Module 1.1: Point Loading of a 1D Cantilever Beam
Table of Contents
Page Number
Introduction
2
Problem Description
3
Theory
3
Geometry
4
Preprocessor
Element Type
Real Constants and Material Properties
Meshing
Loads
8
8
9
10
11
Solution
12
General Postprocessor
13
Results
15
Validation
17
UCONN ANSYS –Module 1.1
Page 1
Introduction
Welcome to the UCONN ANSYS Mechanical Training Suite! Modules 1.1-1.9 are designed to
be an introduction to the fundamental modeling considerations and features in ANSYS. Using
classical beam loadings, we will model fundamental structures in one two and three dimensions
in an environment where theoretical answers are known and can be compared against the created
models. We will study the tradeoffs and benefits of modeling in one two or three dimensions.
Also, we will investigate how different boundary conditions affect the number of mesh elements
required to achieve a converged solution. Modules 1.1-1.9 are also designed as an introduction to
Linear Static Structural problems, a general category of Finite Element problems which can be
solved in one load step and one iteration. These problems are generally quick to solve using the
software and are easier to set up. Completion of this first series of modules will help the user
gain proficiency in the layout of the APDL environment and draw attention to the modeling
process, common modeling mistakes and other modeling considerations. While most tutorials in
this suite use the ANSYS Mechanical APDL package, a small introduction to ANSYS Workbench
is explored in modules 1.3W, 1.5W and 1.7W.
UCONN ANSYS –Module 1.1
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Problem Description
y
x
Nomenclature:
L =110m
b =10m
h =1 m
P=1000N
E=70GPa
=0.33
Length of beam
Cross Section Base
Cross Section Height
Point Load
Young’s Modulus of Aluminum at Room Temperature
Poisson’s Ratio of Aluminum
In this module, we will be modeling an Aluminum cantilever beam with a point load at the end
with one dimensional elements in ANSYS Mechanical APDL. We will be using beam theory and
mesh independence as our key validation requirements. The beam theory for this analysis is
shown below:
Theory
Von Mises Stress
Assuming plane stress, the Von Mises Equivalent Stress can be expressed as:
(1.1.1)
Since the nodes of choice are located at the top surface of the beam, the shear stress at this
location is zero.
(
.
(1.1.2)
Using these simplifications, the Von Mises Equivalent Stress from equation 1 reduces to:
(1.1.3)
Bending Stress is given by:
(1.1.4)
Where
and
. From statics, we can derive:
(1.1.5)
(1.1.6)
With Maximum Stress at:
= 66 KPa
UCONN ANSYS –Module 1.1
(1.1.7)
Page 3
Beam Deflection
The governing equation of a beam in bending is given by the Euler-Bernoulli relationship:
(1.1.8)
Plugging in equation 1.7.5, we get:
(1.1.9)
Integrating once to get an angular displacement, we get:
(1.1.10)
At the fixed end (x=0),
, thus
0
(1.1.11)
Integrating again to get deflection:
(1.1.12)
At the fixed end.y(0)= 0 thus
, so deflection (
is:
(
)
The maximum displacement occurs at the point load( x=L)
(1.1.13)
(1.1.14)
Geometry
3
Opening ANSYS Mechanical APDL
1. On your Windows 7 Desktop click the Start button
2. Under Search Programs and Files type “ANSYS”
3. Click on
Mechanical APDL (ANSYS) to start
ANSYS. This step may take time.
1
UCONN ANSYS –Module 1.1
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Page 4
Preferences
1. Go to Main Menu -> Preferences
2. Check the box that says Structural
3. Click OK
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2
3
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Keypoints
Since we will be using 1D Elements, our goal is to model the length of the beam.
Go to Main Menu -> Preprocessor -> Modeling -> Create ->Keypoints ->
On Working Plane
1. Click Global Cartesian
2. In the box underneath, write 0,0,0 creating a keypoint at the origin.
3. Click Apply
4. Repeat Steps 3 and 4 for the point 110,0,0
5. Click OK
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2
5
3
6. The Triad in the top left corner is blocking keypoint 1. To get rid of the triad, type
/triad,off in Utility Menu -> Command Prompt
8 7
7. Go to Utility Menu -> Plot -> Replot
Your graphics window should look as shown:
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Line
1. Go to Main Menu -> Preprocessor -> Modeling -> Create ->
Lines -> Lines -> Straight Line
2. Select Pick
3. Enter 1,2 for keypoints
4. Click OK
2
Go to Utility Menu -> Ansys Toolbar -> SAVE_DB
The resulting graphic should be as shown:
3
4
SAVE_DB
Since we have made considerable progress thus far, we will create a temporary save file for our
model. This temporary save will allow us to return to this stage of the tutorial if an error is made.
