1. 05/04/25
05/04/25 1
1
Thermal Finite Element Analysis
Thermal Finite Element Analysis
Tutorial
Tutorial
By Dr. Ashland O. Brown
By Dr. Ashland O. Brown
University of the Pacific
University of the Pacific
Mechanical Engineering Dept.
Mechanical Engineering Dept.
abrown@pacific.edu
abrown@pacific.edu
Copyright 2006
Copyright 2006
Heat Transfer Finite Element
Heat Transfer Finite Element
Tutorial ported to
Tutorial ported to
COSMOSWorks Professional
COSMOSWorks Professional
2007-2008 Software by
2007-2008 Software by
SolidWorks Corporation
SolidWorks Corporation
Expected completion time for
Expected completion time for
this tutorial is 45 minutes to 1
this tutorial is 45 minutes to 1
hour
hour
Companion Tutorial for Heat
Companion Tutorial for Heat
Transfer Course
Transfer Course
Reference Text: Heat and Mass
Reference Text: Heat and Mass
Transfer, 3rd Edition, by
Transfer, 3rd Edition, by
Yunus A. Cengel
Yunus A. Cengel
2. 05/04/25
05/04/25 2
2
Educational Objectives
Educational Objectives
The educational goal is to provide undergraduate
The educational goal is to provide undergraduate
engineering students with an understanding of a specific
engineering students with an understanding of a specific
engineering topic and FE theory, along with an ability to
engineering topic and FE theory, along with an ability to
apply commercial FE software to typical engineering
apply commercial FE software to typical engineering
problems. The educational goal will be accomplished
problems. The educational goal will be accomplished
through four educational objectives based upon Bloom’s
through four educational objectives based upon Bloom’s
Taxonomy and ABET Criteria 3 as follows;
Taxonomy and ABET Criteria 3 as follows;
1.
1. Engineering topics
Engineering topics (Comprehension: 3a, 3k).
(Comprehension: 3a, 3k).
Understanding the fundamental basis of engineering
Understanding the fundamental basis of engineering
topics through the use of finite element computer
topics through the use of finite element computer
models.
models.
3. 05/04/25
05/04/25 3
3
Educational Objectives
Educational Objectives
2.
2. FE Theory (Comprehension;3a)
FE Theory (Comprehension;3a) Understand the
Understand the
fundamental basis of FE Theory.
fundamental basis of FE Theory.
3.
3. FE Modeling Practice (Application; 3a, 3e,3k)
FE Modeling Practice (Application; 3a, 3e,3k) Be able to
Be able to
implement a suitable finite element model and construct
implement a suitable finite element model and construct
a correct computer model using commercial FE
a correct computer model using commercial FE
software.
software.
4.
4. FE Solution Interpretation and Verification
FE Solution Interpretation and Verification
(Comprehension and Evaluation; 3a,3e)
(Comprehension and Evaluation; 3a,3e) Be able to
Be able to
interpret and evaluate finite element solution quality
interpret and evaluate finite element solution quality
including the importance of verification.
including the importance of verification.
4. 05/04/25
05/04/25 4
4
Problem Description
Problem Description
Analysis Objectives
Analysis Objectives
• Reinforce knowledge and visualization of performing heat
Reinforce knowledge and visualization of performing heat
transfer analysis using the finite element method of analysis
transfer analysis using the finite element method of analysis
(FEA).
(FEA).
• Gain experience using a commercial FEA package to build a
Gain experience using a commercial FEA package to build a
FEA model and determining temperatures in a 3-D plate model.
FEA model and determining temperatures in a 3-D plate model.
• Authenticate and compare the COSMOSWorks FEA steady-
Authenticate and compare the COSMOSWorks FEA steady-
state temperatures for a 3-D shorten bar model with a similar
state temperatures for a 3-D shorten bar model with a similar
2-D bar model in the Cengel text.
2-D bar model in the Cengel text.
• Compare the COSMOSWorks 3-D FEA mesh of nodes and
Compare the COSMOSWorks 3-D FEA mesh of nodes and
elements with the explicit 2-D mesh of 13 nodes and 12
elements with the explicit 2-D mesh of 13 nodes and 12
elements from the Cengel text.
elements from the Cengel text.
5. 05/04/25
05/04/25 5
5
Problem Description
Problem Description
An long bar with a thermal conductivity of 1.5 W/m-K is attached to a
An long bar with a thermal conductivity of 1.5 W/m-K is attached to a
wall and has fixed temperatures on its upper and lower surfaces. Air is
wall and has fixed temperatures on its upper and lower surfaces. Air is
blown over the vertical right surface with a known temperature and
blown over the vertical right surface with a known temperature and
convective heat transfer coefficient while the left side is insulated.
convective heat transfer coefficient while the left side is insulated.
It is desire to find the
It is desire to find the
temperature distribution in the
temperature distribution in the
bar and the rate of heat transfer
bar and the rate of heat transfer
between the bar and the
between the bar and the
moving
moving
fluid per unit length of the bar.
fluid per unit length of the bar.
-- Note that the thickness of the
-- Note that the thickness of the
bar is shown as 0.1 m below,
bar is shown as 0.1 m below,
but it is actually a very long bar
but it is actually a very long bar
(in the z-direction). This
(in the z-direction). This
assumed dimension will not
assumed dimension will not
effect this 2-D problem.
effect this 2-D problem.
