Appendix

Using ANSYS workbench for structural analysis

A.1 Introduction

The strength design of machines and structures has long been made based on the design by formula or rule approach, but it has been reported that the application of the design by analysis allows removing the unnecessary conservatism caused by applying the design by formula approach [1]. For structural components that have complex geometries and/or geometric discontinuities, i.e. stress raisers, the elementary theory of elasticity and/or the mechanics of materials is no longer effective for evaluating stress distributions in such components. Thus the design by formula approach tends to bring about excessive conservatism.

Owing to the astonishing development of computer technology, however, FEM has markedly increased its speed and performance to become a useful tool for strength design of machines and structures. In addition, commercial FEM software has become more and more user-friendly. Strength design engineers used to ask analysis specialists to make stress analyses for their strength designs, whereas they have now begun to use FEM as one of their design tools. They can use CAD data directly for FEM analyses. They can make combined analyses, e.g., fluid-structure coupling analyses, without much difficulty in their daily design activities.

ANSYS Workbench is powerful platform software that is the backbone for an integrated, comprehensive simulation system. This chapter describes how to operate ANSYS Workbench to carry out structural or stress analyses of a fundamental type of component parts for demonstrating elementary use of the software. The example problem to analyse in this chapter is not a multiphysics one, but it provides a good example for ANSYS Workbench Mechanical (AWM). The result obtained by the present analysis is compared with that by an empirical stress concentration factor diagram based on the photo-elasticity, showing a good agreement between the two.

A.2 Problem description: A stepped round bar subjected to tension

Perform an FEM analysis of a 3D stepped round bar subjected to an applied tension at the free end and clamped to the rigid wall at the other end, as described below. Calculate the stress concentration at the foot of the fillet of the bar and the tensile stress distribution on a cross section of the bar.

  • Geometry: lengths l1 = 50 mm, l2 = 50 mm, diameters D = 40 mm, d = 20 mm, fillet radius ρ = 3 mm
  • Material: mild steel having Young's modulus E = 200 GPa and Poisson's ratio ν = 0.3.
    The value of Young's modulus is the datum registered as that of a structural steel in the standard database of the ANSYS Workbench and is slightly lower than that used in Chapter 3.
  • Boundary conditions: A stepped bar is rigidly clamped to a wall at the left end and subjected to a uniform tensile stress of σ0 = 100 MPa at the right free end, as shown in Fig. A.1.
Fig. A.1
Fig. A.1 Stepped round bar subjected to a uniform tensile stress σ0.

A.3 Starting workbench

Double-click the ANSYS Workbench shortcut icon to start the workbench. The Unsaved Project – Workbench window as well as the Getting Started window open, as shown in Fig. A.2.

  • [COMMAND]    Windows Start Menu → ANSYS 17.0 → Workbench 17.0
Fig. A.2
Fig. A.2 ANSYS Workbench and Getting Started windows.

After reading ‘Welcome to ANSYS Workbench!’, click the close button in the upper right corner of the Getting Started window.

Fig. A.3 shows the components of the Workbench window. Click the Static Structure icon in the Analysis Systems toolbox to display the Static Structural window in the Project Schematic window, as shown in Fig. A.3. The symbols in the third row of the cells in the Static Structural window indicate the statuses of the cells as shown in Table A.1. The status symbol of the checkmark for the Engineering Data cell in Fig. A.4 indicates that the material of the stepped round bar to be analysed has been selected and is ready to be shared with other cells such as the Model and Solution cells.

Fig. A.3
Fig. A.3 Components of the ANSYS Workbench window.
Fig. A.4
Fig. A.4 Engineering Data cells in the Project Schematic window.

Table A.1

Symbols for cell statuses and their meanings
SymbolMeaningDetailed explanation
Image 1Attention requiredImmediate action is required for the cell, or a user cannot proceed further
Image 2UnfulfilledThe previous cells do not have sufficient data
Image 3Up to dateThe cell is up to date and the data in the cell is ready to be shared with other cells
Image 4Refresh requiredThe data in the previous cells have been changed since last update. The cell needs to be refreshed
Image 5Update requiredThe input data of the cell has been changed and the output data needs to be updated
Image 6Input changes pendingThe cell is locally updated but may change

Table A.1

Clicking the Engineering Data cell shown in Fig. A.4 launches the A2: Engineering Data screen, as shown in Fig. A.5. Click and highlight the A3 cell for the structural steel listed in the Outline of Schematic A2: Engineering Data window. The structural steel cell is selected as the material for the stepped round bar to be created and analysed.

