting) the wave roof from an underlying surface Fig. 10 The control vertices of the underlying surface can be modified giving the effect that the underlying surface is controlling the wave roof 5 Discussion The three themes which are interwoven here (the programming language theme, the design process theme and the pedagogic theme) all come together when we address the central issue: How can a computational tools invoke a computational mindset and in turn contribute to design thinking? Using DesignScript is a new way of designing with its own expressive possibil- ities. But there is a level of understanding required to harness this expressiveness and this suggests a level of rigor and discipline. The argument is that the experience of learning and using DesignScript contributes not just to the expressiveness and clarity of the resulting design but also to the skills and knowledge of the user. In short,“a new toolset suggests a new mindset”.
- 27. Algebraic Expansions: Broadening the Scope of Architectural Design through Algebraic Surfaces Günter Barczik, Daniel Lordick, and Oliver Labs 1 Introduction: An Expanded Architectural Design Vocabulary We conduct a design research project that radicalizes the relationship between tools and design possibilities: we significantly expand the architectural design vocabulary by employing mathematics and computer science as vehicles for accessing shapes that otherwise would be unthinkable: algebraic surfaces, the zero-sets of certain polynomials. Algebraic surfaces can exhibit geometric features that cannot - or have so far not - be found in nature: puzzling convolutions in which complex geometry and topology combine with high degrees of tautness, harmony and coherence (Fig.1). Albeit mostly curved, they can contain straight lines and any number of plane curves (Fig.1, 1-3). They also look different from every direction, a quality we propose to call polyoptical from the Greek for an object with many faces. Having been studied in mathematics for the last two centuries they became accessible for designers only recently via advances in computer technology. This means a cambrian explosion of shapes, a whole zoo of new exotic shapes. Günter Barczik Brandenburg Technical University Cottbus, Germany HMGB architects, Berlin, Germany Daniel Lordick Institute of Geometry, University of Technology Dresden, Germany Oliver Labs Mathematics and its Didactics, Cologne University, Germany Institute for Mathematics and Computer Science, Saarbrücken University, Germany
- 28. 10 G. Barczik, D. Lordick, and O. Labs Fig. 1 Examples of Algebraic Surfaces by Oliver Labs (1-4), Herwig Hauser (5,6) and Ed- uard Baumann (7,8) 2 Two Ways of Dealing with the Zoo of New Shapes The new shapes can be dealt with in two ways: they can be taken literally, or as inspirational objects akin to Le Corbusiers Objects à rèaction poetique. Corbusier collected pieces of wood corroded by water and wind and sea-shells to provoke thinking about geometrical and textural qualities. Over the years, this altered his designs from white boxes to buildings like the chapel in Ronchamp. In a similar way, algebraic surfaces can be employed to stimulate thinking about spatial configurations and relationships. Thus, they can foster a new understanding of the already existing plastic vocabulary. Algebraic surfaces might also be taken literally and interpreted as buildings or parts of buildings. They then add many new words to the textbook of possible archi- tectural shapes. In language, a large vocabulary enables speakers to phrase thoughts more precisely. Similarly, a large vocabulary of shapes should enable designers to formulate more appropriate solutions. We research this expansion in a series of ex- perimental designs - see below. 3 Historic Precedents for Mathematics Inspiring Art and Architecture Such use, or mis-use, of mathematical entities for design may appear contrived,yet it is neither without precedent nor without profound effect on the history of modern art and architecture: when in the first half of the 20th century artists like Naum Gabo or Man Ray formulated a constructivist agenda to add new things to the world, things that could not be generated through observation in or abstraction from nature, nor
- 29. Algebraic Expansions 11 via surrealist drug-induced or aleatoric procedures, they were shocked to discover mathematical models which demonstrated that their goals had already been achieved a century earlier. Those mathematical models had been built to visualize algebraic surfaces and other mathematical objects. The Constructivists started to copy these mathematical objects in painting and sculpture, but they found themselves unable to understand them or generate their own ones as the calculations necessary for their generation could only be done by experts. Similarly in architecture, Le Corbusier handed Yannis Xenkis illustrations of mathematical functions as starting points for the design of the Philips Pavillon for the 1958 World Expo, taken from a book that had been sent to him from the faculty of mathematics of the University of Zrich after Corbusier had explicitly asked its dean for inspirational material. Comparable to the constructivist artists, Xenakis struggled with handling the new shapes. Due to such technical obstacles, those mid-century artists and architects mistook for a dead-end the road to great discoveries. In recent years, sculptors like Anthony Cragg and Anish Kapoor have again be- gun to explicitly add new shapes to the world. Although they do not mention mathe- matics, the geometric possibilities attained through computers and shapes obviously related to mathematical objects feature heavily in their work. Yet, the shapes employed by the mid-20th-century artists as well as those used by Cragg and Kapoor fall significantly short of the ones which can be generated via algebraic geometry in terms of complexity. 4 Five-Step Design Research Program Our experimental design program is divided into five steps: generation, interpreta- tion, adaptation, application and production. First we generate the surfaces via the software packages Surfer, SingSurf and K3DSurf. All three accept a polynomial as input and output visualizations or/and 3D models. Surfer is restricted to visualization, but highly interactive. SingSurf and K3DSurf are not as interactive but generate 3D data that can be exported as polygon meshes. All programs do not determine the zero-sets of the polynomials by solving those equations exactly - currently no applicable software for this exists. Instead, they offer approximations, leading to inaccuracies in the models which occasionally show up as imperfections. Furthermore, the normals of the meshes are most usually disoriented and have to be aligned. Albeit such technical difficulties, in most cases the shapes that are the zero-sets can be successfully imported into CAD software. Once imported, they could as a matter of course be mimiced or re-built as a NURBS surface. The definition of the NURBS surface, though, would have to be based on points or polylines extracted from the mesh. So far, we have opted for smoothing out the meshes via the Catmull-Clark subdivision surface algorithm with most sat- isfactory results (Fig.2). Secondly the surfaces are analyzed in terms of their geometric properties and interpretated as to their architectonic potential. The shapes exhibit exotic sculptural
- 30. 12 G. Barczik, D. Lordick, and O. Labs Fig. 2 Creating and analyzing an Algebraic Surface in perspective renderings and sections (Stefan Schreck) situations that so far are unnamed: connections between different regions that are neither holes nor tunnels and might be named passages, self-intersections, singular points that mathematicians call singularities, to name but a few. The surfaces are mostly continuously curved and rarely flat. Therefore, they do not seem to invite architectonic use at first glance. Yet, as humans happily exploit non-flatness i.e. in undulating parkscapes where people sit, lie, play, gather and disperse in relation to the topography we see this more as an inspiration to question the prevalence of flatness that pervades modern architecture. There also is a strand within the avant- garde architecture of the last few decades that explicitly researches the use of non- flat surfaces, beginning with Claude Parents theory of the oblique and ending, so far, in Kazuyo Sejimas and Ryue Nishizawas Rolex Learning Centre in Lausanne and Sou Fujimotos Primitive Future House project. We pick up this strand to see if the flatland of modern architecture might not be expanded to more spatial configurations and more formfitting uses (Fig.3). In a third step, the algebraic surfaces are adapted geometrically to facilitate hu- mans use - i.e. stretched, twisted, compressed. Additionally, they are converted from Fig. 3 Interpreting three algebraic surfaces as to their spatial potential (David Schwarzkopf, Dana Kummerlöw, Susann Seifert (from left to right))
- 31. Algebraic Expansions 13 Fig. 4 Adapting two algebraic surfaces into enclosed volumes (Dana Kummerlöw (left) and Christopher Jarchow (right)) surfaces into enclosures through various operations like for example section with a cuboid or deforming the surface until it becomes a volume (Fig.4). In a fourth step, experimental architectures are generated by synthesizing the knowledge and know-how acquired in the first three steps (Fig.5-7). The resulting building designs are furthermore situated in urban contexts. While it can be argued that the extra-ordinary shapes of algebraic surfaces by definition have difficulty be- coming part of any urban context, we argue that human settlements have always contained special buildings that have often been the most radical expression of what was possible at any given time. Those special buildings have also played impor- tant roles in the social life of communities, attracting visitors and inspiring social and cultural exchange. The building designs which incorporate the unprecedented shapes of algebraic surfaces can therefore play important roles in human commu- nities, providing spatial focus points and inspiring new forms of social exchange. Additionally, the polyoptical qualities of such shapes [see above] means that they can relate differently to the more and more diversified urban fabrics of todays cities. The last step consists of printing the designs in 3D (Fig.8). While we use the technology to print only models of the designs, it is rapidly progressing to print larger and larger objects, the largest at the moment exceeding telephone box size. While it is as a matter of course not satisfactory to see building construction as a matter of simply printing large objects of a uniform material, for us in our project the printability of the shapes is proof of concept enough insofar that unprecedented, new and never seen or touched objects are transported from the intellectual world of mathematics into a tangible physical reality. 5 Function Inspired by Form? The steps we take in the experimental design project changes the common design procedure of Form follows function to Form inspires function or even Function fol- lows form. At first, this may be seen as a severe restriction of designers capabilities, restraining their options to a corset defined by a given algebraic surface. Yet, we
- 32. 14 G. Barczik, D. Lordick, and O. Labs Fig. 5 Experimental design project based on an algebraic surface (Xing Jiang) Fig. 6 Experimental design project based on an algebraic surface (Jörg Burkart) understand our project merely as acquiring a new vocabulary. And in any such un- dertaking, existing new vocables have to be learned, played and experimented with before they can become part of the active vocabulary and used at will and as differ- ent situations and problems of formulation necessitate. This can also be seen in the way that children learn and get to know new shapes: nobody is born with a knowl- edge of eucledian geometry or, for that matter, any shape at all. Those have to be encountered in the world through perception and thus build up a spatial vocabu- lary. We argue that only when one forgets these learning experiences our procedure, mimicing them, appears wrong.