C
m
W
h
C
T
0
2
0
/
50
30
C
T 0
200
C
T 0
200
Wall
Insulated
6. 05/04/25
05/04/25 6
6
Problem Description
Problem Description
Assumptions:
Assumptions:
The problem can be accurately represented
The problem can be accurately represented
with second order tetrahedral elements with
with second order tetrahedral elements with
10 nodes each
10 nodes each
This is a steady state analysis
This is a steady state analysis
The material is homogeneous and isotropic
The material is homogeneous and isotropic
7. 05/04/25
05/04/25 7
7
Background Information
Background Information
General
General
The purpose of this tutorial is to provide visualization of the
The purpose of this tutorial is to provide visualization of the
heat transfer concepts covered in your course and to
heat transfer concepts covered in your course and to
introduce the concept of using finite element analysis (FEA)
introduce the concept of using finite element analysis (FEA)
in analyzing a steady-state heat transfer problem. You begin
in analyzing a steady-state heat transfer problem. You begin
with building a 3-D solid model of this problem using the
with building a 3-D solid model of this problem using the
SolidWorks software. Once the 3-D model is constructed you
SolidWorks software. Once the 3-D model is constructed you
then submit it to COSMOSWorks to perform the FEA. FEA
then submit it to COSMOSWorks to perform the FEA. FEA
consists of two major steps: pre-processing and post-
consists of two major steps: pre-processing and post-
processing. Preprocessing involves preparing the 3-D
processing. Preprocessing involves preparing the 3-D
model, meshing the model, and defining material properties
model, meshing the model, and defining material properties
along with placing boundary conditions on this model; the
along with placing boundary conditions on this model; the
post-processing involves running the FEA analysis and then
post-processing involves running the FEA analysis and then
displaying the results.
displaying the results.
8. 05/04/25
05/04/25 8
8
Background
Background
Finite Element Theory – Basics
Finite Element Theory – Basics
FEA works with the discretization of the actual structural
FEA works with the discretization of the actual structural
geometry into small portions called finite elements. These
geometry into small portions called finite elements. These
finite elements are joined together by shared nodes, also
finite elements are joined together by shared nodes, also
termed element connectivity. The elements and nodes jointly
termed element connectivity. The elements and nodes jointly
are referred to as the mesh. The real-life structure being
are referred to as the mesh. The real-life structure being
analyzed can be quite complex and hence a closed–form
analyzed can be quite complex and hence a closed–form
solution may not be available to provide predicted
solution may not be available to provide predicted
displacement, stress or temperature in the structure. FEA
displacement, stress or temperature in the structure. FEA
provides approximate solutions to the differential equations
provides approximate solutions to the differential equations
defining the physics of structural or thermal models of
defining the physics of structural or thermal models of
problems. The unknowns for each finite element are
problems. The unknowns for each finite element are
displacements at the nodes for structural analysis and
displacements at the nodes for structural analysis and
temperature at the nodes for thermal analysis : each finite
temperature at the nodes for thermal analysis : each finite
element shares at least one node with its neighboring
element shares at least one node with its neighboring
element.
element.
9. 05/04/25
05/04/25 9
9
Background
Background
Finite Element Theory – Basics
Finite Element Theory – Basics
The equations are formed from the mesh of nodes and the
The equations are formed from the mesh of nodes and the
solutions obtained must satisfy the physical condition that
solutions obtained must satisfy the physical condition that
any nodal displacement or temperature must also be the
any nodal displacement or temperature must also be the
same for all of the neighboring elements. This condition is
same for all of the neighboring elements. This condition is
called capability and is one of the fundamental requirements
called capability and is one of the fundamental requirements
for a valid design analysis. Many such equations are defined
for a valid design analysis. Many such equations are defined
and solved simultaneously to get the approximate solution
and solved simultaneously to get the approximate solution
for a complex structure. Most complex structures have
for a complex structure. Most complex structures have
thousands of such nodes approximating the geometry of the
thousands of such nodes approximating the geometry of the
structure. These nodes then form the basis of thousands of
structure. These nodes then form the basis of thousands of
equations which must be solved simultaneously.
equations which must be solved simultaneously.
10. 05/04/25
05/04/25 10
10
Background
Background
Finite Element Theory – Element Types
Finite Element Theory – Element Types
Commercial FEA codes contain many types of finite elements.
Commercial FEA codes contain many types of finite elements.
We will only discuss only three such finite elements in this
We will only discuss only three such finite elements in this
tutorial: one dimensional (1-D); two dimensional (2-D); and three
tutorial: one dimensional (1-D); two dimensional (2-D); and three
dimensional (3-D) finite elements .
dimensional (3-D) finite elements .
One-dimensional elements
One-dimensional elements
The bar elements is a 1-D element which does not sustain
The bar elements is a 1-D element which does not sustain
bending, but can sustain axial loads. Rigid bars and trusses are
bending, but can sustain axial loads. Rigid bars and trusses are
examples of these type of 1-D elements. Another type of 1-D
examples of these type of 1-D elements. Another type of 1-D
elements called a beam element which can sustain bending as
elements called a beam element which can sustain bending as
well as axial loads which makes these elements more useful to
well as axial loads which makes these elements more useful to
users.
users.
Two-dimensional elements
Two-dimensional elements
Two dimensional (2-D) elements include plate and shell
Two dimensional (2-D) elements include plate and shell
elements which are usually triangular or quadrilateral in
elements which are usually triangular or quadrilateral in
appearance. These 2-D elements are usually thin and can be
appearance. These 2-D elements are usually thin and can be
used to model very curved objects.
used to model very curved objects.
