A Fast Modal (Eigenvalue) Solver Based on Subspace
and AMG
Sam Murgie
–
Autodesk Inc.
James Herzing
–
Autodesk Inc.
SM1726
–
A Fast Modal (Eigenvalue) Solver Based on Subspace and
AMG
Learning Objectives
At the end of this class, you will be able to:
Understand the theory behind the latest performance improvements to Autodesk Simulation’s linear
dynamics solvers
Decide when to use linear dynamics as opposed to more computationally i
ntensive options
Set up of the base modal analysis
Set up and solve a dynamics response analysis
Set up and solve a random vibration analysis
Set up and solve a buckling analysis
About the Speaker
s
Sam Murgie:
Research Manager at Autodesk, Inc.
in
the Design, Lifecycle and Simulation Group

Managing Simulation (structural and CFD) Solver Team
o
Cloud computing and HPC
o
Finite Element Analysis (FEA) domain expert
o
Software development of engineering features and FEA solvers
o
Research potential new
engineering applications

Member of Simulation Core Team
o
Planning and delivery of Simulation products
o
Help define Simulation products of the future

Over 30 years of Simulation Management experience, specializing in simulation solvers and high
performance co
mputing (HPC)
James Herzing
A Fast
Modal (Eigenvalue) Solver Based on Subspace and AMG
2
James Herzing has been using the Autodesk Simulation software for nearly 9 years, working in various
positions that deal with customer issues, and trying to ensure their success. Currently, he works as part
of the Industry Str
ategy and Marketing division as a member of the Go

to

Market team. He graduated
from the Pennsylvania State University in 2004 with a BS in Mechanical Engineering and a minor in
Engineering Mechanics.
He has presented in 9 Autodesk University classes, an
d is hosting or assisting
in 5 at this year’s Autodesk University.
For any questions, feel free to reach us at:
Sam.Murgie@autodesk.com
James.Herzing@autode
sk.com
Modal analysis of a bridge
Opening the CAD geometry
This exercise uses a DWG
file to demonstrate Autodesk Simulation’s ability to work with
wireframe models, using beam elements instead of solid elements as with a CAD solid
model. AutoCAD layers and blocks are recognized as different parts in Autodesk
Simulation, allowing the user
to prepare the model for simulation such that the title block
and dimensions are on layers other than that actual geometry.
1.
Launch
Autodesk Simulation
Mechanical
.
2.
Click the
Open
button on ribbon bar and navigate to the location where you have
saved your
demonstration files
.
3.
Click on the
Files of type
drop down and choose the
AutoCAD DWG
option. The
model name will be
SHB_ACAD
.dwg
.
A Fast
Modal (Eigenvalue) Solver Based on Subspace and AMG
3
4.
Click
Open
to load the model into Autodesk Simulation.
5.
Change the unit system to
Metric mks (SI).
6.
Change the unit system to
Custom
.
7.
Change Length from
m
to
mm
and click
OK
.
A Fast
Modal (Eigenvalue) Solver Based on Subspace and AMG
4
8.
Define the analysis type as
Natural Frequency (Modal)
.
Model setup
Object Definition
1.
From the
View
tab of the ribbon, click the
Construction Vertices
button to hide
the blue points throughout the model.
2.
Click the + next to
1 <3

D Objects>
under Part 1.
3.
Select all of the lines under the drop down menu.
4.
Right click and choose
Edit Attributes
.
5.
Uncheck the box next to
Construction object
.
6.
Repeat for
2 <
3

D Objects>
,
3 <3

D Objects>
, and
4 <3

D Objects>
.
Defining
Element Information and
Materials
1.
Holding the
Ctrl
key on the keyboard, select the
Element Type
heading for
Parts
1, 2, 3, and 4,
and right click to define them as
Beam
.
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Modal (Eigenvalue) Solver Based on Subspace and AMG
5
2.
Select
the
Element
D
efinition
heading for
Parts
1
and right click to
Edit
the
Element Definition.
3.
With the Element Definition screen open, click on one of the
Sectional
Properties
and choose the
Cross