- 33. Algebraic Expansions 15 Fig. 7 Experimental design project based on an algebraic surface (Dana Kummerlöw) Fig. 8 Model prints of experimental design projects (Joanna Kollat (top left), Stefan Schreck (top right) and Xing Jiang (bottom)) 6 Gradient Thresholds Many algebraic surfaces clearly exhibit different regions of space with different ge- ometric qualities. These regions are almost never exactly demarkated but flow grad- ually into one another. The threshold between them is not a line but a gradient. This can lead to a new kind of multifunctionality or hybrid use where the different zones
- 34. 16 G. Barczik, D. Lordick, and O. Labs are not seperated as i.e. different floor levels but share common areas of ambivalent use. The rigid territories of much architecture might thus be enriched by polyvalent areas with gradient thresholds. 7 Conclusion Our project extends the architectonic vocabulary of shapes by introducing unprece- dented new forms that until recently could not be thought let alone visualized or handled. This zoo of new shapes expands the possibilities of use of space, habita- tion and social interaction and offers alternatives to the flatland and rigid territories of most current architecture. Yet the process of getting to know, let alone mastering the new vocabulary has only just started, and there is indeed the danger of stopping here already and only revelling in appealing new shapes that are rather detached from architectonic design that integrates issues of organization, structure, context and so forth. We think, though, that learning a new vocabulary takes time, patience and much experimentation - especially when the language is completely new to thought and was never spoken before. Algebraic shapes made visible and useable through computers, we think, can continue several strands of research into archi- tectural possibilities that have begun in the last century and reinvigorate them with unrecedented possibilities. Acknowledgements. Thanks to all students and to the 3D Labs of the Universities of Dres- den and Poznan where most of our models were printed. References 1. Barczik, G., Labs, O., Lordick, D.: Algebraic Geometry in Architectural Design. In: Pro- ceedings of the 27th eCAADe, Istanbul, Turkey (2009) 2. Barczik, G., Labs, O., Lordick, D.: Perplexing Beauty: The Aesthetics of Algebraic Ge- ometry in Architecture. In: Proceedings of the IAEA 2010, Dresden (2010) 3. Barczik, G.: Uneasy Coincidence? Massive Urbanization and New Exotic Geometries with Algebraic Geometry as an extreme example. In: Proceedings of the 28th eCAADe, Zürich, Switzerland (2010) 4. Barczik, G.: Leaving Flatland behind. In: Proceedings of the 29th eCAADe, Ljubljana, Slovenia (forthcoming, 2011) 5. Maak, N.: Der Architekt am Strand, München (2010) 6. Cecilia, M., Levene.: El Croquis #155 Sou Fujimoto, Madrid (2011) 7. Migayrou, R.: Claude Parent: L’oeuvre construite, l’oeuvre graphique, Paris (2010) 8. Eduard Baumann’s Algebraic Surfaces, http://www.spektrum.de/sixcms/list.php?page=p sdwv mathekunst z=798888sv%5Bvt%5D=eduard+baumann kategorie=%21Videox=0y=0 9. Herwig Hauser’s Algebraic Surfaces, http://www.freigeist.cc/gallery.html
- 35. Tools and Design Strategies to Study Rib Growth Chris Bardt, Michal Dziedziniewicz, and Joy Ko 1 Introduction Ever since Viollet-le-Duc the 19th century engineer and architect proposed “natural” structures borne out of ideal forms of specific materials, engineers and architects alike have been interested in the notion of an organic approach to form and structure [7]. Functionalism, the idea that form is a resultant of forces and needs, was core to the modernist project but became overly deterministic and untenable for architecture [1]. The course of much of the latter part of the 20th century history was one of the separation of engineering (calculation) and architecture (organization) into two exclusive realms uneasily brought together, with one or the other taking the lead in the generation of form [4]. In the architectural design process, calculation of structural performance customarily entered late in the design process when the form was already largely realized. Computation, now the widely accepted lingua franca of many fields that archi- tecture touches, has played a central role in rekindling interest amongst architects to rejoin calculation and organization as a critical step in creating truly performative forms. Current interests in architecture such as biomimicry, genetic algorithms, and emergence through agent-based methods allude to an organic process; they reflect a desire to bring the architectural process closer to one in which structure and form are interdependent. The rapid pace of development and adoption by the architec- ture community of various experimental software and workflow models – such as the traer-physics library for Processing or the Grasshopper plugins Kangaroo and Geometry Gym–are telltale signs that the computer is no longer seen by architects as merely a mechanism for representation divorced from physical conditions. Al- ready, structural performance is part of the design process because of a traditionally close dialog between architects and structural engineers. Still, the challenge inher- ent to the creation of a truly generative computational tool for architectural design Chris Bardt · Michal Dziedziniewicz · Joy Ko Department of Architecture, Rhode Island School of Design, Providence, Rhode Island
- 36. 18 C. Bardt, M. Dziedziniewicz, and J. Ko remains, which is to establish materials and forces as agents of feedback in a dy- namic way while modeling these processes accurately enough for the application at hand. In this paper, we consider ribbed structures and explore strategies for rib growth in direct response to materials and forces. We have developed a tool and workflow that allows the structure to react, and to grow reactively. This digital “sandbox” inte- grates existing software – the 3D modeler Rhinoceros and the finite elements solver ABAQUS, software platforms that have widespread use in US architecture and en- gineering schools, respectively – putting an engineer and an architect in a position to start sharing platforms. Such a tool does not replace the engineer but has the potential to strengthen the architect, contributing to the architect’s grasp of factors that influence structural performance at the early design stage. We demonstrate the methodological framework to set up an experiment using the problem setting of a gravity-loaded sheet of isotropic material and uniform thickness with a single point of support and propose a simple strategy for rib growth. This includes the calibra- tion of parameters that can influence the quality of the experiment and can be used as a basis for a comparative study that would be difficult to do using existing tools. For the architect, the ability to access and gain awareness about performance drivers and to conduct meaningful experiments at an early stage opens up the opportunity for entirely different design strategies. 2 An Integrated Tool and Workflow The tool described here is not a broad spectrum software, but rather the base for a family of specific applications. A representative application in this family is the problem of growing a pattern of ribs on a square plate supported at a number of points with a specified load towards some design objective of improved structural performance, such as maximum global stiffness of the plate. This tool supports the need for a workflow allowing users to experiment with growth rules based on design objectives and analytical feedback, and to see subsequent additions to the form. As such, this tool is not intended for a customized approach that takes a preexisting geometry (e.g. a pattern of ribs) as a starting point and morphs the geometry (e.g. such as thickening and thinning ribs) to improve on its performance. The primary intended user-base for this tool is architects and architecture stu- dents, so the use of an existing, familiar, environment such as Rhinoceros was a priority. It is not realistic to expect an architect to fully comprehend and have the fa- cility to be able to implement structural analyses classically conducted on this class of problems. However, a number of structural analysis platforms are now accessi- ble to the practitioner who may have a good grasp of the fundamental principles underlying the modeled process but has limited to no understanding of numerical modeling. ABAQUS – a commercial finite elements analysis package that is pop- ular amongst US engineering schools and select practices – is such a platform, but is not a magic “black box”, and requires at minimum for the user to understand what