1. Go to Utility Menu -> ANSYS Toolbar ->SAVE_DB This creates a save checkpoint
2. If you ever wish to return to this checkpoint in your model generation, go to Utility
Menu -> RESUM_DB
WARNING: It is VERY HARD to delete or modify inputs and commands to your model
once they have been entered. Thus it is recommended you use the SAVE_DB and
RESUM_DB functions frequently to create checkpoints in your work. If salvaging your
project is hopeless, going to Utility Menu -> File -> Clear & Start New -> Do not read file
->OK is recommended. This will start your model from scratch.
UCONN ANSYS –Module 1.1
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Preprocessor
Element Type
1. Go to Main Menu -> Preprocessor ->
Element Type -> Add/Edit/Delete
2. Click Add
3. Click beam -> 3D Elastic 4
4. Click OK
5. Click Close
6. Go to Utility Menu -> ANSYS
Toolbar -> SAVE_DB
2
* BEAM4 is a one dimensional linear element with 6 degrees
of freedom (UX,UY,UZ,ROTX,ROTY,ROTZ). It has
tension, compression, bending, and torsional capabilities.
For more information, consult the ANSYS HELP by
clicking HELP
5
3
4
*
ANSYS HELP
ANSYS Mechanical APDL at its
core is a command line driven
FEA code. Similar to the Java
APL or the Matlab HELP feature,
ANSYS has its own library of
internal functions known as
Commands that are used in the
backend from the GUI front end.
The ANSYS HELP library
also provides useful information
on the theory behind ANSYS
calculations and modeling best
practices. We encourage you to
explore the vast volumes of
ANSYS HELP to increase your
proficiency in ANSYS beyond
the scope of these tutorials
UCONN ANSYS –Module 1.1
Page 8
Real Constants and Material Properties
1. Go to Main Menu -> Material Props -> Material Models
2. Go to Material Model Number 1 -> Structural -> Linear -> Elastic -> Isotropic
2
3. Enter 7E10 for Young’s Modulus (EX) and .33 for Poisson’s Ratio (PRXY)
4. Click OK
5.
out of Define Material Model
Behavior
6. Go to Utility Menu -> SAVE_DB
3
3 4
Now we will add the thickness to our beam.
1. Go to Main Menu -> Preprocessor ->
Real Constants -> Add/Edit/Delete
2. Click Add
3. Click OK
2
6
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4. Under Real Constants for BEAM4 ->Shell thickness
at node I TK(I) enter:
10 for cross sectional area
10/12 for moment of inertia IZZ
10 for thickness along Z axis
1 for thickness along Y axis
5. Click OK
6. Click Close
4
5
Meshing
1. Go to Main Menu -> Preprocessor ->
Meshing -> Mesh Tool
2. Go to Size Controls: -> Global -> Set
3. Under SIZE Element edge length put 55.
4. Click OK
5. Click Mesh
6. Click Pick All
7. Click Close
8. Go to Utility Menu -> SAVE_DB
2
5
5
7
6
3
Loads
4
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Saving Geometry
We will be using the geometry we have just created for the next 3 modules. Thus it would be
convenient to save the geometry so that it does not have to be made again from scratch.
1. Go to File -> Save As …
2. Under Save Database to
pick a name for the Geometry.
For this tutorial, we will name
the file ‘1D Cantilever’
3. Under Directories: pick the
Folder you would like to save the
.db file to.
4. Click OK
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3
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Displacements
1.
2.
3.
4.
