Module 1.1: Point Loading of a 1D Cantilever Beamcassenti/AnsysTutorial/Module 1... · UCONN ANSYS –Module 1.1 Page 2 ... 3. Click on Mechanical APDL (ANSYS) to start ANSYS. This

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


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.


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


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.

1

2

3


Preferences

1. Go to Main Menu -> Preferences

2. Check the box that says Structural

3. Click OK

1

2

3


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:

1

2

8

7


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

4

2

3

2

3

4


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

2

3

3

4

3

4

2


Now we will add the thickness to our beam.


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

2

3

4


Meshing


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


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

2

5

5

6

3

4

3

4


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


The fixed end will look as shown below:

2

4

5

3


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


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).

4

2

4

3

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.


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:

2

3


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.


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.


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

4 6

8

9

10

11


Validation

Documents

Module 1.1: Point Loading of a 1D Cantilever Beamcassenti/AnsysTutorial/Module 1... · UCONN ANSYS –Module 1.1 Page 2 ... 3. Click on Mechanical APDL (ANSYS) to start ANSYS. This