Section Libraries
button.
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Modal (Eigenvalue) Solver Based on Subspace and AMG
6
4.
Click on the drop down on the right of the menu that reads User

Defined.
Choose
Hollow Rectangular
as the cross

section type.
5.
Enter the values
b1 = 500, h1 = 500, b2 = 400, and h2 = 400 mm
. Click
OK
twice.
6.
Repeat defining the Element Definition for Pa
rt 2 and 3.
7.
For the cross

section of
Part 2
, choose
Wide Flange Beam
. Enter values
H =
2900, B = 3000, Tw = 100, and Tf = 100 mm.
A Fast
Modal (Eigenvalue) Solver Based on Subspace and AMG
7
8.
For the cross

section of
Part 3
, choose
Round
. Enter a
Radius of 125 mm
.
9.
Right click on
Part 1
and select
Copy: Element Data
.
10.
Right click on
Part 4
and choose
Paste: Element Data
.
11.
Select
Material
for
Part 1
. Hold down
Ctrl
and select the Material for
Part 2, 3,
and 4
.
12.
Right click and choose
Edit Material
.
13.
Click
+
next to Steel, and
+
next to AISI. Select
AISI 1005 Steel
. Click
OK
.
Defining Boundary Conditions
1.
From the
Selection
tab of the ribbon, click the
Vertices
button.
2.
From the
Selection
tab of the ribbon, click the
Rectangle
button.
3.
Holding Ctrl, select the nodes on each end of the model at the ends of the bridge
.
4.
Right click and select
Add: Nodal Boundary Conditions
.
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Modal (Eigenvalue) Solver Based on Subspace and AMG
8
5.
From the
Boundary Condition
menu click the
Fixed
button to constrain all
degrees of freedom of the selected nodes.
6.
The analysis is now ready to be performed.
Select the
Analysis tab
from the
Ribbon bar and select
Run Simulation
.
Reviewing the results
Reviewing the results of a Natural Frequency (Modal) analysis is a little different than
that of other analysis types. The main reason for this is that you are looking primarily
at t
he mode shapes and frequencies of your part to see how it will react under certain
loading conditions, instead of reviewing stress, strain and displacement. In addition,
when working with a beam model such as this, there are other slight differences that
can be seen in the results environment.
A Fast
Modal (Eigenvalue) Solver Based on Subspace and AMG
9
Reviewing Results
1.
Review the frequency of mode 1 in the lower left corner.
2.
Click the
Next
button
to review mode 2.
3.
Click through Mode 3, 4, and 5. Verify that all values fall within the acceptable
range set by
the local standards (all < 1.2 cycles/s).
3D visualization
1.
Zoom in to view the various 3D visualized cross

sections of the beams.
2.
With
Ctrl
held, select parts
1, 2, 3, and 4
.
3.
Right click and choose

