Axial Deformation Coaxial Tube

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This tutorial illustrates how to build and compute a stress analysis of an aluminum

tube with a brass core subjected to an axial load. Finite element models using

solid elements will be analyzed. This example problem was obtained from the

“Mechanics of Materials” 2nd Edition Text – Timothy A. Philpot.

Find additional SIMULIA tutorials and more at www.simulia.com/learning

Determine normal

stresses both in outer

tube and inner core

Finite Element Analysis - Coaxial Tube and Core

(Axial Deformation)

Coaxial Tube and Core (Axial Deformation) © Dassault Systèmes, 2011 SIMULIA Learning Community

Programs Utilized: Abaqus/CAE Student Edition 6.10-2

Problem Description:

This tutorial illustrates how to build and compute a stress analysis of an aluminum tube

with a brass core subjected to an axial load. Finite element models using solid elements

will be analyzed. The pre-processing program used is Abaqus/CAE Student Edition 6.10-

2, and Abaqus command is used for the analysis. The geometry and material properties of

the cantilever beam section are shown in Figure 1 and Table 1, respectively.

[Timothy A. Philpot, “Mechanics of Materials”]

Figure 1. Beam Schematic (MecMovies Example M5.6)

Property Value

Length (m) 0.5

Alum OD (m) 0.030

Alum ID (m) 0.022

Brass D (m) 0.022

E Alum (Pa) 70x109

E Brass (Pa) 105x109

Poisson’s Ratio 0.3

Table 1. Corresponding Dimensions and Material Properties


2

Creating the Model Geometry

Go to the Start Menu and open Abaqus CAE

You may be prompted with an Abaqus/CAE 6.10 Student Edition box (Figure

2). Close this box by clicking the X in the top right hand corner.

Figure 2. Abaqus/CAE 6.10 Student Edition box

Once the Student Edition box is exited, the Abaqus CAE Viewport should look

similar to Figure 3. (Please note the model tree is the series of functions listed on

the left hand side of the viewport, while the module is the list of icons to the right

of the model tree)

Figure 3. Abaqus CAE Viewport

To create the solid model geometry of the tube, a solid circle must be generated

must be generated.

Using the left mouse button, double click Parts in the model tree and the Create

Part (Figure 4a) dialog box appears. Enter a new Name: for the part (SOLID),

Model Tree


3

and under the Base Feature tab choose Solid for Shape and Extrusion for Type.

Change the Approximate size: option from the default 200 to 1. The Create Part

dialog box should look identical to Figure 4b.

Click Continue… and the graphics window will change to a set of gridlines.

Figure 4a. Create Part Dialog Box Figure 4b. Create Part Dialog Box (SOLID)

Click the Create Circle: Center and Perimeter icon in the module. In the

viewport click once with the cursor at coordinates (0 , 0). An indicator shows the

x,y position of the cursor at the top left side of the viewport. Then click with the

cursor again at coordinates (-0.08 , 0). A yellow circle should be visible in the

viewport (Figure 5). (Please note, when the circle is created, the feature is exited

by clicking the Esc key on your computer keyboard.)

Figure 5. Circle Sketch


4

NOTE: If you accidentally create an unwanted circle, you can select Edit >

Delete from the dropdown menu at the top of the screen and use the mouse to

select the entity to delete.

Next click the Sketcher Options icon in the module and the Sketcher

Options dialog box will appear. Click the Dimensions tab and change the

Decimal places: option to 4. The Sketcher Options dialog box should look

similar to Figure 6.

Figure 6. Sketcher Options Dialog Box

Click OK.

Click the Add Dimension icon in the module. Click anywhere on the

circumference of the circle, drag the cursor away, and click. This will reveal the

arbitrary radius of the circle in red.

At the bottom of the viewport enter a New dimension: for the radius. Enter 0.015

in the box since the diameter is 0.03 m. Hit Enter. The correct circle dimension

will update in the viewport.

Press Esc on the computer keyboard to exit the dimensioning tool.

Click Done.

The Edit Base Extrusion dialog box will appear. Change Depth: to 0.5 and click

OK. Sketch mode will automatically be exited, and the model geometry should

look identical to the beam shown in Figure 7.