- 37. Tools and Design Strategies to Study Rib Growth 19 is needed to generate the simulation: seed number and meshes, loads and boundary conditions, material properties. This amount of additional information is very rea- sonable to grasp for the architect, essential to avoid simulation errors, and can lead to more effective interdisciplinary collaborations. The ultimate goal is to achieve a completely integrated tool in which ABAQUS is a plugin and Rhinoceros acts as the only operating environment. Currently our tool links Rhinoceros and ABAQUS – which have different base languages – through an independent “master” routine which communicates to each software through its command line batching protocol (Fig. 1). With the release of Python-based Rhinoceros 5.0 we hope to breach the barrier between languages. Fig. 1 An independent master routine (in Python) acts as the intermediary between VBscript-based Rhinoceros for geometry generation and Python based ABAQUS for the analysis, and calls out to either side in the generation process while also archiving and interpreting data. A set of templates have been developed that the master can rewrite into scripts to be used by either side of the process Rhinoceros: generating new models based on the results of the analysis ABAQUS: analysing models and passing results The master routine (Python) While the role of Rhinoceros is primarily geometry-modeling, and that of ABAQUS is primarily analysis, there are a number of overlapping functionalities in the two software and subsequently a number of ways to distribute functionality responsibilities, with varying results. Where equivalent methods are present, ease of use and the establishment of a clear dividing line between geometry and analysis roles should govern. These were the guiding principles in the development of our integrated tool. Rhinoceros handles all the geometric operations within the process while keeping the variants in the realm of so called Boundary Representation (Open Nurbs native geometry definitions) which are converted into ABAQUS-importable IGES files. For growing ribs of fixed cross section, a customized curve overlap, offset and ex- trusion routine were developed in place of the built-in solid body Boolean functions. Additionally, Rhinoceros responds to and records the list of growth nodes, which in turn determine the number of variants to be output and passed to the master routine alongside the IGES files for testing. In ABAQUS, boundary conditions, meshing and material properties need to be specified for a simulation to be performed. Since the location and geometry of each support (in our case, a support “stem”) is fixed in generating a given growth pattern,
- 38. 20 C. Bardt, M. Dziedziniewicz, and J. Ko these supports are modeled within ABAQUS requiring no change to the ABAQUS script within a given run. Meshing is done using a tetrahedral meshing to handle forms that are not constrained to a predeterminedgrid. This is done via a specification of a seeding of the boundary, which in turn is a function of the seed number (an average node-vertex to node-vertex distance). By fixing the seed number we fix the nodes on the surface and hence, obtain a consistent set of vertices throughout a run. For a design objective of least square deflection of the plate, these plate vertices are further identified by looking at the coordinates of each vertex of the instance created and matching the vertices in the sheet with corresponding field outputs. By using ABAQUS, there is the advantage of an extensive material library which is constantly expanding through such additions like the Granta material selection plugin. 3 Case Study: A Design Experiment to Model Rib Growth 3.1 Historical Significance of Rib Forms The relation of ribs to surface form has intrigued architects and engineers for hun- dreds of years. The early medieval masons developed ribs based on drawn arcs of circles, and the vaults spanning these ribs were distorted and uneven irregular sur- faces “stretched” to fit between the splayed rib structures [9]. The ribs served as the structure, to a large extent, carrying the vaults. The 16th century development of sophisticated drawing systems allowed masons to control the stonecutting of vaults to such an extent that the vaults became shell structures and the ribs a reinforcing lattice work – in effect reversing the structural role of vaults and ribs from the early Gothic period [6]. Historically, there has been a fundamental ambiguity between rib and surface. Which comes first – the form of the rib or the the surface which is being rein- forced by the rib? In the 20th century, rib and surface research was conducted by a new breed of designer, the architect-engineer such as Nervi, Maillart, Dieste, Can- dela. Their research took the form of experimental long span structures such as thin shells, ribbed shells, and lamella structures often using the new technology of reinforced concrete. These experiments were limited to statically determinate structures, geometries optimized for given parameters. Any kind of experimenta- tion that went beyond these structures proved difficult, an example being Frank Lloyd Wrights tapered, dendriform, mushroom columns which were subject to a combination of tensile, coplanar and non axial loads. The local building commit- tee refused to approve the column for construction until its performance had been empirically demonstrated [8]. In recent decades, the problem of generating optimal patterns of reinforcement in plate and shell structures – topology optimization – has been studied intensively by the mathematical and engineering communities. Some notable precedents have in- formed our work, including Bendsoe and Kikuchi’s work [2] which spawned studies of a large range of loading conditions, optimality and efficiency criteria and hybrid materials (many detailed in [3]) that utilize the homogenization method–a powerful
- 39. Tools and Design Strategies to Study Rib Growth 21 tool in variational calculus–which results in solutions that are density distributions of material. For practical concerns of buildability and formwork, we looked to tech- niques that produced distinct pattern of reinforcements. In [5], Ding and Yamazaki proposed a technique based on the adaptive growth rule of branching systems using a design criterion of maximum global stiffness, which has the benefit of producing distinct patterns. While it seems quite general to a number of support and load- ing conditions, only typical support and loading conditions on a square plate were implemented. 3.2 Creating the Methodological Framework for an Experiment The integrated tool and workflow is designed as a sandbox in which experiments to test intuition-led strategies can be conducted with relative ease. In devising this initial experiment, a number of assumptions were made. The surface that we con- sider in this experiment is a square plate with uniform thickness and a single cir- cular column of support. The ribs are uniform in cross-section and of fixed length. The surface and ribs are made of the same isotropic elastic material and form a monolithic ribbed surface. The boundary conditions applied are total encastre for the support allowing displacement of the ribbed surface. Since the surface here is a plate, we can consider a design objective of least square deflection of the surface. The set of mesh nodes on the plate, N , stays constant through a given run so we can define deflection in the least-squares sense by Σi∈N Δz2 i , where Δzi is the vertical deflection of the ith node relative to the height of the plate above the support. The growth strategy used here is based on a “greedy algorithm” approach where at each step in the iteration, the choice that minimizes the squared deflection amongst all local possibilities is taken. This growth strategy comprises the following rules: • Growth initializes at the position of the support, which we call the origin. • An active growth point is either the end of a connected set of ribs emanating from the origin or the origin itself. • At each active growth point, there are k equivariant possible directions of growth. At all active growth points other than the origin, the length of the rib grown at each step is a fixed length l. The length of a rib emanating from the origin is length r +l, where r is the radius of the circular support. • A finite elements analysis for the whole structure is carried out at each growth point for each direction of growth, and rib growth occurs at the point and direc- tion that minimizes the least squared deflection amongst all local possibilities. • When the rib hits the boundary of the plate, the rib is cut short and the point of intersection with the boundary becomes an active growth point. This initial experiment is intended to be interactive with the user so no a priori stopping condition is given other than the number of steps that the user specifies, or when the ribs at all active points grows back onto itself. Fig. 2. illustrates the rules governing this growth strategy.