3D Visualization
.
4.
Review your mode shapes with all
beams now looking the same.
Animate Results
1.
Click on the
Start Animation
button
to view the movement of the bridge
for each mode shape.
2.
Click on
Animate
, and choose the
Setup option
. Verify that the settings are as
you want for your animation.
3.
Click on
Animate: Save as AVI
to save an animation of one of your mode shapes.
A Fast
Modal (Eigenvalue) Solver Based on Subspace and AMG
10
*Note:
It is important to understand that although you are able to view
displacement values in a Natural Frequency (Modal) analysis, the actual numbers
hold no value. The col
or contour and displaced shape will give you an
understanding of what part of your model is displacing the most, and in what
direction, but the actual displacement values are
NOT
the actual distance moved
from the analysis.
Weight and Center of Gravity
1.
Click on the
FEA Editor
tab.
2.
From the
Analysis
tab of the ribbon, click the
Weight and Center of Gravity
button.
3.
Verify that the weight of the bridge is close to the designed value.
Response Spectrum Analysis
Analysis Setup
1.
In the
FEA Editor tab
, right click on
Analysis Type
, choose
Set Current
Analysis Type: Linear: Response Spectrum
.
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Modal (Eigenvalue) Solver Based on Subspace and AMG
11
2.
When prompted to create a new design scenario, choose
Yes
.
3.
From the
Setup
tab of the ribbon, click the
Parameters
button.
4.
Choose the
Spectrum Data
button.
5.
V
erify that “
Use modal results from design scenario
”
is set to
1
, since the
modal analysis was done in the first load case.
6.
Set the
Input Spectrum Type
to
g vs. Period
.
7.
Type a
1
in
X Dir, Y Dir
, and
Z Dir
in the
Factors
section.
8.
Click the
Import
button and
browse to
Earthquake.csv
.
9.
Press
Import
.
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Modal (Eigenvalue) Solver Based on Subspace and AMG
12
10.
From the
Analysis
tab of the ribbon, click the
Run Simulation
button
.
Reviewing the results, Response Spectrum
Reviewing the results of a Response Spectrum analysis is much more like that of a
normal linear or
nonlinear stress analysis. Since the results are based off of the modal
analysis that was previously run, there will still be results for each mode (as well as a
resultant case), but you will be looking at the stress, strain, and displacement values to
se
e how the part reacts to a load, in this case, a simulated earthquake loading.
A Fast
Modal (Eigenvalue) Solver Based on Subspace and AMG
13
Reviewing Results
1.
From the
Results Contours
tab of the ribbon, click on
Displacement:
Magnitude
.
2.
From
Load Case Options
, tab through and find the worst case displacement
of
the different modes.
3.
From
Stress
on the ribbon, click on
Beam and Truss
, and choose
Worst
Stress
.
4.
Again, scroll through your modes and find the highest stress.
A Fast
Modal (Eigenvalue) Solver Based on Subspace and AMG
14
Well, let’s hope that Sydney never sees a 7.1 magnitude earthquake, because it doesn’t lo
ok
like things would end so well! Fortunately, the Sydney Harbor Bridge has been around for
75+ years and is still standing!!!
Frequency Response Analysis
Running an Updated Modal Analysis
Change Analysis Type
1.
In
Design Scenario 2
, right click on Analys
is Type <Response Spectrum> and
select
Natural Frequency (Modal)
.
2.
Answer “
Yes
” when asked if you would like to copy the design scenario.
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Modal (Eigenvalue) Solver Based on Subspace and AMG
15
Dividing Beams Elements
1.
In the model tree, select
parts 1, 2 and 3,
right click and choose
V
isibility
.
2.
Click on the Selection tab, choose
Rectangle
from shape panel and
Line
from the
select panel.
3.
Box select all of the lines, right click and pick
Divide
.
4.
Choose to divide the lines into
5
segments.
Applying Nodal Weights
5.
From the Select panel, choose
Verti
ces
.
6.
Select columns of vertices as shown below.
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Modal (Eigenvalue) Solver Based on Subspace and AMG
16
7.
Click on the
Setup
tab and choose
Weight
from the Loads panel.
8.
Click on Units of mass and enter
2000 lbf*s^2/in.
9.
Uncheck the
Uniform
box and replace the
X Direction
with
0
.
10.
Click
OK
.
Analyzing
1.
Click on the