Fig. A.5
Fig. A.5 Tool boxes and property tables stored in the A2: Engineering Data screen.

The status symbol for the Geometry cell is the solid question mark as shown in Fig. A.6, meaning the geometry data of the model to carry out the analysis is required (see Table A.1). Geometry data can be created in two ways: (1) by creating the model in the Design Modeler (DM) window of ANSYS Workbench; or (2) by importing a CAD model created by commercial 3D CAD applications. Here we create the same stepped round bar model as that analysed in Chapter 3 in the DM window.

Fig. A.6
Fig. A.6 Project Schematic window displaying various standalone systems in it.

A.4 Creation of a 3D analysis model using the design modeller

Click the Geometry cell to display the DM window as shown in Fig. A.7; this depicts the components of the DM window. The DM window can be used in two basic modes of creating a model: (1) the sketching mode that is used to draw 2D sketches; and (2) the modelling mode that converts 2D sketches into 3D models. First, sketch a 2D stepped plate on, say, the XY plane, then rotate the plate about the X-axis to get the 3D stepped round bar.

Fig. A.7
Fig. A.7 Components of the Design Modeler (DM) window.

Click the XYPlanes branch in the Tree Outline window to display the O-XYZ Cartesian coordinate system in the Graphics window, as shown in Fig. A.8.

Fig. A.8
Fig. A.8 O-XYZ Cartesian coordinates in the Graphics window of the DM.

Click the Look At Face/Plane/Sketch icon [A] in Fig. A.9, or the rightmost icon, in the top tool bar of the window to display the XY plane, as shown in Fig. A.9. Click the Sketching tab of the Sketching Toolboxes window to display menus, as shown in Fig. A.10. Click the Grid button in the Settings window and check the Show in 2D and the Snap boxes to display the grid in the DM window. Select Millimeter as the unit to use in the Units menu in the menu bar, as shown in Fig. A.11. The grid spacing is set to 10 mm. The spacing of the grid is automatically changed according to the scaling of the display. The display can be zoomed in and out by rolling the middle mouse wheel forward and backward, respectively. Click the Pan icon [A] in the tool bar, as shown in Fig. A.10, and the arrow cross appears in the DM window to execute the translation movement of the XY coordinates in all directions.

Fig. A.9
Fig. A.9 XY plane displayed in the Graphics window and Look At Face/Plane/Sketch icon [A] in the Tool Bar of the Design Modeler window.
Fig. A.10
Fig. A.10 Menus in the Settings menu in the Sketching Toolboxes window.
Fig. A.11
Fig. A.11 Grids of 10 mm spacing in the Graphics window of the DM.

Click the Draw and the Line buttons. Click at the beginning of a horizontal line at a point of (0 mm, 20 mm) and click again at the end point of (50 mm, 20 mm), as shown in Fig. A.12. Continue drawing vertical and horizontal lines until the drawing of the outline of the stepped plate is completed, as shown in Fig. A.13.

  • [COMMAND]    Sketching Toolboxes → Dimensions → Horizontal/Vertical
Fig. A.12
Fig. A.12 A horizontal line of 50 mm in length drawn on the XY plane in the Graphics window.
Fig. A.13
Fig. A.13 Outline of the stepped plate drawn on the XY plane in the Graphics window.

Click the horizontal or the vertical button in the Dimensions menu and click a horizontal or a vertical line of the lines drawn. The colour of the line clicked is changed into yellow. Hold down the button on the line and drag the line to a convenient location. The dimension and the extension lines are generated for the line designated and the dimension line is named H1, for example, as shown in Fig. A.14. The H or the V sign indicates that the line is horizontal or vertical. The number following the sign H or V indicates the order of drawing a horizontal or the vertical line. In order to edit the dimensions of the lines to give them the desired values, click a dimension value of a line in the Details View window as shown in Fig. A.14, enter the change, and press the return key.