- 40. 22 C. Bardt, M. Dziedziniewicz, and J. Ko growth node 3. 2. 7. 9. 8. 4. 1. 6. 5. potential growth grown rib support outline sheet outline Fig. 2 Configurations along a hypothetical pattern growth governed by the growth strategy A number of parameters can influence the effectiveness and accuracy of the cal- culation of rib growth according to this growth strategy. These in general depend on the study at hand; in our case, we wished to conduct a comparative study in which the position of the support moves along the diagonal of the plate (Fig 3). Diagnostics were run to determine a choice of plate dimensions, stem radius, material properties and seed number so that the maximum deflection of the plate supported at each point being considered was sufficiently small and so that the results could be meaningfully compared. The dimensions of the rib unit can greatly influence the effectiveness of the growth; too high a volume increment and the rib can easily increase the deflec- tion in the plate; too low a volume increment and the iterations in growth typically reduce and meaningful growth patterns may not be obtained. Since our interest is the pattern of growth, we focused on the influence parameter of the depth of the
- 41. Tools and Design Strategies to Study Rib Growth 23 Support at (0.0) radius 1”edge 10.5”seed no 0.3 Support at (-1.-1) radius 1”edge 10.5”seed no 0.3 Support at (-2.-2) radius 1”edge 10.5”seed no 0.3 Fig. 3 A comparative study showing 20 iterations of rib growth corresponding to the pro- posed growth strategy starting with a support at the center and moving out towards the di- agonal. Parameters for these runs: plate parameters given by edge length 10.5 inches (26.67 cm) and depth of 1/8th inch (0.3175 cm); stem radius of 1 inch; material properties given by Young’s modulus of 69 GPa and Poisson’s ratio of 0.3; seed number of 0.3; rib parameters with length of 1 inch (2.54 cm), thickness of 1/8th inch (0.3175 cm) and depth of 1 inch (2.54 cm); 16 directions of growth at each node. rib, fixing the length and the thickness. Fig. 4 shows three choices of rib length of a choice of support position corresponding to the position of the support offset at from the center of the plate. The monotonically decreasing deflection curve corre- sponds to continued growth of ribs leading to a meaningful growth pattern, whereas a flattening out corresponds to no further growth. From this initial experiment, a natural evolution of the proposed growth strategy is one based on a variable volume increment which might reveal structure at a finer scale and would be a natural quantity on which a stopping condition could be based. Additionally, initiating growth at multiple points with different rates of growth could be a more effective strategy to cover more ground with less material intensity of ribs.
- 42. 24 C. Bardt, M. Dziedziniewicz, and J. Ko Fig. 4 Deflection, in the least squared sense, corre- sponding to each iteration of a run for three choices of rib depth for the case where the center of support is offset from the center of sheet by (−1,−1). Remain- ing run parameters are the same as those used for the comparative study Fig 3. 4 Conclusion The integrated tool and workflow provides a digital sandbox in which experiments to test intuition-led strategies on a class of problems, including ones on rib growth, can be conducted. By interacting with the structure, the architect gains valuable awareness to structural factors which can inform design decisions. Acknowledgements. We would like to thank Viswanath Chinthapenta for launching us on our journey with ABAQUS, to Shane Richards for lending us his time and expertise in our parallel journey in fabrication, and to the Brown University Engineering School for granting us access to their Computational Mechanics Research Facility. References 1. Banham, R.: Theory and Design in the First Machine Age. MIT Press, Cambridge (1980) 2. Bendsoe, M.P., Kikuchi, N.: Generating optimal topologies in structural design using a homogenization method. Comput. Methods Appl. Mech. Eng. 71, 197–224 (1988) 3. Bendsoe, M.P., Sigmund, O.: Topology Optimization, 2nd edn. Springer, Heidelberg (2004) 4. Le C.: Towards a New Architecture. John Roder, London (1931) 5. Ding, X., Yamazaki, K.: Adaptive growth technique of stiffener layout pattern for plate and shell structures to achieve minimum compliance. Engineering Optimization 37(3), 250–276 (2005) 6. Evans, R.: The Projective Cast, Architecture and Its Three Geometries. MIT Press, Cambridge (1980) 7. Hearn, M.F. (ed.): The Architectural Theory of Viollet-le-Duc, Readings and Commen- tary. MIT Press, Cambridge (1990) 8. Lipman, J.: Frank Loyd Wright and the Johnson Wax Buildings, Rizzoli (1986) 9. Willis, R.: On the Construction of the Vaults of the Middle Ages. Royal Institute of British Architects, London (1842)
- 43. Free Shape Optimal Design of Structures Kai-Uwe Bletzinger Abstract. Actual trends in numerical shape optimal design of structures deal with handling of very large dimensions of design space. The goal is to allowing as much design freedom as possible while considerably reducing the modeling effort. As a consequence, several technical problems have to be solved to get procedures which are robust, easy to use and which can handle many design parameters efficiently. The paper briefly discusses several of the most important aspects in this context and presents many illustrative examples which show typical applications for the design of light weight shell and membrane structures. 1 Introduction Shape optimal design is a classical field of structural optimization. Applied to the design of free form shells and membranes or, more generally, light weight structures, it is of big importance in architecture, civil engineering or various applications of industrial metallic or composite shells as e.g. in automotive or aerospace industries [1, 2, 3]. In the “old” days of the pre-computer age optimal shapes had been found by experiments such as inverted hanging models or soap film experiments. Still, those shapes are of great importance for practical design as they define structures of minimal amount of bending which, in turn, are as stiff as possible. As a conse- quence, “stiffness” is one of the most important design criteria one can think of. The methods discussed in the sequel refer to this design criterion in various ways. A standard approach of optimal shape design is to discretize the structure and to use geometrical discretization parameters as design variables, e.g. nodal coordinates. As optimization is a mathematical inverse problem it exhibits typical pathological properties which in particular become obvious or even dominant if the number of design parameters becomes large. In particular, one has to deal with questions like Kai-Uwe Bletzinger Lehrstuhl für Statik, Technische Universität München, Germany
- 44. 26 K.-U. Bletzinger irrelevant degrees of freedom tangential to the surface, highly non-convex design spaces, and mesh dependency, just to mention the most important. The state-of-the- art answer to those problems is to use CAGD methods for the discretization of ge- ometry: The success of that approach, however, is a consequence of the reduced number of design parameters rather than a consequent elimination of the source of deficiencies. In other words, if the number of CAGD parameters used for structural optimization is increased, the pathological properties become obvious, again. If geometrical parameters of a fine discretization are used, as e.g. the coordinates of a finite element mesh, strategies have to be developed to stabilize the original deficiencies of the inverse problem. Fig. 1 Stiffened shell structures made from folded paper 2 Design Noise and the Infinity of Design Space The principal challenge of form finding can briefly be explained by an illustrative example. The task is to design the stiffest structure made from a piece of paper