11. 05/04/25
05/04/25 11
11
Background
Background
Finite Element Theory – Element Types
Finite Element Theory – Element Types
Three-dimensional
Three-dimensional
These type of elements are used for modeling 3-D geometry
These type of elements are used for modeling 3-D geometry
and are the most widely used element types. Tetrahedral and
and are the most widely used element types. Tetrahedral and
brick elements are typically used to model solid geometric
brick elements are typically used to model solid geometric
shapes. The Tetrahedrons are usually more flexible than the
shapes. The Tetrahedrons are usually more flexible than the
brick elements in modeling very complex geometric shapes.
brick elements in modeling very complex geometric shapes.
12. 05/04/25
05/04/25 12
12
Problem-Solving Steps
Problem-Solving Steps
1) Use SolidWorks to create a 3-D model of the bar.
1) Use SolidWorks to create a 3-D model of the bar.
2) Submit the model to COSMOSWorks.
2) Submit the model to COSMOSWorks.
3) Define the material properties for the model.
3) Define the material properties for the model.
4) Define the thermal boundary conditions for the
4) Define the thermal boundary conditions for the
model.
model.
5) Mesh the model using 2
5) Mesh the model using 2nd
nd
order tetrahedral solid
order tetrahedral solid
elements.
elements.
6) Run the FEA.
6) Run the FEA.
7) Examine the results to find the necessary
7) Examine the results to find the necessary
information.
information.
14. 05/04/25
05/04/25 14
14
Left /Right Side of SolidWorks Window
Left /Right Side of SolidWorks Window
SolidWorks Feature
SolidWorks Feature
Manager icon
Manager icon
SolidWorks Manager
SolidWorks Manager
Design tree
Design tree
COSMOSWorks icon
COSMOSWorks icon
COSMOSWorks
COSMOSWorks
Manager tree
Manager tree
15. 05/04/25
05/04/25 15
15
Creating SolidWorks Model
Creating SolidWorks Model
1. Create a new part.
1. Create a new part.
Click on the
Click on the
Standard toolbar.
Standard toolbar.
2. Select the
2. Select the Part
Part icon
icon
3. Click
3. Click OK
OK
16. 05/04/25
05/04/25 16
16
Creating SolidWorks Model
Creating SolidWorks Model
Open a Sketch
Open a Sketch
Open a 2-D sketch. Click on the toolbar.
Open a 2-D sketch. Click on the toolbar.
Click on the Front Plane to view the 2-D sketch from
Click on the Front Plane to view the 2-D sketch from
the front.
the front.
Sketch a rectangle. Click on the toolbar.
Sketch a rectangle. Click on the toolbar.
Click on the origin to start the rectangle and drag up
Click on the origin to start the rectangle and drag up
and to the right to create the rectangle. (Don’t worry
and to the right to create the rectangle. (Don’t worry
about dimensions; these can be added later.)
about dimensions; these can be added later.)
17. 05/04/25
05/04/25 17
17
Creating a SolidWorks Model of the
Creating a SolidWorks Model of the
Plate
Plate
Create a Base Feature of the
Create a Base Feature of the
Plate by using the Boss
Plate by using the Boss
Extrusion Icon
Extrusion Icon
1. First
1. First Left-mouse-click
Left-mouse-click on the
on the
Boss Extrusion Icon
Boss Extrusion Icon, a
, a
window with three mutually
window with three mutually
orthogonal Planes will appear.
orthogonal Planes will appear.
2.
2.Left-mouse-click
Left-mouse-click on the
on the
Front Plane
Front Plane shown in the
shown in the
graphics window
graphics window
18. 05/04/25
05/04/25 18
18
Setting Up the Drawing Units to
Setting Up the Drawing Units to
Millimeters in SolidWorks
Millimeters in SolidWorks
Setting Up the Drawing
Setting Up the Drawing
Units
Units
1.
1. Left-mouse-click
Left-mouse-click the
the Tools
Tools
menu and select Options
menu and select Options
2. When the
2. When the Systems
Systems
Options
Options window appears
window appears
select the
select the Document
Document
Properties
Properties indentation.
indentation.
19. 05/04/25
05/04/25 19
19
Setting Up the Drawing Units to Meters
Setting Up the Drawing Units to Meters
in SolidWorks
in SolidWorks
3. When the
3. When the Document
Document
Properties
Properties window appears
window appears
select
select units
units and
and left-mouse-
left-mouse-
click
click on it.
on it.
4. When the
4. When the units
units window
window
appears
appears select
select meters
meters in both
in both
places and click OK to close.
places and click OK to close.
20. 05/04/25
05/04/25 20
20
Creating a SolidWorks Model of the
Creating a SolidWorks Model of the
Plate
Plate
1.
1. Left-mouse-click
Left-mouse-click on the
on the
Rectangle Icon
Rectangle Icon and
and sketch
sketch
a rectangle
a rectangle in the center of the
in the center of the
graphics window
graphics window
2.Dimension this rectangle by
2.Dimension this rectangle by
left-mouse-clicking
left-mouse-clicking on the
on the
Smart Dimension Icon
Smart Dimension Icon and
and
clicking on the vertical and
clicking on the vertical and
horizontal lines of the
horizontal lines of the
rectangle.
rectangle.
3. To dimension
3. To dimension double click
double click
the line and give the rectangle
the line and give the rectangle
a
a width of 0.4meters
width of 0.4meters by a
by a
height of 0.6 meters
height of 0.6 meters
21. 05/04/25
05/04/25 21
21
Creating a SolidWorks Model of the
Creating a SolidWorks Model of the
Plate
Plate
4. Once both sides of the
4. Once both sides of the
rectangle are dimensioned,
rectangle are dimensioned,
click OK ,then left-mouse-click
click OK ,then left-mouse-click
on the
on the confirmation
confirmation
corner
corner to extrude the plate.
to extrude the plate.
