Final Report

Optimal Design of Complex Mechanical Systems Project Report
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ME 59700
Optimal Design of Complex Mechanical Systems
Project report
On
The Optimal Design of Thin Walled Structures for
Maximum Specific Energy Absorption Using LS-OPT
Date: 05/08/2016
Submitted by:
Prasad Tapkir, Prasad Mehta

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1. Introduction:
In this age of high speed vehicles, the implementation of energy absorbing systems in automobile
designs is an important aspect to be considered. This system acts as a transformation medium,
which receives kinetic energy which may take place due to crashing and converts this energy into
another form. This whole process assures the decreasing rate of human suffering and financial
penalties. Energy absorption systems include reversible absorber and collapsible absorber [2] [3].
Our project puts emphasis on collapsible energy absorber, which absorbs the energy by plastic
deformation of a thin-walled structure. The thin-walled structures have number of sections such as
circular, square, tapered, honeycomb, and octagonal section [2]. For instance, circular or square
thin-walled tubes play their role in energy absorption process. However, for further improvement
in safety, the proposed work includes optimal design of thin-walled tube with square cross section.
In current practices, to address the design optimization of the thin-walled structures, the optimal
dimensions are determined using optimization toolbox of MATLAB. The global approximation
techniques such as Artificial Neural Networks (ANN), Inverse distance weighing (IDW), and the
Kriging sequential approximation method are used to determine the population of design variables
[1] [4]. The usage of these approximation method determines the accuracy of the optimal solution.
For a record, kriging method and corresponding meta-model are the most accurate among these
approximations. In many cases, considering the linearity or non- linearity of the objective functions
and subjective constraints, global optimal is found using different optimization tools such as genetic
algorithm (GA), constrained nonlinear minimization (FMINCON), unconstrained nonlinear
minimization, and multi-objective genetic algorithm (MOGA). However, in our case, the objective
function and corresponding constraints are obtained by using LS-DYNA, while the different steps
of optimization mentioned above are performed using the architecture provided in LS-OPT.
In order to find optimal solution, crash analysis in LS-DYNA serves the basis to determine the
specific energy absorption and crushing force, which are the factor to be focused. Thus, for making
the car safer, the objective of our proposed method is to maximize the specific energy absorption
and to minimize crushing force. The mass of the thin-walled structure subjective constraints on the
dimensions of the thin-walled structures. The optimization procedure is performed using LS-OPT,
where LS-OPT extract objective functions and subjective constraints from LS-DYNA. As there are
numerous sampling methods, Latin hypercube sampling is used to distribute the desired number of
samples with utmost effectiveness. As mentioned earlier, kriging meta-model is used to fit these
sample points in corresponding approximation. In the last phase of the project, using the fit of
kriging meta-model and genetic algorithm, the optimal dimensions of thin-walled structures and
corresponding specific energy absorption is determined.

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2. Theoretical Background:
This section of the report provides a theoretical background for concept such as crashworthiness of
the vehicle, importance of LS-DYNA, interface of LS OPT, and methodology to link LS OPT and
LS DYNA.
The crashworthiness is the ability of the system (vehicle) to protect the occupants in the event of
crashing. The consequences of crashing mainly depend on two factors, first is the type and the
intensity of the impact, and the second is the methodology by which the crashworthiness of the
vehicle is determined. Thus, in the event of crashing, designer is not able to control the type or the
intensity of impact, but designer may emphasize on the crashworthiness of the vehicle to protect
the occupants. Considering the different methods to determine the crashworthiness, designer is
supposed to evaluate important factors such as internal energy, crushing force, and the mass of the
vehicle. After determining these factors, the design is able to understand the concept of specific
energy absorption, which is a function of internal energy generated while crashing and the mass of
the component being crushed. The effective crashworthiness provides us the maximum specific
energy absorption and least peak crushing force. Therefore, the designer is supposed to obtain these
important parameters of crashworthiness by using analysis package, while the task of maximizing
the specific energy absorption is done by using optimization package. In our proposed work, we
have used LS-DYNA for obtaining the important parameters, whereas the optimization is
performed using LS-OPT.
In LS-DYNA, the CAD model of component to be crashed is called from solid modeling package.
Usually, the component under testing is crashed against the rigid wall structure. Some of the times,
component is kept stationary and wall is hit against the component. In both cases, due to material
and modelling properties, the component is deformed or collapsed. The results of crash analysis is
determined by the type of deformation of the component. For instance, after crashing, if the
deformation is in the form of progressive folding or collapsing then the results are obtained are
more effective and reliable for optimization purposes. The variables for optimization, for instance
thickness, is set as a parameter in LS-DYNA. Lastly, the important parameters of the crash analysis,
which are mentioned earlier in the report are obtained from standard output database of LS-DYNA
package. The number of outputs depend on the requirement of optimization methodology.
Focusing on optimization methodology, designer is supposed to use different optimization tools in
MATLAB. In contrast, we preferred to use LS-OPT, as this package is highly compatible with LS-
DYNA and corresponding output database. Unlike MATLAB, LS-OPT does not demand actual
equations of objectives to be achieved. It directly extracts the output database and parameters of
LS-DYNA and put them as inputs to the optimization loop for the desires number of iterations. For
creating a Meta model, LS-OPT provides number of options such as radial based meat model,
kriging method, polynomial based meta model, and artificial neural network. While the sampling
method is chosen based on the accuracy demanded by optimization process. The designer decides
stores the LS-DYNA outputs as histories and responses in LS-OPT database. In latter stage of the
optimization, designer use these histories and responses to set objective functions and constraints
of the optimization. Based on the desired number of iterations, LS-OPT achieves the objective
functions by keeping the constraints within their bounds and optimizes the parameters, which are
set in LS-DYNA database.