5

Figure 7. Final Model Geometry

Partitioning the Geometry

The model will be partitioned into two sections, a hollow outer tube, and a solid central

core. To do this, click the Partition Face: Sketch icon in the model tree. Click the

circular cross section of the beam at one end. If this is done correctly, the circle will turn

red.

Click Done.

Next you will be prompted to Select an edge or axis that will appear vertical and on

the right. Click anywhere on the circumference of the circle that you just selected as a

face.

If this procedure has been done correctly, you will automatically be entered into the

sketch mode. Using the same center point as the previous circle, draw a circle of radius

0.011 using the same Create Circle: Center and Perimeter, and Dimensioning tool. Be

sure that the 1 center and 2 perimeter points all lay along the same horizontal line (Figure

8).


6

Figure 8. Partitioned Sketch

Press Esc on the computer keyboard to exit the Dimensioning tool.

Click Done.

The sketching mode will automatically be exited and the three dimensional geometry will

appear in the part module. Notice that the face has been partitioned and an inner circle

with the appropriate radius can be seen.

At the top of the viewport click the Render Model: Wireframe icon and the model

view will change such that only the edges are visible. Notice how the partition that was

just created did not extrude through the whole model.

Next, we will extrude the inner circle edge through the length of the beam; this is the

final partition and will create an inner core and outer tube.

Click the Create Datum Axis: Principal Axis icon in the module. At the bottom of

the viewport click Z-Axis. A yellow datum axis will appear along the beams length. Press

Esc on the computers keyboard to exit this tool.

Finally click and hold the Partition Cell: Define Cutting Plane icon and a series of

partitioning icons will appear. With the mouse button still suppressed, hover the cursor

over the Partition Cell: Extrude/Sweep Edges icon and let go of the mouse button.

Now that the correct partitioning tool has been activated, click the circumference of the

inner circle that was drawn using the first partitioning tool. If this has been done correctly

the circumference will turn from black to red.

Click Done.

You will then be prompted How do you want to sweep?, click Extrude Along

Direction.

Click the yellow datum axis that was created in the previous steps.

Click OK.


7

Click Create Partition. The model should now look similar to that in Figure 9.

Figure 9. Partitioned Geometry (Wireframe)

To return to the shaded view of the model click the Render Model: Shaded icon at

the top of the viewport.

Defining Material Properties

Two materials will be created for this model, Aluminum, and Brass. To define material

properties for this model, double click on Materials in the model tree and the Edit

Material dialog box will appear (Figure 10a). Enter a Name: for the material (ALUM),

and click the Mechanical tab, highlight Elasticity and click Elastic. Enter values of

Young’s Modulus = 70E09 Pa, and Poisson’s Ratio = 0.3. After the material properties

have been entered, the Edit Material dialog box should look identical to Figure 10b.

Figure 10a. Edit Material Dialog Box Figure 10b. Edit Material Dialog Box (ALUM)


8

Next, create another material named BRASS with Young’s Modulus = 105E09 Pa, and

Poisson’s Ratio = 0.3 (Figure 11).

Figure 11. Final Edit Material Dialog Box (BRASS)

Click OK.

Please note there is no dropdown menu or feature in Abaqus that sets specific units. All

of the dimensions have been input in meters; therefore the respective Young’s Modulus

units should be entered in Pa (Pascals). The units chosen for the definition of the

material properties should be consistent and dictate what units should be used for the

dimensions of the structure.

At this point in preprocessing, the model should be saved. Click File then click Save.

Name the file Philpot_Example_M5_6. The file will save as a Model Database (*.cae*)

file. It may be of interest to save the file after each section of this tutorial.

Creating Sections

Two solid sections will be created for this model. To create a solid section in

Abaqus, double click Sections in the model tree and the Create Section dialog

box will appear (Figure 12a). Enter a Name: for the section (ALUM), and ensure

Solid is selected under the Category Tab, and Homogeneous under the Type tab.

Your Create Section dialog box should look identical to that in Figure 12b.

