ANSYS 1D Structural Truss Tutorial _ Stepped Bar in Tension - Online Finite Element Analysis...

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06/06/2016 ANSYS 1D Structural Truss Tutorial : Stepped Bar in Tension - Online Finite Element Analysis Consultancy Service

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ANSYS 1D Structural Truss Tutorial : Stepped

Bar in Tension

Disclaimer:

This tutorial is an educational tool designed to assist those who wish to learn how to use the ANSYS finite element software package. It is not intended as a guide for determining suitable modelling methods or strategies for any application. The authors of this tutorial have used their best efforts in preparing the tutorial. These efforts include thedevelopment, research and testing of the theories and com putational models shown in the tutorial. The authors make nowarranty of any kind, expressed or implied, with regard to any text or models contained in this tutorial. The authors shall not be liable in any event for incidental or consequential damages in connection with, or arising out of, the furnishing,

performanc e, or use of the text and models provided in this tutorial. There is no gaurantee that there are no mistakes or errors in the information provided and the authors assume no responsibility for the use of any of the informationcontained in this tutorial.

Overview

In this tutorial you will examine the 1-D displacement of a stepped bar in tension using ANSYS. The problem isadapted from example 1.1. on page 9 of the textbook Practical Stress Analysis with Finite Elements (2nd Ed) byBryan J. Mac Donald. You will determine the displacement distribution and stress distribution in the bar due to theapplied loading and boundary conditions. A one-dimensional structural truss element (often also called a "spar","spring" or "link" element) will be used for this analysis. We will use SI system units for this tutorial: length = m,mass = kg, time = sec, force = N, stress/pressure = Pa. In this case the bar is made from steel and the applied forceis 10,000 N.

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Figure 1: An overview of the problem to be solved

It should be clear that the problem shown in figure 1 is a one-dimensional problem as the loads and reaction forceswill all act in the same direction. It is convienient to divide the problem into three finite elements (E1, E2, E3)corresponding the the three "steps" in the bar as shown in figure 2. Each element has two end-points where it either

joins another element or interacts with the outside world (e.g. is constrained or experiences a load) and these pointsare called nodes (N1, N2, N2, N4)


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Figure 2: Dividing the problem into three finite elements and four nodes.

We can easily calculate the cross sectional area of each element from the information given in the example in thebook "Practical Stress Analysis with Finite Elements":

Element 1 = ½ * (0.0005 + 0.000366666) = 0.0004333 m2

Element 2 = ½ * (0.000366666 + 0.000233333) = 0.000299 m2

Element 3 = ½ * (0.000233333 + 0.0001) = 0.000166 m2

The figure below shows the finalised model where the bar is modelled as a series of three elastic springs (or trusses)with equivalent stiffness to the three uniform cross section elements shown in the figure above.

http://www.amazon.com/gp/product/0955578167/ref=as_li_ss_tl?ie=UTF8&camp=1789&creative=390957&creativeASIN=0955578167&linkCode=as2&tag=glasnepubli05-20


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Figure 3: The idealised finite element model of the tapered bar.

It can be clearly seen from figure 3 that the bar has been divided into three truss elements (E1, E2 and E3). Each of these will have a length of 0.2m. The points at each end of each element are called “nodes”. These are numbered 1 to4 in figure 3 and the x coordinate of each node is: N1 x = 0, N2 x = 0.2m, N3 x = 0.4m and N4, x = 0.6m

Step 1: Launch ANSYS

You may need to adapt these instructions depending on your operating system and the options available to you. Wewill show how to launch ANSYS on a machine running Windows 7.

1. Click on the windows icon in the left lower corner of your screen.

2. Click on All Programs to expand the programs list.

3. Find Ansys XX.X in the list of programs and click on it. Where XX.X is the version number of ANSYS availableto you. If you are running ANSYS ver 14.0 then the XX.X will be 14.0, i.e. you should click on Ansys 14.0

4. Click on the Mechanical APDL Product Launcher to launch the classic ANSYS interface. Your screen shouldlook like the figure below

5.


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6. When the product launcher displays your screen should look like this:


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7. It is very important that you specify the working directory and the job name. We advise setting up a specialdirectory for your ANSYS work and always using this. Similarly you should give each ANSYS model a differentJob Name. If you forget to do this then ANSYS will automatically give each analysis the name "file" and thingswill quickly become confused. In this case, let's use the Job Name "Tutorial_01"

8. Depending on the type of ANSYS license you have, there may be various options in the License drop downmenu. Mulitphysics, Mechanical, Structural or any of the Academic licenses are suitable for this tutorial. Beaware that if you have another option selected in this box then it may effect the options available in the main

ANSYS GUI when it launches.


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9. Click on "Run" in the product launcher window to start the main ANSYS GUI. Once the main GUI launchesyou can close the product launcher window.

10. Once the main GUI opens it is useful to set the preferences: in the Main Menu select Preferences and makesure that Structural and h-method are selected.

Step 2: Define Element Type

1. In the Main Menu select Preprocessor > Element Type > Add/Edit/Delete

2. Click on Add in the dialog box that appears.

3.