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3. Methodology:
This section explains the analysis and optimization methodologies. The analysis methodology
includes the preset parameters and procedure to perform crash analysis, whereas, optimization
methodology describes the flow of optimization process from sampling to the final result.
3.1.Crash analysis:
a) Basic model of tube was developed using Solidworks. Tube dimensions taken were
50x50x500mm.
b) This model was imported in LS-Dyna and meshed uniformly.
c) Rigid wall was created to crash the tube and velocity of 15 m/s was given to the tube.
d) The keywords used were, boundary conditions, control, contact, database, mat, parts, elements
and parameter (thickness).
e) In database from ASCII, GLSTAT, MATSUM, RCforce were selected. Also, D3plot and
Histories- Shell database were selected to extract outputs.
f) The termination for crash was assigned as 0.02 seconds.
3.2.Optimization Methodology:
a) Extraction of important parameters:
The first step of the optimization process is to provide a path of LS-DYNA solver to LS-
OPT interface. With the help of this path, output of LS-DYNA is called in LS-OPT stage
block to establish histories and responses. We extracted reaction forces, internal energy,
and mass from LS DYNA database.
b) Setup:
For setting up the parameter to be optimize, in our case shell thickness (t), we provided
upper bound (2 mm), lower bound (0.5 mm), and initial guess (2 mm) for shell thickness.
c) Sampling:
As mentioned, the accuracy of the final output depends on distribution of the sampling, we
preferred Latin hypercube sampling (LHS) to sample the variable values with 5 samples
points.
d) Building a Meta model:
As accuracy of the optimal thickness depends on type of sampling and corresponding Meta
model, we preferred kriging meta- model as during the course we have observed that
kriging method provides the best approximation for the given optimization problem.
e) Building a composite:
The purpose of composite is to set an expression for mean crushing force and specific
energy absorption. In composite, we used histories and responses of stage block and set
expressions for specific energy absorption (SEA) and mean rushing force as,
SEA= (Internal energy/Mass) and Pmean= (Internal energy/0.5)
f) Optimization:
In optimization step, we have used genetic algorithm to optimize the thickness and set our
objective function and constrains as,
To Maximize f = SEA (t)
Subject to Pmax (t) ≤ Panalysis
tLB ≤ t ≤ tUB
Where, Panalysis= 1.38e5 N
g) Termination:
In termination step, we set out iteration limit up to 10 iteration to get final output.

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4. Results and Discussions:
This section of the report provides the estimate of internal energy, peak crushing force, and specific
energy absorption with respect to time frame of crash analysis and sampled values of thickness.
4.1.Internal energy Vs time Vs thickness:
Fig 1
4.2. Peak crushing force VS time Vs thickness:
Fig 2

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4.3. The overall statistics at peak crushing force:
Fig 3

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5. Conclusions:
a) As we can observe that for thickness value between 1.93 mm and 2 mm, the computed value
of specific energy absorption is greater than predicted value.
b) In the same thickness range the maximum crushing force is 9.2e4 N, which is less than the
constraint we set for optimization (1.38e5 N).
c) As optimization process was terminated only after two iterations, the LS-OPT did not converge
the value of thickness to optimal value.

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6. References:
1) M. Mirzaei, M. Shakeri, M. Sadighi, and H. Akbarshahi, Crashworthiness Design for Cylindrical
Tube using Neural Network and Genetic Algorithm, Procedia Engineering 14 (2011) 3346–3353.
2) M. Mirzaei, M. Shakeri, M. Sadighi, and S. Seyedi, Using of neural network and genetic algorithm
in multiobjective optimization of collapsible energy absorbers, International Conference on
Engineering Optimization.
3) S. Salehghaffari, M. Rais-Rohani, and A. Najafi, Analysis and Optimization of Externally Stiffened
Crush Tubes, 51st AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials
Conference.
4) Mastinu, G., M. Gobbi, and C. Miano, Optimal Design of Complex Mechanical Systems, 2010:
Springer, 359.
5) LS-OPT User’s Manual.
6) LS-DYNA User’s Manual.

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