Analysis tab
from the ribbon.
2.
Press
Run Simulation
in the Analysis panel.
You can now review your results to see the minor changes that were made by added the
mass of the “cars” on the bridge.
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Modal (Eigenvalue) Solver Based on Subspace and AMG
17
Frequency Response of a Bridge with Cars
Change Analysis Type
1.
In
Design Scenario 3
, right click on Analysis Type <Natural Frequency (Modal)>
and select
Frequency Response
.
2.
Answer “
Yes
” when asked if you would like to copy the design scenario.
Determine Nodes for Loading
1.
From the Analysis tab, click the
Check Model
bu
tton from the Analysis panel.
2.
In the results environment, click on the Results Options tab and click on
Show
Numbers: Node Numbers
.
3.
Zoom in and determine the node numbers you want to excite (we will use
nodes
271, 302, 312, 317
)
4.
Click on the
FEA Editor
tab
.
Alternately, you could have selected the nodes in the results environment,
right clicked and
i
nquired to see the node numbers.
Defining the Analysis Parameters
Excited Nodes Tab
1.
From
the Setup tab, click on the
Parameters
button from the Model Setup panel.
2.
Click on the
Analysis Setup
button.
3.
Point to design scenario
3
for the proper modal results.
4.
Click the radio button next to
Node Number of Applied Excitation
.
5.
Enter the number of the first excited node,
271
.
6.
Click the ra
dio button next to
Force Input
for Type of Excitation.
7.
Choose the
Z
radio button for the
Direction of Excitation
.
8.
Enter a
1
for
Scaling Factor for Amplitudes
and click
Apply
.
9.
Click
New
next to node set, and type
2
.
10.
Repeat steps 4 through 7
until no more nodes are left.
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Modal (Eigenvalue) Solver Based on Subspace and AMG
18
Exciting Frequencies Tab
1.
Click on the
Exciting Frequencies
tab.
2.
Check
the box next to
Include Natural Frequencies
.
3.
Click the
Insert Row
button.
4.
Type
0.084
in the first row of Frequency, and
0.6
in the second row.
Damping
Ratio Tab
1.
Click on the
Damping Ratio
tab.
2.
Click the
Insert Row
button.
3.
Enter
0.084
and
0.6
in the Frequency (Hz) column.
4.
Enter
.01
in both cells for Damping Ratio.
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Modal (Eigenvalue) Solver Based on Subspace and AMG
19
Amplitudes Tab
1.
Click on the
Amplitudes tab
.
2.
Click on the
Import
button.
3.
Click
Browse
and find the file called
Frequency.csv
.
4.
Click
Open
and
Import
.
5.
Click
OK
.
Analyze the Model
1.
Click on the
Analysis
tab.
2.
Choose
Run Simulation
from the Analysis panel.
Review Results
1.
From the Results Contour tab, click on
Beam and Truss
in the Stress panel.
2.
Choose
Worst
as the type of stress in Beam and Truss.
3.
Click on the
Next
button to scroll through the results to see the stress for each
excited frequency.
A Fast
Modal (Eigenvalue) Solver Based on Subspace and AMG
20
Critical Buckling of a Shipping Container
Opening the CAD geometry
This
exercise uses a DWG
file to demonstrate Autodesk Simulation’s ability to work with
wireframe models, using beam elements instead of solid elements as with a CAD solid
model. AutoCAD layers and blocks are recognized as different parts in Autodesk
Simulatio
n, allowing the user to prepare the model for simulation such that the title block
and dimensions are on layers other than that actual geometry.
1.
Launch
Autodesk Simulation
Mechanical
.
2.
Click the
Open
button on ribbon bar and navigate to the location where
you have
saved your
demonstration files
.
3.
Click on the
Files of type
drop down and choose the
Autodesk Inventor Files
(*.ipt, *.iam)
option. The model name will be
Critical Buckling.iam
.
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Modal (Eigenvalue) Solver Based on Subspace and AMG
21
4.
Click
Open
to load the model into Autodesk Simulation.
5.
Define the analysis type as
Critical Buckling
.
Model Meshing
Defining Mesh Settings
1.
Select
parts 1 through 8
in the model tree.
2.
Right click and choose
CAD Mesh Options: Part
.
3.
Choose the
Plate/Shell
option.
4.
Move the slider to
50%
and click
OK
.
5.
Click on the Mesh tab and choose
3D Mesh Settings
in the Mesh panel.
6.
Click on the
Options
button and set retries to
0
.
7.
Click on
Model
and
uncheck
the box next to
“Use automatic geometry

