module 1.1: point loading of a 1d cantilever beamcassenti/ansystutorial/module 1... · uconn ansys...
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UCONN ANSYS –Module 1.1 Page 1
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 8
Element Type 8
Real Constants and Material Properties 9
Meshing 10
Loads 10
Solution 13
General Postprocessor 14
Results 15
Validation 17
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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.
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Problem Description
Nomenclature:
L =110m Length of beam
b =10m Cross Section Base
h =1 m Cross Section Height
P=1000N Point Load
E=70GPa Young‟s Modulus of Aluminum at Room Temperature
=0.33 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 (1.1.7)
y
x
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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:
(1.1.13)
The maximum displacement occurs at the point load( x=L)
(1.1.14)
Geometry
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.
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Preferences
1. Go to Main Menu -> Preferences
2. Check the box that says Structural
3. Click OK
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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
Let‟s check our work.
6. Click the Dynamic Model Mode icon. On the graphics window,
right click and drag the cursor down. You should now be able to see
the two key points you have just created.
7. 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. 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
Go to Utility Menu -> Ansys Toolbar -> SAVE_DB
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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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. Go to Utility Menu -> ANSYS
Toolbar -> SAVE_DB
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
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
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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
4. Under Real Constants for BEAM4 ->
Shell thickness at node I TK(I) enter 1
for the thickness
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
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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
Loads
Displacements
1. Go to Utility Menu -> Plot -> Nodes
2. Go to Utility Menu -> Plot Controls -> Numbering…
3. Check NODE, Node Numbers to ON
4. Click OK
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1. Go to Main Menu -> Preprocessor -> Loads -> Define Loads ->
Apply -> Structural -> Displacement -> On Nodes
2. Click Pick -> Single with your cursor, click on first nod
3. Click All DOF to secure all degrees of freedom=
4. Under Value Displacement value put 0.
5. Click OK
6. Go to Utility Menu -> SAVE_DB
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 Lab Direction of Force/mom select FY
3. Under Value Force/moment value type -1000
4. Press OK
5. Go to Utility Menu -> SAVE_DB
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).
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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.
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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. Click the e Front View and use the Dynamic Model Mode by right clicking
and dragging down slightly.
5. Go to Utility Menu -> PlotCtrls -> Numbering -> NODE -> OFF -> OK.
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 unless more
complicated loading conditions are applied. 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.
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Results
Max Deflection Error
The percent error (%E) in our model max deflection can be defined as:
= 0 % (1.6.13)
Max Equivalent Stress Error
Using the same definition of error as before, we derive that our model has 0% error in the max
equivalent stress. Using equation (1.6.13) above, the percent error for 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. Since Beam4 has
two integration points and two-point Gaussian Quadrature is fourth degree accurate, the answer
will have no error baseline because this function is first degree. 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.
1. Go to Utility Menu -> List -> Results -> Nodal Solution …
2. Select Nodal Solution -> DOF Solution -> Y-component of displacement
3. Click OK
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. Go to PRNSOL Command -> File -> Close
7. Open 1D_P_YDeflection.lis in Excel
8. Click Fixed Width
9. Click Next >
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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Validation