Click Continue…

Figure 12a. Create Section Dialog Box Figure 12b. Create Section Dialog Box (ALUM)


9

The Edit Section dialog box will then appear where a Material can be prescribed

for this section. Click the dropdown box next to Material: and select ALUM.

The Edit Section dialog box should look similar to that in Figure 13.

Figure 13. Edit Section Dialog Box

Click OK.

Using the same procedure, create another solid homogenous section named

BRASS and select BRASS in the Material: dropdown in the Edit Section dialog

box.

Assigning Sections

Now that the solid sections have been created, they can be assigned to the geometry. In

the model tree, click the + to the left of the Parts (1) icon, this will further expand the

model tree’s options. Next, click the + to the left of the part called SOLID, further

expanding the model tree (Figure 14).

Figure 14. Model Tree Expansion (Parts)

After the model tree has been expanded, double click Section Assignments. Use the

cursor to click the inner circle at the end of the beam. If this has been done correctly, the

outline of both of the inner circle’s circumference will change to the color red. Click

Done.

The Edit Section Assignment dialog box will appear. Click the dropdown menu next to

Section: and select BRASS. The Edit Section Assignment dialog box should look

similar to Figure 15.


10

Figure 15. Edit Section Assignment Dialog Box (BRASS)

Click OK. The inner core section of the model now should now turn to a turquoise color

(Figure 16).

Figure 16. Assigned Section

Next, the ALUM section will be assigned to the outer tube. Click the cross

section face of the outer tube and the inner and outer diameter will turn a red

color.

Click Done. The Edit Section Assignment dialog box will appear, change the

Section: dropdown menu to ALUM.

Click OK. The complete model should now be a turquoise color.

To ensure that each section has been assigned to the appropriate geometry, click

the Color Code dropdown menu at the top of the viewport (Figure17).

Figure 17. Color Code


11

Change the dropdown menu to Sections and the model will be color coded with

respect to the assigned sections (Figure 18).

Figure 18. Assigned Sections

Click Done.

Creating a Mesh

To create a mesh for the model geometry, double click Mesh (Empty) in the

model tree.

Before a mesh can be generated, the solid model will be further partitioned so that

a finer mesh can be obtained at the midpoint of the beam. The refined mesh area

is where the stress results will be taken. Note that this part of the procedure is

completed because of node limitations on Student Edition of the software. If the

nodal limitations were higher, a mesh could be generated without refinement in

some areas.

The first partition that will be created will be along the beams length. Click the

Create Datum Plane: Offset From Principal Plane icon in the module. At

the bottom of the viewport click YZ Plane and enter an offset of 0.0 hit Enter.

Next the geometry will be partitioned using the datum plane. Click and hold the

Partition Cell: Extrude/Sweep Edges icon and a series of partitioning icons

will appear. With the mouse button still suppressed, hover the cursor over the

Partition Cell: Use Datum Plane icon and let go of the mouse button.


12

Now that the correct partitioning tool has been activated, hold shift on the

keyboard and click the inner circle (grey color) and outer circle (green color) of

the model.

Click Done.

When prompted to Select a datum plane, click the YZ datum plane that was just

created and click Create Partition. The model should look similar to Figure 19.

Figure 19. First Partition

Two datum planes will be created to partition the part. Click the Create Datum

Plane: Offset From Principal Plane icon in the module. At the bottom of the

viewport click XY Plane and enter an offset of 0.20 hit Enter. Click XY Plane

again and enter an offset of 0.30 hit Enter. If this procedure has been done

correctly the model should look similar to Figure 20.


13

Figure 20. Datum Planes

Click Esc to exit the Datum Plane tool.

Next the geometry will be partitioned using the datum planes. Click the Partition

Cell: Use Datum Plane icon if it is not already selected.

Now that the correct partitioning tool has been activated, draw a box around the

whole model. If this has been done correctly all of the available edges will turn

red.

Click Done.

Next, click one of the datum planes and click Create Partition at the bottom of

the viewport. A partition should be created at the respective datum plane.

Finally draw a box around the whole model, all of the available edges will turn

red.

Click Done.