5. Now extrude the plate as
5. Now extrude the plate as
Blind
Blind extrusion to a depth of
extrusion to a depth of
0.1 meters
0.1 meters and click
and click OK.
OK.
22. 05/04/25
05/04/25 22
22
Creating a SolidWorks Model of the
Creating a SolidWorks Model of the
Plate
Plate
6. Extrude the plate to a
6. Extrude the plate to a
depth of 0.1 meters and it
depth of 0.1 meters and it
should look similar to this
should look similar to this
model.
model.
23. 05/04/25
05/04/25 23
23
Verifying Dimensions
Verifying Dimensions
To verify the dimensions,
To verify the dimensions,
right-click on
right-click on Annotations
Annotations
under the Feature Manager
under the Feature Manager
and check both
and check both Display
Display
Annotations
Annotations and
and Show
Show
Feature Dimensions
Feature Dimensions.
.
To correct any errors,
To correct any errors,
simply double-click on the
simply double-click on the
erroneous dimension and
erroneous dimension and
reenter.
reenter.
Click on the Rebuild icon
Click on the Rebuild icon
to redraw the model.
to redraw the model.
Save the drawing by
Save the drawing by
clicking
clicking Save As…
Save As… under
under
the
the File
File menu.
menu.
24. 05/04/25
05/04/25 24
24
Verify that COSMOSWorks is loaded
Verify that COSMOSWorks is loaded
into your Computer
into your Computer
1. Left Click the
1. Left Click the Tools
Tools item in the
item in the
menu and select
menu and select Add-Ins
Add-Ins.
.
2. The
2. The Add-Ins
Add-Ins box should
box should
appear; verify that the
appear; verify that the
COSMOSWorks 2007
COSMOSWorks 2007 box is
box is
check
check.
.
25. 05/04/25
05/04/25 25
25
Opening the Plate Model in
Opening the Plate Model in
COSMOSWorks
COSMOSWorks
1.
1.Left-mouse-click
Left-mouse-click the
the
COSMOSWorks Manager
COSMOSWorks Manager
tab
tab
Right-mouse-click
Right-mouse-click the
the
SolidWorks Model Icon
SolidWorks Model Icon
that you just created in the
that you just created in the
SolidWorks Manager
SolidWorks Manager and
and
select
select Study.
Study.
26. 05/04/25
05/04/25 26
26
Creating a Study in
Creating a Study in
COSMOSWorks
COSMOSWorks
• In the
In the Study
Study dialog box
dialog box
type in the name for this
type in the name for this
thermal study:
thermal study: Long Bar
Long Bar
• Select
Select Solid Mesh
Solid Mesh
• Under
Under Type
Type of Study
of Study
select
select Thermal
Thermal
• Close by
Close by clicking
clicking OK.
OK.
• Notice that
Notice that
COSMOSWorks
COSMOSWorks
creates the study in
creates the study in
the COSMOSWorks
the COSMOSWorks
Manager.
Manager.
27. 05/04/25
05/04/25 27
27
Assigning Material Properties to the
Assigning Material Properties to the
Plate Model
Plate Model
In the COSMOSWorks
In the COSMOSWorks
Manager, right-click the
Manager, right-click the
Solids
Solids icon and click
icon and click Apply
Apply
Material to All…
Material to All…
The material dialog box
The material dialog box
appears.
appears.
Under
Under Select material
Select material
source
source,
, left-mouse-click
left-mouse-click
from
from Library Files
Library Files and
and
select from other metals
select from other metals
Zirconium
Zirconium
Also, verify that Linear
Also, verify that Linear
Elastic Isotropic is selected
Elastic Isotropic is selected
under the Material model
under the Material model
tab and click OK.
tab and click OK.
COSMOSWorks assigns the
COSMOSWorks assigns the
material property to the
material property to the
model. Notice that a check
model. Notice that a check
mark now appears over the
mark now appears over the
icon in the COSMOSWorks
icon in the COSMOSWorks
Manager.
Manager.
28. 05/04/25
05/04/25 28
28
Applying Boundary Conditions to
Applying Boundary Conditions to
the Plate Model
the Plate Model
In the COSMOSWorks
In the COSMOSWorks
Manager, right-click
Manager, right-click
Load/Restraint
Load/Restraint and
and
click
click Convection
Convection.
.
The CONVECTION
The CONVECTION
Property Manager
Property Manager
appears.
appears.
29. 05/04/25
05/04/25 29
29
Applying Convection B.C.
Applying Convection B.C.
In the graphics area, click
In the graphics area, click
the right vertical face that
the right vertical face that
is exposed to convection.
is exposed to convection.
This is Face<1> and it
This is Face<1> and it
appears in the
appears in the Selected
Selected
entities
entities box.
box.
Under
Under Convection
Convection
Parameters
Parameters, enter the
, enter the
values for
values for h
h and
and T
T∞
∞ in SI
in SI
units and click or press
units and click or press
Enter
Enter.
.
30. 05/04/25
05/04/25 30
30
Applying Convection B.C.
Applying Convection B.C.
COSMOSWorks applies
COSMOSWorks applies
convection to the selected
convection to the selected
face and creates a
face and creates a
Convection icon
Convection icon in the
in the
Load/Restraint folder.
Load/Restraint folder.
Convection symbols
Convection symbols
appear on the selected
appear on the selected
surface.
surface.
31. 05/04/25
05/04/25 31
31
Applying Specified Temperature B.C.
Applying Specified Temperature B.C.