- 45. Free Shape Optimal Design of Structures 27 which is able to act as a bridge carrying load. The solution is well known. As the piece of paper is unable to act in bending stiffeners have to be introduced by folding the paper. However, there exists an infinite number of solutions which all of them do the job creating stiff solutions of at least similar quality which is by far better than the quality of the initially flat piece of paper. Surprisingly enough, even an arbitrary pattern of random folds appears to be a possible solution, Fig.1. The figure of the randomly crinkled paper is an ideal paradigm for the infinity of the design space or, more ostensive, the “design noise”. As for the actual example the crinkled paper can be understood as the weighted combination of all possible stiffening patterns one can easily think of a procedure to derive any of the individual, basic solutions of distinct stiffening patterns by applying suitable “filters” to the design noise. It is clear that the kind of “filter” as well as the “filter process” can be freely chosen as an additional and most important design decision. It is possible to define a procedure as implied by the actual example and to, first, generate a “highly frequent” design noise and to apply geometrical filters in a second step. It is, however, also possible to apply “indirect” filters by preselecting and favoring certain classes of solutions in advance. There is no doubt that the mentioned second way is the more ingenious one as a large set of other, perhaps even better solutions, might be undetected. It remains to the insight of the applying per-son about how to define a procedure of pre-selection, regularization or “pre-filtering”, just to refer to the introduced picture. Most often, however, there remain some secrets or at least some vagueness. From this point of view form finding truly is an art. Fig. 2 Direct numerical stiffness optimization and filtering of a plate subjected to self-weight
- 46. 28 K.-U. Bletzinger 3 Direct Filtering of Numerical Models Numerical form finding techniques allow the direct approach of filtering the de- sign noise. As an example, consider a circular plate as shown in Fig.2 which is discretized by finite shell elements. The nodal positions of the finite element nodes shall be found such that the stiffness of the structure is maximized. With- out any additional treatment numerical optimization procedures suggest a highly crinkled shape. Obviously, the simulation resolves the physics of the random stiff- ening pattern similar to the paper experiment. The smallest crinkles are defined by the possible resolution of the finite element mesh. Finer meshes allow even higher frequencies. Additionally, high frequent crinkles result in extreme element distortions which come together with additional artificial, non-physically stiff ele- ment behavior which is known as “locking”. That means that filtering play a dou- ble role (i) to prevent non-physical artifacts by controlling mesh distortion and (ii) to help to identify the preferred optimal shape within the infinity of the de- sign space. For the plate in Fig.2 a coarse low pass filter has been applied. It is a simple hat function of rotational symmetry with a base length of the size of the plate diameter. Consequently, the dome is identified as optimal structure which is well known from the inverted hanging model experiment. It appears that the type of filter (e.g. hat, cubic spline or Gauss distribution) is of minor impor- tance in contrast to the size of the filter basis which directly controls the minimum size of stiffening “crinkles”. The filter size is a very effective as well as efficient control for exploring the design space as it is shown in the following examples [1, 2, 3, 4]. 4 CAGD Based Parameterization Techniques and Structural Shape Optimization The industrial state of the art in structural optimization is characterized by the com- bined application of CAGD methods (Computer Aided Geometric Design), finite element analysis, and non-linear programming. The idea is to define the degrees of freedom for shape optimization and form finding by some few but character- istic control parameters of the CAGD model. The choice of a CAGD model is indeed identical to an implicit pre-selection of a design filter which directly af- fects the result. As most often a CAGD model is quite complex, modifications are cumbersome and it is difficult to explore the design space by adjusting the implicit design filter. Often architects and engineers are not totally aware about that and miss alternatives. Still, however, the remaining design space might be large enough and the limitations might be accepted. The most actual trend is defined by the Isogeometric Analysis, where NURBS shape functions are used for both, the design modeling as well as the structural analysis [5, 6, 7, 8, 9].
- 47. Free Shape Optimal Design of Structures 29 As a consequence, design models must be analysis suitable which create new chal- lenges for the CAGD community regarding geometrical compatibility and treating trimmed surfaces. T-splines have been suggested as remedy [10, 11]. 5 Minimal Surfaces The form finding of tensile structures is defined by the equilibrium of external and internal pre-stress forces. The choice of pre-stresses of surface and edge cables is the “filter” applied to screen the design space. As the shape is uniquely defined by the equilibrium of forces and stresses there is no material related term in the equations. Consequently, nodes of the discretization mesh can float freely on the surface because surface strains are not inducing elastic stresses relevant for the form finding process. Additional regularization of the method is necessary for procedural reasons not as means to explore the design space. In contrast to the most of the available methods the Updated Reference Strategy (URS) is consistently derived from continuum mechanics [12, 13]. Therefore, it appears to be very robust and can easily be applied for all kind of applications, for membranes as well as cables and their combinations. It can be interpreted as a generalization of the well-known force density method [14]. 6 Illustrative Examples 6.1 Pre-stressed Surfaces These examples, Fig.3 and Fig.4, present the direct application of URS for the de- sign of pre-stressed surfaces due to isotropic (minimal surfaces) and anisotropic surface stresses. Note, that even ideal minimal surfaces can easily be determined which is a challenge for many available structural form finding methods. The im- plemented procedure is able to treat form finding under additional effects as there are additional surface loads (e.g. pressure), interior edge cables (needs additional formulation of constraints on cable length) and consideration of stiffening members in bending and compression (kind of tensegrity structures). For further information refer to www.membranes24.com. 6.2 Norwegian Pavilion at EXPO 2010, Shanghai This example shows the application of the URS technique in architecture and civil engineering for the form finding of the roof for the Norwegian pavilion at the EXPO 2010 in Shanghai, Fig.5, [15].
- 48. 30 K.-U. Bletzinger Fig. 3 “Bat Wing”, Form finding of hybrid structure: Isotropic surface stress, edge cables, spokes in compression and bending Fig. 4 Form finding of minimal surfaces and ideal spherical soap bubbles 6.3 Bead Design of Plates and Shells for Single Loads A bend cantilever made of a thin (metal) sheet is loaded as shown, Fig.6. A filter radius as large as the width of support is used. The model consists of appr. 5.000 shape variables. The optimal shape (most right) is reached after 19 iteration steps.
- 49. Free Shape Optimal Design of Structures 31 Fig. 5 The roof of the Norwegian pavilion at 2010 EXPO, Shanghai: Application of URS Another example demonstrates the mesh independence of the method, Fig.7. A quadratic plate is loaded in the center and supported at the corners. The question is to find the optimal topology of stiffening beads. A filter radius is chosen as large as half of the width of support. Additionally, a constraint on the maximum bead depth is given. As shown, the optimal solution is characterized by the filter but it is mesh independent. The choices of filter type and size are additional degrees of design freedom which may be used to explore the design space. Note the smooth final surface although local radial filters are applied. Fig.8 shows the result of a joint project together with Adam Opel GmbH. The optimal distribution of beads has been determined to maximize the five lowest eigen- frequencies of a thin metal sheet. The number of iterations appears always to be not more than 40 for every problem size. Fig. 6 Shape optimization of a cantilever shell
- 50. 32 K.-U. Bletzinger Fig. 7 Optimal bead design of initially plane sheet Fig. 8 Bead optimization of a thin metal sheet for the automotive industry 6.4 Shape Optimization of a Wind Turbine Blade The shape of a wind turbine blade is optimized for two cases, Fig.9 to Fig.11: To maximize stiffness for given mass and to minimize mass for defined stiffness. The pressure distribution has been determined from a CFD simulation is applied to a linear elastic structural model for shape optimization as a preliminary design study. The next steps will consider a complete non-linear structural model in a fully cou- pled FSI-environment for shape optimization. More than 9.000 shape variables have been used. Again, note, the smooth shape although small design filters have been used to prevent numerical noise. The initial shape has been generated from a Rhino 3D c model which also can be used for a isogeometric analysis for the fully cou- pled, transient analysis of the blade in a numerical wind tunnel [7, 8, 9]. The latter study has been done in a joint work together with Yuri Bazilevs at University of California at San Diego [16].