Click the datum plane that has not been selected and click Create Partition. Up

to this point the model should look similar to Figure 21.


14

Figure 21. Partitioned Geometry

Click Done.

The first step in creating a mesh is to seed the part edges. Click the Seed Edges

icon in the mesh module.

To easily seed the model edges, a YZ view would be ideal. At the top toolbar,

click View and hover the cursor over Toolbars if there is not a check mark to the

left of the Views option, click it and a Views toolbar will appear (Figure 22).

Figure 22. Views Toolbar

Click the YZ icon in the toolbar to rotate the model into that respective plane.

Draw a box around the portion of the model corresponding to Box 1 shown in

Figure 23. Note its respective locations along the length of the beam.


15

Figure 23. Boxes

Click Done.

The Local Seeds dialog box will appear. In the Bias option select Single and note

that the 4 red arrows are pointing towards the midpoint of the beam. This is the

direction of the bias. If the arrows are pointing in the opposite direction the Flip

bias: feature can be used to change the direction.

In the Sizing Controls option change the Minimum size: to 0.007 and the

Maximum size: to 0.07 (Figure 24).

Figure 24. Local Seeds Dialog Box

Click OK. Small purple seeds will appear on the selected edges.

Next, draw a box around the portion of the model corresponding to Box 2 shown

in Figure 23. Click Done.

The Local Seeds dialog box will appear. The Bias should already be set to Single,

and the Minimum size: to 0.007 and Maximum size: to 0.07 (Figure 24). The

red arrows may be pointing to the right, if so, click Select… next to the Flip bias:

Box 1 Box 2

Box 3


16

option. Click Done. The arrows should now be pointing to the left, towards the

midpoint of the beam.

Click OK.

Finally the mid section of the beam will be evenly seeded. Draw a box around the

portion of the model corresponding to Box 3 shown in Figure 23. Click Done.

The Local Seeds dialog box will appear. Ensure that the Bias is set to None.

Enter a value of 0.007 for the Approximate element size: option (Figure 25).

Figure 25. Local Seeds Dialog Box (0.007)

Click OK. The model will now appear to be seeded with purple points along the

selected edges (Figure 26).

Figure 26. Seeded Geometry

Click Done.


17

The part is now ready to be meshed. In the mesh module, click the Mesh Part

icon . At the bottom of the viewport you will be prompted if it is OK to mesh

the part? Click Yes.

If this procedure was done correctly, a visible mesh will appear (Figure 27).

Rotate the part back into an isometric view by clicking the Apply Iso View icon

.

Figure 27. Final Meshed Geometry

Creating an Instance

Now that the part has been meshed, it can be brought into the assembly. To do

this task, click the + to the left of Assembly in the model tree. The model tree will

expand and should look identical to Figure 28.

Figure 28. Model Tree Expansion (Assembly)

Double click on the Instances icon in the expanded model tree. This feature will

allow multiple parts to be brought into the assembly. The Create Instance dialog

box will appear (Figure 29).


18

Figure 29. Create Instance Dialog Box

The SOLID part is selected by default because only one part has been created for

this tutorial. If multiple parts had been created, then this step would allow them to

be entered into the assembly.

Click OK. If this step was done correctly the model should turn a blue color

(Figure 30).

Figure 30. Create Instance

Creating a Step

A Step is where the user defines the type of loading, e.g. Static or Dynamic, and

defines the boundary conditions, e.g. support constraints and forces.

In the model tree, double click the Steps icon. The Create Step dialog box will

appear (Figure 31a). Create a Name: for the step called LOADING. Under

Procedure type choose Static, General. The Create Step dialog box should look

identical to Figure 31b.


19

Figure 31a. Create Step Dialog Box Figure 31b. Create Step Dialog Box (STATIC)

Click Continue…, and the Edit Step dialog box will immediately appear. Accept

all default options and click OK. The Edit Step dialog box should look similar to

that in Figure 32.

Figure 32. Edit Step Dialog Box

Apply Constraint Boundary Conditions

Boundary conditions will be defined which will simulate a fixed (also known as

“clamped”) beam at one end.