In the COSMOSWorks
In the COSMOSWorks
Manager, right-click
Manager, right-click
Load/Restraint
Load/Restraint and click on
and click on
Temperature
Temperature. The
. The
TEMPERATURE Property
TEMPERATURE Property
Manager appears.
Manager appears.
Click on the top and bottom
Click on the top and bottom
surfaces in the graphics area;
surfaces in the graphics area;
they appear as Face<1> and
they appear as Face<1> and
Face<2> in the
Face<2> in the Selected
Selected
entities
entities box. (You may have
box. (You may have
to use the
to use the Rotate View
Rotate View tool
tool
to select a particular surface.)
to select a particular surface.)
Enter the surface temperature
Enter the surface temperature
under
under Temperature
Temperature in SI
in SI
units and click or press
units and click or press
Enter
Enter.
.
COSMOSWorks applies a
COSMOSWorks applies a
specified temperature to both
specified temperature to both
faces and creates a
faces and creates a
Temperature icon
Temperature icon in the
in the
Load/Restraint folder.
Load/Restraint folder.
32. 05/04/25
05/04/25 32
32
Applying Adiabatic B.C.
Applying Adiabatic B.C.
In the COSMOSWorks
In the COSMOSWorks
Manager,
Manager, Right-mouse-
Right-mouse-
click
click Load/Restraint
Load/Restraint and
and
click on
click on Heat Flux
Heat Flux. The
. The
HEAT FLUX Property
HEAT FLUX Property
Manager
Manager appears.
appears.
Left-mouse-click
Left-mouse-click on the
on the
left vertical surface that is
left vertical surface that is
adiabatic; this appears as
adiabatic; this appears as
Face<1>
Face<1> in the
in the Selected
Selected
entities
entities box.
box.
Enter 0 for the
Enter 0 for the Heat Flux
Heat Flux
and click or press
and click or press
Enter
Enter.
.
COSMOSWorks applies a
COSMOSWorks applies a
zero heat flux to the
zero heat flux to the
surface and creates a
surface and creates a Heat
Heat
Flux icon
Flux icon in the
in the
Load/Restraint folder.
Load/Restraint folder.
33. 05/04/25
05/04/25 33
33
Creating the Mesh
Creating the Mesh
In the COSMOSWorks Manager
In the COSMOSWorks Manager,
,
Right-mouse-click
Right-mouse-click the
the Mesh Icon
Mesh Icon and
and
select
select Create Mesh
Create Mesh
The Mesh Property Manager appears
The Mesh Property Manager appears
Select
Select Options
Options
The
The Options
Options dialog box appears with
dialog box appears with
Mesh tab active
Mesh tab active.
.
In the Options Manager
In the Options Manager select the
select the
following:
following:
Quality -
Quality -High
High
Controls Automatic Transition-
Controls Automatic Transition-
Unchecked
Unchecked
Controls Smooth Surface
Controls Smooth Surface
Checked
Checked
Automatic Looping
Automatic Looping
Unchecked
Unchecked
Jacobian Check -
Jacobian Check - 4 points
4 points
Mesh to use -
Mesh to use - Standard
Standard
Finally to mesh the model and run the
Finally to mesh the model and run the
FEA analysis
FEA analysis select
select the
the Run
Run button
button click
click
OK
OK
34. 05/04/25
05/04/25 34
34
Running the Study
Running the Study
Click
Click Run analysis after
Run analysis after
meshing
meshing and accept the
and accept the
default mesh size.
default mesh size.
Finally, click or press
Finally, click or press
Enter
Enter to mesh the model
to mesh the model
and run the finite element
and run the finite element
analysis.
analysis.
35. 05/04/25
05/04/25 35
35
Hiding Boundary Conditions and
Hiding Boundary Conditions and
Viewing Temperature Plot
Viewing Temperature Plot
In the COSMOSWorks
In the COSMOSWorks
Manager,
Manager, right-mouse-
right-mouse-
click
click on
on Load/Restraint
Load/Restraint
and click to
and click to Hide All
Hide All to
to
remove the boundary
remove the boundary
condition icons in the
condition icons in the
graphics window.
graphics window.
In the COSMOSWorks
In the COSMOSWorks
Manager, click the plus
Manager, click the plus
sign beside the
sign beside the
Thermal
Thermal folder.
folder.
Double-click
Double-click Thermal 1
Thermal 1 to
to
view the temperature
view the temperature
distribution throughout the
distribution throughout the
model.
model.
The color temperature plot
The color temperature plot
is displayed. As expected,
is displayed. As expected,
the top and bottom of the
the top and bottom of the
plate are the hottest and
plate are the hottest and
the front center where it is
the front center where it is
being cooled by convection
being cooled by convection
is the coolest.
is the coolest.
36. 05/04/25
05/04/25 36
36
Post-Processing Temperature Results
Post-Processing Temperature Results
The
The Probe
Probe tool on the
tool on the
toolbar can be used to list
toolbar can be used to list
the temperature at
the temperature at
specific locations.
specific locations.
This is easiest if the
This is easiest if the
model is turned
model is turned
perpendicular to the
perpendicular to the
screen by using the
screen by using the
Standard Views icon.
Standard Views icon.
Click
Click Probe
Probe on the
on the
toolbar. The Probe list
toolbar. The Probe list
box appears.
box appears.
37. 05/04/25
05/04/25 37
37
Post-Processing Temperature Results
Post-Processing Temperature Results
Click four to six points
Click four to six points
along the
along the mid-plane
mid-plane of
of
the plate. As you click the
the plate. As you click the
points the
points the Probe
Probe list box
list box
lists the temperature and
lists the temperature and
the X, Y, and Z coordinates
the X, Y, and Z coordinates
of the selected point.
of the selected point.