based
mesh size function”
and
“Use virtual imprinting.”
8.
Click
OK
and
Mesh Model
.
Element Definition and Material Definition
Defining
Element Definition
1.
Select
parts 1 through 8
in the model tree.
2.
Right click and choose
Edit: Element Definition.
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Modal (Eigenvalue) Solver Based on Subspace and AMG
22
3.
In thickness, type a value of
0.125 in.
and click
OK
.
Defining Materials
4.
With parts
1 through 8
still selected, right click and choose
Edit: Material
.
5.
Click the
+
next to
Aluminium
and choose
Aluminum 6061

O
and click
OK
.
6.
Select
parts 9 through 15
in the model tree.
7.
Right click and choose
Edit: Material
.
8.
Click the
+
next to
Ste
el
and
ASTM
,
and choose
Steel (ASTM
–
A36)
. Click
OK
.
Applying Loads and Boundary Conditions
Apply Boundary Conditions
1.
Click on the
Selection
tab and choose
Point and Rectangle
in the Shape panel.
2.
Choose
Surface
in the Select panel.
3.
Select the
bottom
surface
of each of the three supports.
4.
Click on the
Setup
tab and choose
General Constraint
from the Constraints tab.
5.
Click on the
Fixed
button.
6.
Click
OK
.
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Modal (Eigenvalue) Solver Based on Subspace and AMG
23
Apply Loads
1.
Rotate the model to view the top of the shipping container.
2.
Select the
top
surface of the container.
3.
From the
Setup
tab, click on
Force
from the Loads panel.
4.
Enter a magnitude of

10
,000 lbf
, and select the
Y
radio button.
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Modal (Eigenvalue) Solver Based on Subspace and AMG
24
5.
Click
OK
.
Analysis Parameters and Analysis
Define Analysis Parameters
1.
From the
Setup
tab, click on
Anal
ysis Parameters
.
2.
In the
Multipliers
tab, type a
1
in the
Acceleration Multiplier
box.
3.
Click on the
Gravity/Acceleration
tab.
4.
Click the button for
Gravity / Acceleration Load
.
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Modal (Eigenvalue) Solver Based on Subspace and AMG
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5.
Type a

1
in the
Y
multiplier and
0
in
X and Z
.
6.
Click
OK
.
Analyzing the Model
1.
Click on the
Analysis
tab.
2.
Click on
Run Simulation
from the Analysis panel.
Result Evaluation
and Copying Design Scenarios
Review the Critical Buckling Results
1.
In the Results environment, review the
Buckling Load Multiplier
in the bottom
left corner.
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Modal (Eigenvalue) Solver Based on Subspace and AMG
26
2.
I
n the Results Contour tab, click on the
Next
button to scroll through the other
modes.
3.
Notice that the first value is the lowest.
4.
Click on the tab for the
FEA Editor
.
Copying to a Second Design Scenario
1.
In the FEA Editor, right click on
Design Scenario
1
and choose to
copy
.
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Modal (Eigenvalue) Solver Based on Subspace and AMG
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Modifying Loads, Reanalyzing and Reviewing Results
Modify Loads
and Analyzing
1.
In Design Scenario 2, click the
+
next to
Load and Constraint Groups
.
2.
Click the
+
next to
Surface Forces
.
3.
Modify the
Magnitude
of the force from

1
0
,000
to

22,000 lbf
.
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Modal (Eigenvalue) Solver Based on Subspace and AMG
28
4.
Click
OK
.
5.
Click on the
Analysis tab
.
6.
Click on
Run Simulation
in the Analysis Panel.
Review Results
1.
In the Results environment, review the
Buckling Load Multiplier
in the bottom
left corner.
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