Double click BCs in the model tree and the Create Boundary Condition dialog

box will appear (Figure 33a). Create a Name: for the boundary condition called

FIXED, and under the Step drop downvchoose LOADING. Under the Category

option choose Mechanical, and choose Symmetry/Antisymmetry/Encastre

under the Types for Selected Step option. The Create Boundary Condition

dialog box should look identical to that in Figure 33b.


20

Figure 33a. Create BC Figure 33b. Create BC (FIXED)

Click Continue…

While holding the Ctrl and Alt keys on the computer keyboard click and drag the

cursor to rotate the part in the viewport. Another way to rotate the part would be

to hit F3 on the computer keyboard to enter the rotation tool. When the rotation

has been completed press Esc on your keyboard to exit the tool.

Rotate the part such that the right end of the beam (which was previously hidden

due to the isometric view) is in visible in the viewport. Using the cursor, hold

shift on the computer keyboard and click the face of the model which is to be

constrained. Four total sections of this face must be clicked due to the partitions

that were created earlier. If this is done correctly selected surface will turn from a

blue to purple color (Figure 34).

Figure 34. Selected Face

Click Done.


21

The Edit Boundary Condition dialog box will immediately appear. Click

ENCASTRE (U1=U2=U3=UR1=UR2=UR3=0). The Edit Boundary Condition

dialog box should look identical to that in Figure 35.

Figure 35. Edit Boundary Condition Dialog Box (FIXED)

Click OK. If this procedure has been done correctly, the model should look

similar to that in Figure 36.

Figure 36. Beam (w/ BC’s)

Apply a Load Boundary Condition

A 30 kN load will be applied to the beam in the –Z direction acting as a

compressive axial load. Double click Loads in the model tree and the Create

Load dialog box will appear (Figure 37a). Create a Name: for the load called

PRESSURE and ensure that LOADING is selected for the Step. Choose

Mechanical under the Category option and Pressure under the Types for


22

Selected Step option. The Create Load dialog box should look identical to that

in Figure 37b.

Figure 37a. Create Load Dialog Box Figure 37b. Create Load (PRESSURE)

Click Continue…

While holding Shift on the computer keyboard click the surfaces on the opposite

end of the beam as the constraint boundary condition. If this is done correctly

selected surface will turn from a blue to purple color (Figure 38).

Figure 38. Selected Faces for Pressure Application

Click Done. The Edit Load dialog box will immediately appear (Figure 39a).

Enter a value of 4.244E07 into the Magnitude: option. This entry will apply a

pressure over the selected area equivalent to a load of 30,000 N. The Edit Load

dialog box should look identical to that in Figure 39b.


23

Figure 39a. Edit Load Dialog Box Figure 39b. Edit Load Dialog Box (30 kN)

Click OK. If this step was done properly, then small purple arrows will appear on

the faces where the load was applied pointing in the -Z direction (Figure 40).

Figure 40. 30,000-N Load

Creating a Job

To create a job for this model, double click the Jobs icon in the model tree. Up to

this point, you have been preprocessing the model. A job will take the input file

created by the preprocessor and process the model, i.e. perform the analysis.

In the Create Job dialog box, create a Name: for this job called

PHILPOT_EXAMPLE. Blank spaces are not allowed in a job name. Thus the

use of the underscore in the name. The Create Job dialog box should look

identical to that in Figure 41.


24

Figure 41. Create Job Dialog Box (PHILPOT_EXAMPLE)

Click Continue…

The Edit Job dialog box will immediately appear (Figure 42).

Figure 42. Edit Job Dialog Box

Accept the default values and click OK.

Setting the Work Directory

To ensure that the input files write to the correct folder, setting the work directory

must be accomplished. At the top of the screen, click File and in the dropdown

menu click Set Work Directory… (Figure 43).


25

Figure 43. Set Work Directory

The Set Work Directory screen will immediately appear (Figure 44). Click

Select… and use standard Windows practice to select (and possibly create) a

subdirectory.

Figure 44. Set Work Directory (FOLDERS)

Click OK.

Click OK.

Writing the Input File (.inp)

To write the input file of the job that was created, first click the + next to the

Jobs(1) icon in the model tree.