Click
Click Plot Icon
Plot Icon.
.
A
A Probe Result
Probe Result window
window
appears with a graph of
appears with a graph of
temperatures at the
temperatures at the
selected points versus
selected points versus
node numbers.
node numbers.
38. 05/04/25
05/04/25 38
38
Viewing the Actual Finite Element Mesh
Viewing the Actual Finite Element Mesh
and Details of the Analysis
and Details of the Analysis
1.In the COSMOSWorks
1.In the COSMOSWorks
Manager, right-mouse-click
Manager, right-mouse-click
on
on Mesh
Mesh and select
and select Show
Show
Mesh
Mesh.
.
Notice that all the
Notice that all the
elements are tetrahedral
elements are tetrahedral
solid mesh elements.
solid mesh elements.
2.To view the
2.To view the number of
number of
finite elements and nodes
finite elements and nodes
used in this steady state
used in this steady state
thermal analysis,
thermal analysis, Right-
Right-
mouse-click
mouse-click on the
on the Mesh
Mesh
Icon
Icon and select
and select Details….
Details….
39. 05/04/25
05/04/25 39
39
Discussion and Conclusions
Discussion and Conclusions
The temperature difference between the hand
The temperature difference between the hand
calculations and the COSMOS solution was less
calculations and the COSMOS solution was less
than 1% in most instances, but can be explained
than 1% in most instances, but can be explained
by the difference in mesh sizes for the two
by the difference in mesh sizes for the two
numerical methods. The finite difference hand
numerical methods. The finite difference hand
calculations used 13 nodes with 12 elements,
calculations used 13 nodes with 12 elements,
versus the COSMOSWorks finite element
versus the COSMOSWorks finite element
analysis that used 10,505 nodes with 6,684
analysis that used 10,505 nodes with 6,684
elements. These nodal differences in
elements. These nodal differences in
temperatures will disappear altogether as the
temperatures will disappear altogether as the
number of nodes becomes the same for both
number of nodes becomes the same for both
numerical methods.
numerical methods.
41. 05/04/25
05/04/25 41
41
Finite Element Theory
Finite Element Theory
The discretization process, better known as meshing,
The discretization process, better known as meshing,
splits the continuous 3-D computer aided drawn models
splits the continuous 3-D computer aided drawn models
into finite elements with nodes. The type of elements
into finite elements with nodes. The type of elements
created in this process depends on the type of geometry
created in this process depends on the type of geometry
meshed, and the accuracy of the analysis that needs to
meshed, and the accuracy of the analysis that needs to
be executed. Most commercial FEA software codes have
be executed. Most commercial FEA software codes have
multiple types of finite elements. We will define only three
multiple types of finite elements. We will define only three
types of elements in this tutorial: one-dimensional
types of elements in this tutorial: one-dimensional
elements or line elements, two-dimensional elements or
elements or line elements, two-dimensional elements or
shell elements and three-dimensional elements or solid
shell elements and three-dimensional elements or solid
tetrahedral elements. COSMOSWorks Professional
tetrahedral elements. COSMOSWorks Professional
Educational Edition 2007-2008 offers three types of
Educational Edition 2007-2008 offers three types of
elements: three-dimensional tetrahedral solid elements,
elements: three-dimensional tetrahedral solid elements,
for meshing solid geometry, two-dimensional triangular
for meshing solid geometry, two-dimensional triangular
shell elements, for meshing very curved surface
shell elements, for meshing very curved surface
geometry and one dimensional beam elements for
geometry and one dimensional beam elements for
meshing frame structures. These three types of finite
meshing frame structures. These three types of finite
elements will solve most typical engineering problems.
elements will solve most typical engineering problems.
42. 05/04/25
05/04/25 42
42
Finite Element Theory
Finite Element Theory
The beginning point for COSMOSWorks is a 3-D geometric
The beginning point for COSMOSWorks is a 3-D geometric
model of the problem, a part or assembly, representing the
model of the problem, a part or assembly, representing the
object that needs to be analyzed. We then assign material
object that needs to be analyzed. We then assign material
properties and define structural or thermal boundary
properties and define structural or thermal boundary
conditions for the model. For structural analysis the model
conditions for the model. For structural analysis the model
must be constrained to generate stresses, without proper
must be constrained to generate stresses, without proper
constraints the model would have free body motion in space
constraints the model would have free body motion in space
whereby no loads or stresses are developed. We next split
whereby no loads or stresses are developed. We next split
the geometry into relatively small and simple shaped entities
the geometry into relatively small and simple shaped entities
called finite elements. Creating finite elements is commonly
called finite elements. Creating finite elements is commonly
called meshing. The smaller the mesh size the more
called meshing. The smaller the mesh size the more
accurate the finite element analysis, but at a cost of more
accurate the finite element analysis, but at a cost of more
computer time to solve the additional equations generated.
computer time to solve the additional equations generated.
The COSMOSWorks mathematical solver approximates a
The COSMOSWorks mathematical solver approximates a
solution to the constitutive partial differential (PD) equations
solution to the constitutive partial differential (PD) equations
of the meshed model. COSMOSWorks has three high speed
of the meshed model. COSMOSWorks has three high speed
math solvers; one using a direct-method of solution to the
math solvers; one using a direct-method of solution to the
PD equations and two using a iterative method of solution
PD equations and two using a iterative method of solution
to the PD equations.
to the PD equations.