  • [COMMAND]    Sketching Toolboxes → Modify → Fillet; Radius: 3 mm
Fig. A.14
Fig. A.14 Dimension and extension lines for the stepped plate drawn on the XY plane in the Graphics window.

Click the Modify and the Fillet buttons. Enter 3 mm in the Radius box and pick the vertical and the horizontal lines that form the interior corner of the joint of the stepped plate, as depicted in Fig. A.15. Click the Revolve icon in one of the tool bars and pick the sketch of the stepped plate in the DM window. Click the Not selected cell for the Geometry cell of the Details of Revolve 1 table in the Details View window to display the Apply and the Cancel buttons. Click the Apply button for the Geometry cell. The Apply and the Cancel buttons are changed into the name of the geometry, i.e., Sketch 1 selected to revolve. Click the Not selected cell for the Axis cell to display the Apply and the Cancel buttons. Pick the x-axis about which the 2D stepped plate is to be revolved, as shown in Fig. A.16. Push the Apply button and the cell is changed into 2D Edge. Click the Generate icon in one of the tool bars. The 2D stepped plate is transformed into the stepped circular cylindrical bar, as shown in Fig. A.17.

Fig. A.15
Fig. A.15 Circular fillet of 3 mm in radius set at the interior corner of the joint of the stepped plate.
Fig. A.16
Fig. A.16 Giant 3D arrow indicating that the x-axis is the axis of revolution for creating the stepped round bar from the stepped plate.
Fig. A.17
Fig. A.17 Stepped round bar created by revolving the stepped plate around the x-axis.

Click the Workbench icon in the task bar to return to the Workbench window to confirm that the solid question mark is changed for the Up to date mark, as shown in Fig. A.18. Double-click the Model cell marked by the Refresh required symbol, as shown in Fig. A.19. The Static Structural – Mechanical window appears, as shown in Fig. A.20. The stepped circular cylindrical bar is displayed in the window and the symbol by which the Model cell is marked turns into the Update required symbol, as shown in Fig. A.20. The software is switched from the DM to the Mechanical for the static structural analysis, or the static stress analysis of the stepped circular cylindrical bar. Fig. A.20 also shows the components of the ANSYS Workbench Mechanical window.

Fig. A.18
Fig. A.18 Selection of the Geometry cell in the Project Schematic window.
Fig. A.19
Fig. A.19 Selection of the Model cell in the Project Schematic window.
Fig. A.20
Fig. A.20 Components of the ANSYS Workbench Mechanical (AWM) window.

Note: If you already have a model to analyse with ANSYS Workbench, the modelling process described in Section A.4 can be omitted. Instead, the model to analyse is imported by right-clicking the Geometry cell, as shown in Fig. A.21. The image file formats that can be imported into the ANSYS Workbench are IGES, Parasolid, STEP, etc.

Fig. A.21
Fig. A.21 Hierarchical menu of the Model cell for importing a CAD file of the 3D stepped bar model.

A.5 Stress analysis of a stepped round bar subjected to uniform tension

A.5.1 Finite-element discretisation of the round bar volume

The ANSYS Workbench Mechanical (AWM) is an object-oriented software. The hierarchical structure of the command objects are displayed in the Tree Outline window, as shown in Fig. A.22. The folder-like object or the branch named ‘Model (A4)’ represents a stepped round bar which has properties like Geometry, Coordinate System, Mesh, Static Structural responses, etc. as lower branches. The label ‘A4’ in the parenthesis indicates the ID of the Geometry cell (see Fig. A.6). Specific contents of each property are stored in a respective branch. Thus, the analytical procedures are reduced to adding lower branches which store detailed contents of the above-mentioned properties. Changing a command involves just deleting the branch and adding a new object which stores desired contents.

Fig. A.22
Fig. A.22 Hierarchical structure of the command objects displayed in the Tree Outline window.