- 51. Free Shape Optimal Design of Structures 33 Fig. 9 Rhino 3D model of wind turbine blade (left); wind pressure distribution (right) Fig. 10 Screen dump of the Rhino-Plug-In developed at Lehrstuhl für Statik used as pre- and post-processor for isogeometric design and analysis of non-linear shell structures Fig. 11 Optimized shapes from a free mesh, filter based optimization procedure
- 52. Other documents randomly have different content
- 53. decrease or the barometric gradient. Lay your scale through the station, and as nearly as possible at right angles to the adjacent isobars. If the station is exactly on an isobar, then measure the distance from the station to the nearest isobar indicating a lower pressure. The scale must, however, be laid perpendicularly to the isobars, as before. Divide the number of hundredths of an inch of pressure difference between the isobars (always .10 inch) by the number expressing the distance (in latitude degrees) between the isobars; the quotient is the rate of pressure decrease per latitude degree. Or, to formulate the operation, R = P / D, in which R = rate; P = pressure difference between isobars (always .10 inch), and D = distance between the isobars in latitude degrees. Determine the rates of pressure decrease in the following cases:— A. For a number of stations in different parts of the same map, as, e.g., Boston, New York, Washington, Charleston, New Orleans, St. Louis, St. Paul, Denver, and on the same day. B. For one station during a winter month and during a summer month, measuring the rate on each map throughout the month, and obtaining an average rate for the month. Have these gradients at the different stations any relation to the proximity of low or high pressure? To the velocity of the wind? Pressure Gradients on Isobaric Charts of the Globe.—The change from low pressure to high pressure or vice versa with the seasons, already noted as being clearly shown on the isobaric charts of the globe, evidently means that the directions of pressure decrease must also change from season to season. The rates of pressure decrease likewise do not remain the same all over the world throughout the year. If we examine isobaric charts for January and July, we shall find that these gradients are stronger or steeper over the Northern Hemisphere in the former month than in the latter.
- 54. CHAPTER VIII. WEATHER. Hitherto nothing has been said about the weather itself, as shown on the series of maps we have been studying. By weather, in this connection, we mean the state of the sky, whether it is clear, fair, or cloudy, or whether it is raining or snowing at the time of the observation. While it makes not the slightest difference to our feelings whether the pressure is high or low, the character of the weather is of great importance. The character of the weather on each of the days whose temperature, wind, and pressure conditions we have been studying is noted in the table in this chapter. The symbols used by the Weather Bureau to indicate the different kinds of weather on the daily weather maps are as follows: clear; fair, or partly cloudy; cloudy; rain; snow. Enter on a blank map, at each station, the sign which indicates the weather conditions at that station at 7 A.M., on the first day, as given in the table. When you have completed this, you have before you on the map a bird’s-eye view of the weather which prevailed over the United States at the moment of time at which the observations were taken. Describe in general terms the distribution of weather here shown, naming the districts or States over which similar conditions prevail. Following out the general scheme adopted in the case of the temperature and the pressure distribution, separate, by means of a line drawn on your map, the districts over which the weather is prevailingly cloudy from those over which the weather is partly cloudy or clear. In drawing this line, scattering observations which do not harmonize with the prevailing conditions around them may be disregarded, as the object is simply to emphasize the general characteristics. Enclose also, by means of another line, the general area over which it was snowing at the time
- 55. of observation, and shade or color the latter region differently from the cloudy one. Study the weather distribution shown on your chart. What general relation do you discover between the kinds of weather and the temperature, winds, and pressure? Proceed similarly with the weather on the five remaining days, as noted in the table. Enter the weather symbols for each day on a separate blank map, enclosing and shading or coloring the areas of cloud and of snow as above suggested. In Figs. 40-45 the cloudy areas are indicated by single-line shading, and the snowy areas by double-line shading. Now study carefully each weather chart with its corresponding temperature, wind, and pressure charts. Note whatever relations you can discover among the various meteorological elements on each day. Then compare the weather conditions on the successive maps. What changes do you note? How are these changes related to the changes of temperature; of wind; of pressure? Write a summary of the results derived from your study of these four sets of charts.
- 56. Fig. 40.—Weather. First Day.
- 57. Fig. 41.—Weather. Second Day.
- 58. Fig. 42.—Weather. Third Day.
- 59. Fig. 43.—Weather. Fourth Day.
- 60. Fig. 44.—Weather. Fifth Day.
- 61. Fig. 45.—Weather. Sixth Day. The Weather of Temperate and Torrid Zones.—The facts of the presence of clear weather in one region while snow is falling in another, and of the variability of our weather from day to day in different parts of the United States, are emphasized by these charts of weather conditions. This changeableness of weather is a marked characteristic of the greater portion of the Temperate Zones, especially in winter. The weather maps for successive days do not, as a rule, show a repetition of the same conditions over extended regions. In the Torrid Zone it is different. Over the greater part of that zone the regularity of the weather conditions is such that, day after day, for weeks and months, the same features are repeated. There monotony, here variety, is the dominant characteristic of the weather.
- 62. Part IV.—The Correlations of the Weather Elements and Weather Forecasting.
- 63. CHAPTER IX. CORRELATION OF THE DIRECTION OF THE WIND AND THE PRESSURE. The study of the series of weather maps in Chapters V-VIII has made it clear that some fairly definite relation exists between the general flow of the winds and the distribution of pressure. We now wish to obtain some more definite result as to the relation of the direction of the wind and the pressure. In doing this it is convenient to refer the wind direction to the barometric or pressure gradient at the station at which the observation is made. The barometric gradient, it will be remembered, is the line along which there is the most rapid change of pressure, and lies at right angles to the isobars (Chapter VII). Fig. 46. Take a small piece of tracing paper, about 3 inches square, and draw upon it a diagram similar to the one here shown. Select the station (between two isobars on any weather map) at which you intend to make your observation. Place the center of the tracing paper diagram over the station, with the dotted line along the barometric gradient, the minus end of the line
- 64. being towards the area of low pressure. Observe into which of the four sectors (marked right, left, with, against) the wind arrow at the station points. Keep a record of the observation. Repeat the observation at least 100 times, using different stations, on the same map or on different maps. Tabulate your results according to the following scheme, noting in the first column the date of the map, in the second, third, fourth, and fifth columns the number of winds found blowing with, to the right or left of, and against, the gradient. Table I.—Correlation of the Direction of the Wind and the Pressure. Dates With Right Left Against Sums Percentages At the bottom of each column write down the number of cases in that column, and then determine the percentages which these cases are of the total number of observations. This is done by dividing the number of cases in each column by the sum-total of all the observations. When you have obtained the percentage of each kind of wind direction, you have a numerical result. A graphical presentation of the results may be made by laying off radii corresponding in position to those which divide the sectors in Fig. 46, and whose lengths are proportionate to the percentages of the different wind directions in the table. Thus, for a percentage of 20, the radii may be made 1 inch long, for 40%, 2 inches, etc. When completed, the relative sizes of the sectors will show the relative frequencies of winds blowing in the four different directions with reference to the gradient, as is indicated in Fig. 47. The Deflection of the Wind from the Gradient: Ferrel’s Law.—The law of the deflection of the wind prevailingly to the right of the gradient is known as Ferrel’s Law, after William Ferrel, a noted American meteorologist, who died in 1891. The operation of this law has already been seen in the spiral circulation of the winds around the cyclone and the anticyclone, as shown on the maps of our series. In the case of the cyclone the gradient is
- 65. directed inward towards the center; in the case of the anticyclone the gradient is directed outward from the center. In both cases the right-handed deflection results in a spiral whirl, inward in the cyclone, outward in the anticyclone. The operation of this law is further seen in the case of the Northeast Trade Winds. These winds blow from about Lat. 30° N. towards the equator, with wonderful regularity, especially over the oceans. Instead of following the gradient and blowing as north winds, these trades turn to the right of the gradient and become northeast winds, whence their name. From about Lat. 30° N. towards the North Pole there is another great flow of winds over the earth’s surface. These winds do not flow due north, as south winds. They turn to the right, as do the trades, and become southwest or west-southwest winds, being known as the Prevailing Westerlies. Ferrel’s Law thus operates in the larger case of the general circulation of the earth’s atmosphere, as well as in the smaller case of the local winds on our weather maps. Fig. 47.