43. 05/04/25
05/04/25 43
43
Finite Element Theory
Finite Element Theory
The tetrahedral solid elements can be either first order (draft
The tetrahedral solid elements can be either first order (draft
quality) or second order elements (high quality). The user
quality) or second order elements (high quality). The user
decides whether to use draft quality or high quality elements
decides whether to use draft quality or high quality elements
for meshing the 3D geometric model. However only high
for meshing the 3D geometric model. However only high
quality elements are used in analysis of importance. First order
quality elements are used in analysis of importance. First order
tetrahedral elements have four nodes, straight edges and flat
tetrahedral elements have four nodes, straight edges and flat
faces. Second order tetrahedral elements have ten nodes,
faces. Second order tetrahedral elements have ten nodes,
curved surfaces, and are more accurate in modeling complex
curved surfaces, and are more accurate in modeling complex
problems. The second order elements are the elements of
problems. The second order elements are the elements of
choice for accurate results.
choice for accurate results.
The use of the elements with the higher number of nodes has
The use of the elements with the higher number of nodes has
improved accuracy with but with additional computational time
improved accuracy with but with additional computational time
over the elements with less nodes. Each tetrahedral element
over the elements with less nodes. Each tetrahedral element
with either 4 or 10 nodes per element has three degrees of
with either 4 or 10 nodes per element has three degrees of
freedom (DOF) for each node. The degrees of freedom of a
freedom (DOF) for each node. The degrees of freedom of a
node in a finite element mesh define the ability of the node to
node in a finite element mesh define the ability of the node to
perform translation or rotation. The number of DOF that a node
perform translation or rotation. The number of DOF that a node
posses depends on the type element that the element belongs
posses depends on the type element that the element belongs
to.
to.
44. 05/04/25
05/04/25 44
44
Finite Element Theory
Finite Element Theory
Nodes of solid elements have three degrees of freedom
Nodes of solid elements have three degrees of freedom
(DOF) while nodes of shell elements have six degrees of
(DOF) while nodes of shell elements have six degrees of
freedom. This means that in order to describe transformation
freedom. This means that in order to describe transformation
of a solid element from the original to the deformed shape, we
of a solid element from the original to the deformed shape, we
need to know three translational components of nodal
need to know three translational components of nodal
displacement usually x, y and z. In the case of a shell element
displacement usually x, y and z. In the case of a shell element
we need to know six DOF or three translations and three
we need to know six DOF or three translations and three
rotations for each node.
rotations for each node.
Each degree of freedom (DOF) of each node in a finite
Each degree of freedom (DOF) of each node in a finite
element mesh constitutes an unknown. For structural analysis
element mesh constitutes an unknown. For structural analysis
a partial differential equation defining the physics of the
a partial differential equation defining the physics of the
problem is solved for displacements at specific locations on
problem is solved for displacements at specific locations on
each finite element and extrapolated to each node. Once the
each finite element and extrapolated to each node. Once the
displacements are calculated the strains and stresses can be
displacements are calculated the strains and stresses can be
calculated for the model.
calculated for the model.
45. 05/04/25
05/04/25 45
45
Finite Element Theory
Finite Element Theory
Contrary to the first order solid and shell elements, two-node beam
Contrary to the first order solid and shell elements, two-node beam
elements model the two out-out-plane deflections as cubic functions
elements model the two out-out-plane deflections as cubic functions
and the axial translations and torsional rotations as linear. The
and the axial translations and torsional rotations as linear. The
shape of the two-node beam element is initially straight, but it can
shape of the two-node beam element is initially straight, but it can
assume the shape of a cubic function after deformation takes place.
assume the shape of a cubic function after deformation takes place.
Each two-node beam element features six degrees of freedom
Each two-node beam element features six degrees of freedom
(DOF) at each end node: three translations and three rotations. The
(DOF) at each end node: three translations and three rotations. The
same mapping considerations that apply to the first order solid and
same mapping considerations that apply to the first order solid and
shell elements apply to the two-node beam element as well.
shell elements apply to the two-node beam element as well.
Beam elements represent structural elements where all of the cross-
Beam elements represent structural elements where all of the cross-
sectional characteristics are accounted for during the derivation of
sectional characteristics are accounted for during the derivation of
the element stiffness matrix. As a beneficial consequence, the
the element stiffness matrix. As a beneficial consequence, the
cross-sectional characteristics do not need to be reflected in the
cross-sectional characteristics do not need to be reflected in the
finite element mesh, thus greatly simplifying the model preparation
finite element mesh, thus greatly simplifying the model preparation
and analysis.
and analysis.
46. 05/04/25
05/04/25 46
46
Finite Element Theory
Finite Element Theory
In thermal analysis, the primary unknowns are nodal
In thermal analysis, the primary unknowns are nodal
temperatures of the mesh nodes. Temperatures and heat flow
temperatures of the mesh nodes. Temperatures and heat flow
are determined from the solution to the partial differential
are determined from the solution to the partial differential
equations representing conduction or convection in the model.
equations representing conduction or convection in the model.
Since temperature is a scalar displacement, and not a vector-
Since temperature is a scalar displacement, and not a vector-
like displacement, then regardless of what type of elements
like displacement, then regardless of what type of elements
used, there is only one unknown temperature to be found for
used, there is only one unknown temperature to be found for
each node. The fact that there is only one unknown to be found
each node. The fact that there is only one unknown to be found
for each node, rather than three or six, makes thermal analysis
for each node, rather than three or six, makes thermal analysis
less computationally intensive than structural analysis.
less computationally intensive than structural analysis.
Errors in FEA.