Confirm that the units are mm, t, N, s, mV, and mA by clicking the Units menu in the menu bar. Set the size of finite elements before discretising the stepped bar model as displayed in Fig. A.23. As for the other properties of the elements, the standard settings for the elements used in the present analysis are adopted as described in the Defaults table in the Details of ‘Mesh’ window. Among the items listed in the table, for example, the description that the Element Midside Nodes are Program Controlled means that the higher order elements having midside nodes are used by default for linear elastic stress analyses. The type of elements need not be selected.

  1. (1) Meshing
  • [COMMAND]    Tree Outline Window → Project → Model (A4) → Mesh
  1. 1. The category of the Context Tool Bar is changed from Model to Mesh.
  • [COMMAND]    Context Tool Bar (Mesh) → Mesh Control → Sizing
  1. 1. The Sizing branch is created under the Mesh branch.
  2. 2. Enter 2 mm in the Element Size cell of the Definition table in the Details of ‘Sizing’ window, as shown in Fig. A.23.
  3. 3. Click the Select Body icon [A] in Fig. A.23 and place the mouse cursor on the stepped bar model and click the left button of the mouse. The whole body of the model is selected for element sizing, as shown in Fig. A.24.
  4. 4. Click the No Selection cell for the Geometry in the Scope table to display the Apply and the Cancel buttons.
  5. 5. Click the Apply button. The colour of the stepped bar model changes from green into purple to indicate that the whole body of the model is selected to be meshed, as shown in Fig. A.25.
  • [COMMAND]    Context Tool Bar (Mesh) → Mesh → Generate Mesh
  1. 1. The stepped round bar model is meshed, as shown in Fig. A.26.
Fig. A.24
Fig. A.24 Whole body of the present stepped bar model selected for element sizing.
Fig. A.25
Fig. A.25 Whole body of the present stepped bar model selected for finite-element discretisation.
Fig. A.26
Fig. A.26 Whole body of the present stepped bar model discretised by finite elements.
Fig. A.23
Fig. A.23 Scope and the Definition tables in the Details of ‘Sizing’ window.

A.5.2 Imposition of boundary conditions

  1. (1) Imposing constraint conditions on the left-end face of the stepped round bar
  • [COMMAND]  Tree Outline Window → Project → Model (A4) → Static Structural (A5)
  1. 1. Select the Static Structural (A5) branch [A] in Fig. A.27, and the stepped bar model is changed into the volume of the bar model without mesh. The label ‘A5’ in the parenthesis indicates the ID of the Setup cell (see Fig. A.6).
  2. 2. The Context Tool Bar is changed from Mesh to Environment.
  3. 3. Click the Rotate icon [B] to rotate the model and display the left-end face to which the displacement constraint is to be applied, as shown in Fig. A.27.
  • [COMMAND]    Context Tool Bar (Environment) → Supports → Fixed Support
  1. 1. Click the Select Face icon [C], place the mouse cursor on the left-end face of the stepped bar model, and click the left button of the mouse. Select the left-end face of the model to be fixed, as shown in Fig. A.27.
  2. 2. The colour of the left-end face of the stepped bar model turns green.
  3. 3. Click the 1 Face cell for the Geometry, and display the Apply and the Cancel buttons.
  4. 4. Click the Apply button in the Geometry cell of the Scope table in the Details of ‘Fixed Support’ window, as shown in Fig. A.28.
  5. 5. The colour of the left-end face of the stepped bar model changes from green into purple to indicate that the left-end face of the model is selected to be fixed.
  6. 6. The Fixed Support branch is created under the Static Structural (A5) branch.
  7. (2) Applying uniform tensile stress to the right-end face of the stepped round bar model
  • [COMMAND]    Context Tool Bar (Environment) → Loads → Pressure
  1. 1. Click the Rotate icon to rotate the model and display the right-end face to apply a pressure of 100 MPa to the face, as shown in Fig. A.29.
  2. 2. Click the Select Face icon, place the mouse cursor on the right-end face of the stepped bar model, and click the left button of the mouse. Select the right-end face of the model to be subjected to pressure, as shown in Fig. A.29.
  3. 3. The colour of the right-end face of the stepped bar model turns green.
  4. 4. Enter -100 MPa in the Magnitude cell of the Definition table in the Details of ‘Pressure’ window, as shown in Fig. A.29.
  5. 5. Click the 1 Face cell for the Geometry, and display the Apply and the Cancel buttons.
  6. 6. Click the Apply button.
  7. 7. The colour of the right-end face of the stepped bar model changes from green into red to indicate that the right-end face of the model is subjected to pressure, or uniform tensile stress, as shown in Fig. A.30.
  8. 8. The Pressure branch is created under the Static Structural (A5) branch.
Fig. A.27
Fig. A.27 Left-end face of the present stepped bar model to which the displacement constraint is to be applied.
Fig. A.28
Fig. A.28 Left-end face of the present stepped bar model selected for fixed support.
Fig. A.29
Fig. A.29 Right-end face of the present stepped bar model selected to be subjected to pressure, or uniform tensile stress.
Fig. A.30
Fig. A.30 Right-end face of the present stepped bar model subjected to pressure, or uniform tensile stress.