- 66. CHAPTER X. CORRELATION OF THE VELOCITY OF THE WIND AND THE PRESSURE. Prepare a scale of latitude degrees, as explained in Chapter V. Select some station on the weather map at which there is a wind arrow, and at which you wish to study the relation of wind velocity and pressure. Find the rate of pressure change per degree as explained in Chapter VII. Note also the velocity, in miles per hour, of the wind at the station. Repeat the operation 100 or more times, selecting stations in different parts of the United States. It is well, however, to include in one investigation either interior stations alone (i.e., more than 100 miles from the coast) or coast stations alone, as the wind velocities are often considerably affected by proximity to the ocean. And, if coast stations are selected, either onshore or offshore winds should alone be included in one exercise. The investigation may, therefore, be carried out so as to embrace the following different sets of operations:— A. Interior stations. B. Coast stations with onshore winds. C. Coast stations with offshore winds. Enter your results in a table similar to the one here given:— Table II.—Correlation of Wind Velocity and Barometric Gradient. For interior (or coast) stations, with onshore (or offshore) winds, in the United States during the month (or months) of
- 67. Rates of Pressure Change per Latitude Degree ∞-20 20- 10 10-5 5- 31⁄2 31⁄2- 21⁄2 21⁄2 -2 etc. Distances between Isobars in Latitude Degrees 01⁄2 1⁄2-1 1-2 2-3 3-4 4-5 etc. Wind Velocities (miles per hour) Sums Cases Means The wind velocity for each station is to be entered in the column at whose top is the rate of pressure change found for that station. Thus, if for any station the rate of pressure change is 31⁄2 (i.e., .03 inch in one latitude degree), and the wind velocity at that station is 17 miles an hour, enter the 17 in the fourth and fifth columns of the table. When you find that the rate of pressure change for any station falls into two columns of the table, as, e.g., 10, or 5, or 31⁄3, then enter the corresponding wind velocity in both those columns. In the space marked Sums write the sum-total of all the wind velocities in each column. The Cases are the number of separate observations you have in each column. The Means denote the average or mean wind velocities found in each column, and are obtained by dividing the sums by the cases. Study the results of your table carefully. Deduce from your own results a general rule for wind velocities as related to barometric gradients. The dependence of wind velocities on the pressure gradient is a fact of great importance in meteorology. The ship captain at sea knows that a rapid fall of his barometer means a rapid rate of pressure change, and foretells high winds. He therefore makes his preparations accordingly, by shortening sail and by making everything fast. The isobaric charts of the globe for January and July show that the pressure gradients are stronger (i.e., the rate of pressure change is more rapid) over the Northern Hemisphere in January than in July. This fact would lead us to expect that the velocities of
- 68. the general winds over the Northern Hemisphere should be higher in winter than in summer, and so they are. Observations of the movements of clouds made at Blue Hill Observatory, Hyde Park, Mass., show that the whole atmosphere, up to the highest cloud level, moves almost twice as fast in winter as in summer. In the higher latitudes of the Southern Hemisphere, where the barometric gradients are prevailingly much stronger than in the Northern, the wind velocities are also prevailingly higher than they are north of the equator. The prevailing westerly winds of the Southern Hemisphere, south of latitude of 30° S., blow with high velocities nearly all the time, especially during the winter months (June, July, August). These winds are so strong from the westward that vessels trying to round Cape Horn from the east often occupy weeks beating against head gales, which continually blow them back on their course.
- 69. CHAPTER XI. FORM AND DIMENSIONS OF CYCLONES AND ANTICYCLONES. A. Cyclones.—Provide yourself with a sheet of tracing paper about half as large as the daily weather map. Draw a straight line across the middle of it; mark a dot at the center of the line, the letter N at one end, and the letter S at the other. Place the tracing paper over a weather map on which there is a fairly well enclosed center of low pressure (low), having the dot at the center of the low, and the line parallel to the nearest meridian, the end marked N being towards the top of the map. When thus placed, the paper is said to be oriented. Trace off the isobars which are nearest the center. In most cases the 29.80-inch isobar furnishes a good limit, out to which the isobars may be traced. Continue this process, using different weather maps, until the lines on the tracing paper begin to become too confused for fairly easy seeing. Probably 15 or 20 separate areas of low pressure may be traced on to the paper. It is important to have all parts of the cyclonic areas represented on your tracing. If most of the isobars you have traced are on the southern side of cyclones central over the Lakes or lower St. Lawrence, so that the isobars on the northern sides are incomplete, select for your further tracings weather maps on which the cyclonic centers are in the central or southern portions of the United States, and therefore have their northern isobars fully drawn. When your tracing is finished you have a composite portrait of the isobars around several areas of low pressure. Now study the results carefully. Draw a heavy pencil or an ink line on the tracing paper, in such a way as to enclose the average area outlined by the isobars. This average area will naturally be of smaller dimensions than the outer isobars on the tracing paper, and of larger dimensions than the inner isobars, and its form will follow the general
- 70. trend indicated by the majority of the isobars, without reproducing any exceptional shapes. Write out a careful description of the average form, dimensions [measured by a scale of miles or of latitude degrees (70 miles = 1 degree about)] and gradients of these areas of low pressure, noting any tendency to elongate in a particular direction; any portions of the composite where the gradients are especially strong, weak, etc. B. Anticyclones.—This investigation is carried out in precisely the same manner as the preceding one, except that anticyclones (highs) are now studied instead of cyclones. The isobars may be traced off as far away from the center as the 30.20-inch line in most cases. When, however, the pressure at the center is exceptionally high, it will not be necessary to trace off lower isobars than those for 30.30, or 30.40, or sometimes 30.50 inches. Loomis’s Results as to Form and Dimensions of Cyclones and Anticyclones.—One of the leading American meteorologists, Loomis, who was for many years a professor in Yale University, made an extended study of the form and dimensions of areas of low and high pressure as they appear on our daily weather maps. In the cases of areas of low pressure which he examined, the average form of the areas was elliptical, the longer diameter being nearly twice as long as the shorter (to be exact the ratio was 1.94 : 1). The average direction of the longer diameter he found to be about NE. (N. 36° E.), and the length of the longer diameter often 1600 miles. In the case of areas of high pressure, Loomis also found an elliptical form predominating; the longer diameter being about twice as long as the shorter (ratio 1.91 : 1), and the direction of trend about NE. (N. 44° E.). These characteristics hold, in general, for the cyclonic and anticyclonic areas of Europe also. The cyclones of the tropics differ considerably from those of temperate latitudes in being nearly circular in form.