Errors in FEA. The process of creating a mathematical model
The process of creating a mathematical model
and discretizing it into a finite element model introduces
and discretizing it into a finite element model introduces
unavoidable errors. FEA errors can be categorized into three
unavoidable errors. FEA errors can be categorized into three
areas: 1. mathematical modeling errors, 2. discretization errors
areas: 1. mathematical modeling errors, 2. discretization errors
during meshing, and 3. solution errors which are round-off
during meshing, and 3. solution errors which are round-off
errors accumulated by the solver. In most instances these
errors accumulated by the solver. In most instances these
errors are usually very low (3% or less) when compared with
errors are usually very low (3% or less) when compared with
classical closed-form Partial Differential Equation solutions
classical closed-form Partial Differential Equation solutions.
.
47. 05/04/25
05/04/25 47
47
FEA Analogy: Area
FEA Analogy: Area
What do we do to improve the accuracy of the area
What do we do to improve the accuracy of the area
measurement? CREATE A FINER MESH!
measurement? CREATE A FINER MESH!
48. 05/04/25
05/04/25 48
48
FEA Mesh: Elements
FEA Mesh: Elements
Each element is a simple solid.
Each element is a simple solid.
Elements are connected together at locations called
Elements are connected together at locations called
NODES.
NODES.
49. 05/04/25
05/04/25 51
51
Moderate Mesh:
7009 nodes
Sol. Time: 5 sec.
Max. Stress: 27.8 ksi
Coarse Mesh:
1773 nodes
Sol. Time: 2 sec.
Max. Stress: 25.8 ksi
Fine Mesh:
16,107 nodes
Sol. Time: 10 sec.
Max. Stress: 27.6 ksi
Mesh Accuracy : Mesh Size or
Mesh Accuracy : Mesh Size or
Mesh Nodes
Mesh Nodes
50. 05/04/25
05/04/25 52
52
Finite Element Theory
Finite Element Theory
Limitations of COSMOSWorks linear FEA analysis .
Limitations of COSMOSWorks linear FEA analysis . We need to
We need to
appreciate some important limitations of the linear FEA software:
appreciate some important limitations of the linear FEA software:
material is assumed as linear, deformations are small, and loads are
material is assumed as linear, deformations are small, and loads are
static. Material we assign to be analyzed will be assumed to be
static. Material we assign to be analyzed will be assumed to be
linear or that the stress is proportional to strain in linear manner.
linear or that the stress is proportional to strain in linear manner.
There is a COSMOSWorks non-linear FEA software available for
There is a COSMOSWorks non-linear FEA software available for
the solution of unique non-linear problems.
the solution of unique non-linear problems.
In “real-life” there is a yield or ultimate stress that the material
In “real-life” there is a yield or ultimate stress that the material
cannot exceed without rupturing. A linear model omits these “real-
cannot exceed without rupturing. A linear model omits these “real-
life” end conditions. We therefore must review the level of stresses
life” end conditions. We therefore must review the level of stresses
very carefully in our linear FEA results. The fact that we assume
very carefully in our linear FEA results. The fact that we assume
small deformations requires that those deformations be “small” in
small deformations requires that those deformations be “small” in
relation to the size (3% or less) of the structure and that the
relation to the size (3% or less) of the structure and that the
“structural-stiffness” matrix remains relatively the same during the
“structural-stiffness” matrix remains relatively the same during the
deformation process. All loads, as well as restraints, are assumed
deformation process. All loads, as well as restraints, are assumed
not to change with time, meaning that dynamic loading conditions
not to change with time, meaning that dynamic loading conditions
are not being analyzed with COSMOSWorks linear FEA analysis.
are not being analyzed with COSMOSWorks linear FEA analysis.
This time limitation implies that loads are applied slowly enough to
This time limitation implies that loads are applied slowly enough to
ignore inertial effects.
ignore inertial effects.
51. 05/04/25
05/04/25 53
53
Finite Element Textbooks
Finite Element Textbooks
Reference List of Texts
Reference List of Texts
Sprakos, C., Finite Element Modeling, Algor, Inc.,1996.
Sprakos, C., Finite Element Modeling, Algor, Inc.,1996.
Moaveni, S., Finite Element Analysis Theory and
Moaveni, S., Finite Element Analysis Theory and
Application with ANSYS, Prentice Hall,1999.
Application with ANSYS, Prentice Hall,1999.
Chandrupatla, T., Belegundu, A., Introduction to Finite
Chandrupatla, T., Belegundu, A., Introduction to Finite
Elements, Prentice Hall, 2001.
Elements, Prentice Hall, 2001.
Hutton, D., Fundamentals of Finite Element Analysis,
Hutton, D., Fundamentals of Finite Element Analysis,
McGraw Hill, 2004.
McGraw Hill, 2004.
Engineering Analysis with COSMOSWorks Professional
Engineering Analysis with COSMOSWorks Professional
2007, by Paul M. Kurowski, Schroff Development
2007, by Paul M. Kurowski, Schroff Development
Corporation, 2007.
Corporation, 2007.
COSMOSWorks Designer 2007 , Structural Research
COSMOSWorks Designer 2007 , Structural Research
Corporation, 2007.
Corporation, 2007.
52. 05/04/25
05/04/25 54
54
Acknowledgement
Acknowledgement
This work is partially
This work is partially
supported by the National
supported by the National
Science Foundation grant
Science Foundation grant
Division of
Division of
Undergraduate Education
Undergraduate Education
Course Curriculum and
Course Curriculum and
Laboratory Improvement
Laboratory Improvement
(CCLI) Award Number
(CCLI) Award Number
0536197
0536197