A.5.3 Solution procedures

Click the Solution (A6) branch to choose the solutions to obtain, e.g., total deformation, von Mises equivalent stress and a user defined result, or the tensile stress in the x-axis direction. The label ‘A6’ indicates the cell ID.

  • [COMMAND]    Context Tool Bar (Solution) → Deformation → Total
  • [COMMAND]    Context Tool Bar (Solution) → Stress → Equivalent (von Mises)
  • [COMMAND]    Context Tool Bar (Solution) → User Defined Result

After the three commands above are performed, the corresponding branches (Total Deformation, Equivalent Stress, and User Defined Result) are created under the Solution (A6) branch, as shown in Figs A.31–A.33, respectively.

Fig. A.31
Fig. A.31 Total Deformation button of the Deformation menu in the Context Tool Bar (Solution); the Total Deformation branch is not yet created under the Solution (A6) branch.
Fig. A.32
Fig. A.32 Equivalent stress (von Mises) button of the Stress menu in the Context Tool Bar (Solution); the Total Deformation branch was created under the Solution (A6) branch.
Fig. A.33
Fig. A.33 Designated quantity branches created under the Solution (A6) branch.

Select the User Defined Result branch, and enter SX in the Expression cell of the Definition table in the Details of ‘User Defined Result’ window, as shown in Fig. A.34.

  • [COMMAND]    Standard Tool Bar → Solve
Fig. A.34
Fig. A.34 Expression SX entered in the Expression cell of the Definition table in the Details of ‘User Defined Result’ window.

The solution procedure starts. The ANSYS Workbench Solution Status window appears, displaying the status of the solution process, as shown in Fig. A.35. When the solution is finished, the solution status window disappears.

Fig. A.35
Fig. A.35 ANSYS Workbench Solution Status window displaying the status of the solution process.

A.5.4 Contour plots of the results

Contour plots of the results are displayed by clicking branches under the Solution (A6) branch. Fig. A.36 shows, for example, the contour plot of the normal stress in the x-axis direction σx, or SX designated by the Expression cell of the Definition table in the User Defined Result branch. The maximum and the minimum values of each result can be found in the Results table in the Details of the corresponding result and also in the table in the Tabular Data window.

Fig. A.36
Fig. A.36 Contour plots of the normal stress in the x-axis direction σx, or SX showing that the maximum normal stress σxmax obtained by the present analysis is 160.08 MPa.

The Maximum cell of the in the Details of ‘User Defined Result’ window shows that the maximum normal stress σxmax obtained by AWM for the present stepped bar subjected to the applied uniform tensile stress σ0 of 100 MPa is 160.08 MPa, as shown in the Maximum cell of the Results table in the Details of ‘User Defined Result’ window, as set out in Fig. A.36.

Note: The User Defined Result expressions available are listed in the table in the Worksheet window, as shown in Fig. A.37. The table can be accessed by clicking the Solution branch and then by selecting the Worksheet icon in the Standard Tool Bar. This icon does not become apparent until one or more solution quantities are designated.

Fig. A.37
Fig. A.37 Available solution quantities and their expressions listed in the table in the Worksheet window.