- 71. CHAPTER XII. CORRELATION OF CYCLONES AND ANTICYCLONES WITH THEIR WIND CIRCULATION. A. Cyclones.—Something as to the control of pressure over the circulation of the wind has been seen in the preliminary exercises on the daily weather maps. We now proceed to investigate this correlation further by means of the composite portrait method. This method is a device to bring out more clearly the general systems of the winds by throwing together on to one sheet a large number of wind arrows in their proper position with reference to the controlling center of low pressure. In this way we have many more observations to help us in our investigation than if we used only those which are given on one weather map, and the circulation can be much more clearly made out. Provide yourself with a sheet of tracing paper, prepared as described in Chapter XI. Place the paper over an area of low pressure on some weather map, with the dot at the center of the low, and having the paper properly oriented, as already explained. Trace off all the wind arrows around the center of low pressure, making the lengths of these arrows roughly proportionate (by eye) to the velocity of the wind, according to some scale previously determined upon. Include on your tracing all the wind arrows reported at stations whose lines of pressure-decrease converge towards the low pressure center. Repeat this operation, using other centers of low pressure on other maps, until the number of arrows on the tracing paper is so great that the composite begins to become confused. Be careful always to center and orient your tracing paper properly. Select the weather maps from which you take
- 72. your wind arrows so that the composite shall properly represent winds in all parts of the cyclonic area. Deduce a general rule for the circulation and velocity of the wind in a cyclonic area, as shown on your tracing, and write it out. B. Anticyclones.—This exercise is done in precisely the same way as the preceding one, except that anticyclones and their winds are studied instead of cyclones. Deduce a general rule for the circulation and velocity of the wind in an anticyclonic area, as shown on your tracing, and write it out. The control of the wind circulation by areas of low and high pressure is one of the most important laws in meteorology. Buys-Ballot, a Dutch meteorologist, first called attention to the importance of this law in Europe, and it has ever since been known by his name. Buys-Ballot’s Law is generally stated as follows: Stand with your back to the wind, and the barometer will be lower on your left hand than on your right.[4] This statement, as will be seen, covers both cyclonic and anticyclonic systems. The circulations shown on your tracings hold everywhere in the Northern Hemisphere, not only around the areas of low and high pressure seen on the United States weather maps, but around those which are found in Europe and Asia, and over the oceans as well. Mention has already been made, in the chapter on isobars (VII), of the occurrence of immense cyclonic and anticyclonic areas, covering the greater portion of a continent or an ocean, and lasting for months at a time. These great cyclones and anticyclones have the same systems of winds around them that the smaller areas, with similar characteristics, have on our weather maps. A further extension of what has just been learned will show that if in any region there comes a change from low pressure to high pressure, or vice versa, the system of winds in that region will also change. Many such changes of pressures and winds actually occur in different parts of the world, and are of great importance in controlling the climate. The best-known and the most-marked of all these changes occurs in the case of India. During the winter, an anticyclonic area of high pressure is central over the continent of Asia. The winds blow out from it on all sides, thus causing general northeasterly winds over the greater portion of India. These winds are prevailingly dry and clear, and the weather during the time they blow is fine. India then has its dry season. As the summer comes on, the pressure over Asia changes, becoming low; a cyclonic area replaces the winter anticyclone, and inflowing winds take the place of the outflowing ones of the winter. The summer winds cross India from a general southwesterly direction,
- 73. come from over the ocean, and are moist and rainy. India then has its rainy season. These seasonal winds are known as Monsoons, a name derived from the Arabic and meaning seasonal. [4] In the Northern Hemisphere. Fig. 48. The accompanying figure (Fig. 48) is taken from the Pilot Chart of the North Atlantic Ocean, published by the Hydrographic Office of the United States Navy for the use of seamen. It shows the wind circulation around the center of a cyclone which is moving northward along the Atlantic Coast of the United States. The long arrow indicates the path of movement; the shorter arrows indicate the directions of the winds. By means of such a diagram as this a captain is able to calculate, with a considerable degree of accuracy, the position of the center of the cyclone, and can often avoid the violent winds near that center by sailing away from it, or by “lying to,” as it is called, and waiting until the center passes by him at a safe distance. These cyclones which come up the eastern coast of the United States at certain seasons are usually violent, and often do considerable damage to shipping. The Weather Bureau gives all the warning possible of the coming of these hurricanes, as they are called, by displaying hurricane signals along the coast, and by issuing telegraphic warnings to newspapers. In this way ship captains, knowing of the approach of gales dangerous to navigation, may keep their vessels in port until all danger is past. Millions of dollars’ worth of property and hundreds of lives have thus been saved.
- 75. CHAPTER XIII. CORRELATION OF THE DIRECTION OF THE WIND AND THE TEMPERATURE. It is evident, from even the most general observation of the weather elements, that the temperature experienced at any place is very largely dependent upon the direction of the wind. Thus, for instance, in the United States, a wind from some northerly point is likely to bring a lower temperature than a southerly wind. To investigate this matter more closely, and to discover how the winds at any station during any month are related to the temperatures noted at that station, we proceed as follows:— Select the Weather Bureau station at which you wish to study these conditions. Note the direction of the wind and the temperature at that station on the first day of any month. Prepare a table similar to the following one. Table III.—Correlation of the Direction of the Wind and the Temperature. At ..................... during the Month of ........ Wind Directions N. NE. E. SE. S. SW. W. NW. Temperatures
- 76. Sums Total Cases Total Means Mean Enter the temperature at 8 A.M. on the first day of the month in a column of the table under the proper wind direction. Thus, if the wind is NE., and the temperature 42°, enter 42 in the second column of the table. Repeat the observation for the same station, and for all the other days of the month, recording the temperatures in each case in their appropriate columns in the table. Omit all cases in which the wind is light, because winds of low velocities are apt to be considerably affected by local influences. When the observations for the whole month have been entered in the table, add up all the temperatures in each column (sums). Find the mean temperature (means) observed with each wind direction by dividing the sums by the number of observations in each column (cases). Add all the sums together; divide by the total number of cases, and the result will be the mean temperature[5] for the month at the station. The general effect of the different wind directions upon the temperature is shown by a comparison of the means derived from each column with the mean for the month. [5] Derived from the 8 A.M. observations. This does not give the true mean temperature. Fig. 49.
- 77. A graphic representation of the results of this investigation will help to emphasize the lesson. Draw, as in the accompanying figure (Fig. 49), eight lines from a central point, each line to represent one of the eight wind directions. About the central point describe a circle, the length of whose radius shall correspond to the mean temperature of the month, measured on some convenient scale. Thus, if the mean temperature of the month is 55° and a scale of half an inch is taken to correspond to 10° of temperature, the radius of the circle must be five and a half times half an inch, or 23⁄4 inches. Next lay off on the eight wind lines the mean temperatures corresponding to the eight different wind directions, using the same scale (1⁄2 in. = 10°) as in the previous case. Join the points thus laid off by a heavy line, as shown in Fig. 49. The figure, when completed, gives at a glance a general idea of the control exercised by the winds over the temperatures at the station selected. Where the heavy line crosses a wind line inside the circle it shows that the average temperature accompanying the corresponding wind direction is below the mean. When the heavy line crosses any wind line outside the circle, it shows that the average temperature accompanying the corresponding wind direction is above the mean. Such a figure is known as a wind rose. The cold wave and the sirocco are two winds which exercise marked controls over the temperature at stations in the central and eastern United States. The cold wave has already been described in Chapter V. It is a characteristic feature of our winter weather. It blows down from our Northwestern States or from the Canadian Northwest, on the western side of a cyclone. It usually causes sudden and marked falls in temperature, sometimes amounting to as much as 50° in 24 hours. The sirocco is a southerly or southwesterly wind. It also blows into a cyclone, but on its southern or southeastern side. Coming from warmer latitudes, and from over warm ocean waters, the sirocco is usually a warm wind, in marked contrast to the cold wave. In winter, in the Mississippi Valley and on the Atlantic Coast, the sirocco is usually accompanied by warm, damp, cloudy, and snowy or rainy weather. The high temperatures accompanying it (they may be as high as 50° or 60° even in midwinter) are very disagreeable. Our warm houses and our winter clothing become oppressive and we long for the bright, crisp, cold weather brought by the cold wave. In summer when a sirocco blows we have our hottest spells. Then sunstrokes and prostrations by the heat are most common, and our highest temperatures are recorded. The word sirocco (from Syriacus=Syrian) was first used as the name of a warm southerly wind in Italy. The cause and the characteristics of the Italian sirocco and of the American sirocco are similar, and the name may therefore be applied to our wind as well as to the Italian one. In the Southern Hemisphere, at Buenos
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