4. Select Link in the left hand menu and 3Dfinit stn 180 in the right hand menu and then click Ok

5. This will define element type 1 as a LINK 180 element. LINK 180 is actually a 3D truss element but we aregoing to use it as a 1D truss by later supressing some of it's degrees of freedom.

6. Click Close to close the Element Type dialog box.

Step 3: Define Element Cross Sectional Area (Real Constant)

1. In the Main Menu select Preprocessor > Real Constants > Add/Edit/Delete

2. Click on Add in the dialog box that appears.


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3. Click on OK to define a real constant for element type 1 LINK 180.

4.

5. Enter the value for cross sectional area for element 1: 0.000433m2 and then click Ok

6. Now, we have to repeat this process for elements 2 and 3.

7. Click on Add in the Real Constants dialog box and the click on OK in the next box that appears.

8. This time enter the value for the cross sectional area for element 2: 0.000299 m 2 and then click Ok

9. Repeat this process for element 3 using the value given above. When you are finished you should see threereal constant sets defined:


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10. Click on Close to close the real constants dialog box.

Step 4: Define the Material Behaviour

1. In the Main Menu click on Preprocessor > Material Props > Materia l Models, the Define Material Model Behaviour dialog box will now appear.

2. Expand the options in the right hand pane of the dialog box: Structural > Linear > Isotropic

3. In the dialog box that pops up, enter suitable material parameters for steel ( E = 210 x 10 9 Pa, Poissons ratio= 0.3):


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4. Click on Ok to close the dialog box in which you entered the material parameters.

5. Close the Define Material Model Behaviour dialog box by clicking on the X in the upper right corner.

Step 5: Define Nodes and Elements

1. In the Main Menu click on Preprocessor > Modeling > Create > Nodes > In Active CS

2. In the dialog box that appears: enter the x-coordinate for node 1 (i.e. 0) and click on Apply (note that Applyissues the command to create the node but keeps the dialog box open, clicking Ok would also issue thecommand to create the node but would close the dialog box).

3. Now enter the x-coordinate for node 2 (i.e. 0.2) and click Apply

4. Enter the x-coordinate for node 3 (i.e. 0.4) and click Apply

5. Enter the x-coordinate for the final node, node 4 (i.e. 0.6) and click Ok to dismiss the dialog box.


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6. You may have notice nodes appearing on the main window when you clicked apply. You should now be ableto see 4 nodes in the main window (note that node 1 is at the origin so you may not be able to see it due tothe display of the triad at the origin, this is OK):


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7. We must now create the elements that join the nodes together: click on Preprocessor > Modeling > Create> Elements > Auto Numbered > Thru Nodes

8. In the main window click on node 1 and then node 2. Then click Apply in the dialog box. You should see aline element appear joining nodes 1 and 2.

9. Now click on node 2 and then node 3 and click Apply. A line element should appear joining nodes 2 and 3.


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10. Finally, click on node 3 and then node 4 and click Ok. A line element should appear joining nodes 3 and 4.

11. Your display should now look like this:

12. All three elements were created with the default real constant of 1. This means that, at the moment, allelements have the same cross sectional area. This cross sectional area should only be applied to element 1,so we need to change the real constants associated with elements 2 and 3. In order to do this we use thefollowing command: Preprocessor > Modeling > Move/ Modify > Elements > Modify Attrib

13. Pick element number 2 and then click Ok in the dialog box.

14. In the dialog box that appears, change the Attribute to Change to Real Constant and the New AttributeNumber to 2, then click on Ok.

06/06/2016 ANSYS 1D St t l T T t i l St d B i T i O li Fi it El t A l i C lt S i


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15. Repeat this process (steps 12-14) for element 3 to change its real constant to 3.

16. We can check that all is as it should be by going to the Utility Menu (top of the window) and selecting: List >Elements > Nodes & Attributes, you should get this:

17. If your list looks different then it is likely you have made a mistake at some point.

18. The key points are that each element has a different real constant (REL) and that element 1 joins nodes 1 & 2,element 2 joins nodes 2&3 and element 3 joins nodes 3&4.

Step 6: Define Boundary Conditions

1. In this case we are using a 3D truss to model a 1D truss problem so we must prevent the nodes from movingin either the Y or the Z directions. In order to do this we constrain all nodes in the finite element model in boththe Y and Z directions.

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2. Preprocessor > Loads > Define Loads > Apply > Structural > Displacement > On Nodes

3. Select Pick All in the dialog box that appears.

4. Select both UY and UZ in the next dialog box that appears and enter a value of 0 for displacement value

5. Click Ok to close the dialog box. Your screen should now look like this:

6. Now we can apply the problem boundary conditions.

7. The original bar is held rigidly at it's left hand edge. In order to model this we will constrain the leftmost node(i.e. node 1) from moving in the x-direction.