Go to Utility Menu -> Plot -> Nodes
Go to Utility Menu -> Plot Controls -> Numbering…
Check NODE, Node Numbers to ON
Click OK
3
Your plot should look as shown:
4
5. Go to Main Menu -> Preprocessor -> Loads -> Define Loads ->
Apply -> Structural -> Displacement -> On Nodes
6. Click Pick -> Single and with your cursor, click on first node
7. Click OK
8. Click All DOF to secure all degrees of freedom
9. Under Value Displacement value put 0.
10. Click OK
11. Go to Utility Menu -> SAVE_DB
6
8
10
9
7
The fixed end will look as shown below:
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Point Load
1. Go to Main Menu -> Preprocessor -> Loads -> Define Loads ->
Apply -> Structural ->Force/Moment -> On Nodes
2. Under List of Items enter 2 for node 2 and press OK
5
3.
4.
5.
6.
3
4
Under Lab Direction of Force/mom select FY
Under Value Force/moment value type -1000
Press OK
Go to Utility Menu -> SAVE_DB
USEFUL TIP: If you wish to assign new force values, pick the nodes of
interest and replace that component of force with 0 before assigning new
values. This will delete the previous force assignment.
2
4
The load at the end face should look as below:
Solution
1. Go to Main Menu -> Solution ->Solve -> Current LS (solve). LS stands for Load Step.
This step may take some time depending on mesh size and the speed of your computer
(generally a minute or less). Ignore any warnings that may appear on your screen, as they
are irrelevant to the problem at hand.
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General Postprocessor
We will now extract the Preliminary Displacement and Von-Mises Stress within our model.
Displacement
1. Go to Main Menu -> General Postprocessor -> Plot Results -> Contour Plot -> Nodal
Solution
2. Go to DOF Solution -> Y-Component of displacement
3. Click OK
4. To give the graph a title, go to
Utility Menu -> Command Prompt and type
/title, Deflection of a Cantilever Beam with a Point Load.
5. Press enter and write /replot to refresh the window.
6. Press enter
2
3
The Resulting Plot should look as shown below:
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Equivalent (Von-Mises) Stress
Unfortunately, we cannot create a contour plot of Von-Mises stress for 1D elements. We can,
however, look up the moment reactions at each element. If we plug this value into equation
1.1.4, we can readily calculate the bending stress in our model and by extension, the equivalent
stress.
1. Go to Utility Menu -> List -> Results -> Element Solution …
2. Go to Element Solution -> All Available force items
3. Click OK
This chart shows all reaction forces and moments at each node in the domain. Since we are
interested in reaction moments in the z direction, we will look to the last column in the chart:
According to the chart the maximum moment at the fixed end of the beam is .11E6 Nm.
Plugging into equation 1.1.4, we get the expected stress of 66 kPa.
UCONN ANSYS –Module 1.1
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Results
The percent error (%E) in our model max deflection can be defined as:
(
)
=0%
(1.1.15)
Max Deflection Error
Max Equivalent Stress Error
Using equation (1.1.15) above, the percent error for Max Deflection and Equivalent Stress in our
model is 0%. This is due to the fact that ANSYS uses Gaussian Quadrature to interpolate
between the integration points. This changes with respect to the element used. Beam4 used twopoint Gaussian Quadrature, a numerical technique which is fourth degree accurate. Since the
equations for deflection and stress are fourth order and second order respectively, the answer will
have no error because the Quadrature is accurate to the correct degree polynomial. Thus the one
dimensional method has zero percent error in deflection and stress.
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Further Analysis
In addition to this baseline data, we can export both the deflection and Von-Mises data to Excel.
We will use the Y-deflection data as an example of how to do this.
1. Go to Utility Menu -> List -> Results -> Nodal Solution …
2. Select Nodal Solution -> DOF Solution -> Y-component of displacement
3. Click OK
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6
4. The list file should populate. Go to
PRNSOL Command -> File -> Save As …
5. Save the file as 1D_P_YDeflection.lis to the
path of your choice
6.
7.
8.
9.
Go to PRNSOL Command -> File -> Close
Open 1D_P_YDeflection.lis in Excel
Click Fixed Width
Click Next >
8
9
10. Click a location on the ruler between the NODE and
UY columns. This will cause Excel to separate these
columns into separate columns in the spreadsheet
11. Click Next >
12. Click Finish
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UCONN ANSYS –Module 1.1
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Validation
UCONN ANSYS –Module 1.1
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