Right click the job called PHILPOT_EXAMPLE and click the Write Input

option. This choice will write an input file (.inp) of this model to the work

directory.

It may be helpful to go to the folder on the computer to which the work directory

is set to ensure that the input file was written there.


26

Model Analysis (Abaqus Command)

Method #1

Go to the Start Menu and open Abaqus Command

Abaqus is set to a default directory (Example C:\>). To change directories in the

Abaqus Command type the directory of choice followed by a colon (D:) then hit

Enter.

To access a specific directory within that drive type cd followed by the specific

folder name in that directory (e.g., cd users) then hit Enter.

Now that the correct directory has been sourced in the command window type

abaqus inter j=PHILPOT_EXAMPLE and then hit enter. (If you are asked Old

job files exist. Overwrite? (y/n): type y then hit Enter).

If the job has completed successfully the Abaqus prompt should look similar to

Figure 45.

Figure 45. Abaqus Command Prompt (COMPLETED)


27

Method #2

An alternative method for submitting an *.inp file for processing by Abaqus can

be accomplished with Abaqus CAE

Right click the job called PHILPOT_EXAMPLE and click the Submit option. If

you see a warning (Figure 46) Click OK. The intent of this warning is to prevent

the user from accidentally overwriting a previously completed analysis with the

same name.

Figure 46. Warning Message

The model will now be submitted for analysis by Abaqus and the progress can be

viewed in the status window at the bottom of the screen (Figure 47).

Figure 47. Abaqus Progress

Postprocessing using Abaqus CAE

After the analysis has successfully completed in the Abaqus Command window

using Method #1 or using Method #2, return to view the Abaqus CAE viewport.

Because the last step of creating the model was to create a job/write (and possibly

submit) an input file, the PHILPOT_EXAMPLE job should still be highlighted

in Abaqus CAE model tree. Right click the PHILPOT_EXAMPLE and then

click Results.

If this selection was done correctly, the model should turn to a green color and the

beam will have rotated to an isometric view (Figure 48).


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Figure 48. Analysis Results Isometric View

To view the deformed shape of the model, click the Plot Contours on Deformed

Shape icon in the Visualization module. The model should look similar to

that in Figure 49.

Figure 49. Deformed Shape


29

Obtaining Stress Values in Elements

Upon viewing the deformed contour of the geometry, Abaqus CAE defaults to

view Von Mises Stress. To obtain the stresses in an element click Mises in the

Field Output dialog box at the top of the viewport (Figure 50).

Figure 50. Field Output Dialog Box

A dropdown menu will appear and click S33. By doing this, the correct stress

component will be viewed for the results. Now that the correct type if stress is

being viewed, the individual elements can be queried.

At the top toolbar click Tools then click Query… The Query dialog box will

appear, under the General Queries option click Element. (Figure 51).

Figure 51. Query Dialog Box (Element)

Using the cursor click any of the individual solid elements in the model in the

refined mesh area and the S33 value will be displayed at the bottom of the

viewport in the message area (Figure 52).

Figure 52. Message Area (Query Element)

The stress was obtained for an element that was in the outer aluminum tube of the

model. However, stress values are desired for the inner brass core. Click the

Activate/Deactivate View Cut icon in the module. The model should

automatically split in half such that the elements of the inner core are visible.

While the Query dialog box is still open, click on any of the elements in the

refined area of the brass core. The message area will be updated with the stress

value of the currently selected element.


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Conclusion

Save the file by doing either File > Save or clicking the disk icon (Figure 53).

Figure 53. Disk Icon (Saving)

Close Abaqus CAE: File > Exit or Ctrl+Q

This completes the Finite Element Analysis Coaxial Tube and Core (Axial

Deformation).

Download tutorials and more in the SIMULIA Learning Community:

www.simulia.com/learning

Content Provided by: Philpot, Timothy A., Mechanics of Materials, 2nd ed., John Wiley & Sons, New Jersey, 2011 Tutorial Created by: Dimitri Soteropoulos SIMULIA

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Axial Deformation Coaxial Tube

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