Instead of using the User Defined Result command, six stress components can be obtained by the following command:

  • [COMMAND]    Context Tool Bar (Solution) → Stress → Normal/Shear

After the above command is performed, the corresponding branch, i.e. the Normal Stress or the Shear Stress branch, is created under the Solution (A6) branch, as shown in Fig. A.38. The orientation of the normal or the shear stresses shall be designated as, for example, X Axis or XY Plane in the Orientation cell of the Definition table in the Details of ‘Normal Stress’ or ‘Shear Stress’ window.

Fig. A.38
Fig. A.38 User Defined Result designated in the Orientation cell of the Definition table in the Details of ‘User Defined Result’ window.

A.6 Discussion

As previously described, the maximum normal stress σxmax obtained by ANSYS for the present stepped bar is 160.08 MPa. The tensile stress concentration factor is obtained as α = σmax/σ0 ≈ 1.78 by the tensile stress concentration vs radius of curvature diagram [2] (also see Problem 3.19). The relative difference between the maximum stress obtained by AWM and that by the stress concentration factor is (σxmax − ασ0)/(ασ0) ≈ − 10%. This difference is acceptable, but if even more accuracy is required, the operation of mesh refinement would be helpful. Mesh refinement can be achieved by following the procedures below.

  1. (1) Mesh refinement for improving the solution
  • [COMMAND]    Tree Outline Window → Project → Model (A4) → Mesh
  1. 1. The category of the Context Tool Bar is changed from Model to Mesh.
  • [COMMAND]    Context Tool Bar (Mesh) → Mesh Control → Refinement
  1. 1. The Refinement branch is created under the Mesh branch in the Tree Outline window, and the original finite element discretisation image of the stepped round bar in Fig. A.39 is changed into its blank image in Fig. A.40.
  2. 2. Click the Select Face icon and place the mouse cursor on the circumferential shoulder fillet region in the stepped bar model. Click the left button of the mouse, and the fillet region turns green, as shown in Fig. A.40.
  3. 3. Click the Apply button for the Geometry cell, and the colour of the fillet region is changed to blue.
  • [COMMAND]    Context Tool Bar (Mesh) → Mesh → Generate Mesh
  1. 1. The finite elements around the fillet in the present stepped round bar model are remeshed and refined, as shown in Fig. A.41.
  • [COMMAND]    Standard Tool Bar → Solve
  1. 1. The solution procedure starts. The ANSYS Workbench Solution Status window appears, displaying the status of the solution process. The window disappears when the solution is finished.
  2. 2. Click, for example, the User Defined Result branch under the Details of ‘User Defined Result’ window and the contour plot of σx is displayed in the Geometry window.
Fig. A.39
Fig. A.39 Original finite element discretisation image of the stepped round bar before mesh refinement.
Fig. A.40
Fig. A.40 Fillet region selected to be remeshed for the solution improvement.
Fig. A.41
Fig. A.41 Remeshed and refined finite elements around the fillet region in the present stepped round bar model.

The Maximum cell in the Details of ‘User Defined Result’ window shows that the maximum normal stress σxmax obtained by the remeshed stepped bar subjected to σ0 = 100 MPa is 180.21 MPa, as shown in the Maximum cell of the Results table in the Details of ‘User Defined Result’ window, as set out in Fig. A.42. The relative difference between the maximum stress obtained by AWM after the mesh refinement and that by the stress concentration factor is about 1.24%, showing a significant improvement in the solution.

Fig. A.42
Fig. A.42 Contour plots of the improved value of σx, or SX showing that the value of σxmax obtained after the mesh refinement is 180.21 MPa.

A.7 Automatic report generation

Click the ‘Report Preview’ Document Tab, and the report of the present stress analysis is automatically generated. The report provides a summary of the stress analysis made and is composed of the contents, as shown in Fig. A.43. The report can be printed by the following command, published in the MHTML format, or exported into the Word/PowerPoint format.

  • [COMMAND]    Context Tool Bar (Report Preview) → Print
Fig. A.43
Fig. A.43 List of the contents of the automatically generated report of the present structural analysis displayed in the Report Preview window.

References

[1] U. T. Murtaza and M. J. Hyder, Proc. Inter. Multi-Conference of Engineers and Computer Scientists, IMECS, vol. II (2015).

[2] Nishida M. Stress Concentration. Tokyo: Morikita Pub. Co., Ltd.; 1967 (in Japanese).

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