8. Again, select: Preprocessor > Loads > Define Loads > Apply > Structural > Displacement > On Nodes

9. Click on Node 1 and then click Ok

10. This time select UX only and enter a value of 0 for displacement value

11. Click Ok to close the dialog box. Your should have noticed an extra constraint appear at node 1 (blue trianglepointing in the horizontal direction)

Step 7: Define Loads

1. Select Preprocessor > Loads > Define Loads > Apply > Structural > Force/ Moment > On Nodes

2. Pick node 4 and click on Ok

3. In the dialog box that appears make sure that the direction of force is set to FX and that the Force/ Moment value is 100000

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4. Click on Ok to close the dialog box.

5. You should see a red arrow appear on node 4 pointing to the right.

Step 8: Solve the Problem

1. In the Main Menu select Solution > Analysis Type > New Analysis

2. Make sure that Static is selected in the dialog box that pops up and then click on Ok to dismiss the dialog.

3. Select Solution > Solve > Current LS to solve the problem

4. A new window and a dialog box will pop up. Take a quick look at the infromation in the window ( /STATUSCommand) before closing it .

5. Click on Ok in the dialog box to solve the problem.

6. Once the problem has been solved you will get a message to say that the solution is done, close this windowwhen you are ready.

Step 9: Examine the Results

1. In the Main Menu select General Postproc > List Results > Nodal Solution > DOF solution >Displacement Vector Sum and click Ok

2. You should get a screen similar to this:

06/06/2016 ANSYS 1D Structural Truss Tutorial : Stepped Bar in Tension - Online Finite Element Analysis ConsultancyService


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06/06/2016 ANSYS 1D Structural Truss Tutorial : Stepped Bar in Tension Online Finite Element Analysis Consultancy Service


3. As expected, displacement in the y-direction (UY) and displacement in the z-direction (UZ) are zero for eachnode.

4. Node 1 has a zero displacement in all directions - this is as expected.

5. Node 2 has moved 0.2198 x 10-4m in the x-direction, Node 3 has moved 0.5833 x 10 -4m and Node 4 has

moved 1.112 x 10-4m

6. The truss element that we have used is quite basic and it is difficult to get stress results directly from it. In

order to access stress results we have to define an element table.

7. Select General Postproc > Element Table > Define Table > Add

8. Edit the options in the dialog box so that they look like this:



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pp y y


9. It is very important to add the "1" after "LS, " !

10. Click on Ok to define the element table.

11. Click on Close to close the other dialog box.

12. Now select General Postproc > Element Table > List Elem Table you should get a listing like this:



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13. This listing gives the stress in each element, for example element 1 has an axial stress of 0.23079 x 10 8 Pa or 23.079 MPa

Step 10: Validate the Results

We will now validate our obtained results against those given the book "Practical Stress Analysis with FiniteElements": by Bryan J. Mac Donald. The results comparison is summarised in the table below:

Result Quantity Ansys Result Result in book % Accuracy

Displacement of Node 1 0 0 100%

Displacement of Node 2 0.2198 x 10-4 m 2.199 x 10-5m 99%



Stress in Element 1 0.23 x 108 Pa 23.07 x 106 Pa 99%

Stress in Element 2 99%


http://www.amazon.com/gp/product/0955578167/ref=as_li_ss_tl?ie=UTF8&camp=1789&creative=390957&creativeASIN=0955578167&linkCode=as2&tag=glasnepubli05-20


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0.33 x 108 Pa 33.32 x 106 Pa

Stress in Element 3 0.60 x 108 Pa 59.72 x 106 Pa 99%

As the table above clearly shows, our finite element results are consistent with those given in the book. The verysmall differences can be accounted for due to computational round offs.

Summary

This tutorial has given you the following skills:

1. The ability to model 1-D problems in ANSYS.2. The ability to adapt element types to specific situations by supressing degrees of freedom (we used a 3D

element as a 1D element).3. The ability to generate finite element models using the direct method (i.e. defining nodes and then defining

elements linking those nodes, as opposed to taking a solid model and dividing it up into elements which wewill do in subsequent tutorials).

4. The ability to define element types, real constants and material parameters for a finite element model.5. The ability to apply boundary conditions and loads to specific nodes in a finite element model.6. The ability to run a simple linear static analysis.7. The ability to list displacement results for each node in the finite element model.8. The ability to create an element table to obtain additional results from a finite element model and to list these

results.

9. Experience in comparing the results obtained from your finite element model with other results and validatingyour results against the other results.

Log File / Input File

Click here for the log file

The log file for this tutorial may also be used as an input file to automatically run the analysis in ANSYS. In order touse this file as an input file save it to your working directory and then select Utility Menu > File > Read inputfrom... and select the file. You should notice ANSYS automatically building the finite element model and issuing allthe commands detailed above.

Quitting ANSYS

To quit ANSYS select Utility Menu > File > Exit... . In the dialog box that appears click on Save Everything(assuming that you want to) and then click on Ok

Click here to return to the list of ANSYS tutorials


https://sites.google.com/site/onlinefiniteelement/ansys-tutorialshttps://sites.google.com/site/onlinefiniteelement/ansys-tutorials/input-files/Tutorial01_input_file.txt?attredirects=0&d=1


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ANSYS 1D Structural Truss Tutorial _ Stepped Bar in Tension - Online Finite Element Analysis...

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