Mechanical Behaviour of Materials: Simulation Problems

WALL HANGER

PROBLEM

Figure 1 shows a wall hanger model for an extinguisher. The wall hanger is fixed at the four holes and a load of 2000 N is acting at the top part of the circular section. Determine the stress distribution in the wall hanger.

Figure 1. Wall hanger model.

Figure 1. Wall hanger model (fillet radius = 4 mm).

Table 1 indicates the mechanical properties of the steel.

Table 1. Mechanical properties.

Steel
E_Steel	210 GPa
S_{y Steel}	275 MPa
ν_Steel	0.3

GEOMETRY OF THE MODEL

First of all, select the analysis type:

Main Menu > Preferences

Activate "Structural" option.

And change the jobname for this particular problem: "Wall hanger".

Utility Menu > File > Change Jobname

The element type for this problem is "SOLID 10 node 187" (Figure 2).

Main Menu > Preprocessor > Element Type > Add/Edit/Delete

Figure 2. Element type:

Figure 2. Element type: "SOLID 10 node 187".

Define the mechanical properties of the steel: modulus of elasticity (EX) and Poisson's ratio (PRXY), as indicated in Figure 3:

Main Menu > Preprocessor > Material Props > Material Models

The material is defined as "Structural – Linear – Elastic – Isotropic".

Figure 3. Material properties.

For the geometry, create a rectangular area (80 x 80 mm) as indicated in Figure 4.

Main Menu > Preprocessor > Modeling > Create > Areas > Rectangle > By 2 Corners

Figure 4. Rectangular area.

Number the lines:

Utility Menu > PlotCtrls > Numbering

And activate "LINE". Next, remove the area with the option "Delete Areas Only" (Figure 5):

Main Menu > Preprocessor > Modeling > Delete > Areas Only

Figure 5. Delete areas.

Plot the lines (Utility Menu – Plot – Lines).

Define the radius of curvature at the corners with the option "Line Fillet". Figure 6 shows the process for this operation.

Main Menu > Preprocessor > Modeling > Create > Lines > Line Fillet

The fillet radius is 10 mm.

Figure 6.

Figure 6. "Line Fillet" operation.

Create the new area defined by the lines (Figure 7).

Main Menu > Preprocessor > Modeling > Create > Areas > Arbitrary > By Lines

And select the lines consecutively.

Figure 7. Create Areas By Lines.

Now, define a grid for the working plane, as indicated in Figure 8.

Utility Menu > WorkPlane > WP Settings

Figure 8. Define a grid for the working plane.

After that, create four circular areas (radius 3 mm) for the circular holes, as indicated in Figure 9:

Main Menu > Preprocessor > Modeling > Create > Areas > Circle > Solid Circle

Figure 9. Create four circular areas.

Then, subtract the circular areas to generate the holes.

Main Menu > Preprocessor > Modeling > Operate > Booleans > Subtract > Areas

First select the total area, "OK" and then the four circular areas and "OK" (Figure 10).

Figure 10.

Figure 10. "Subtract Areas" operation.

Number the areas from "Utility Menu – PlotCtrls – Numbering".

Figure 11 displays the plate for the model. Now, create another circular area (radius 4 mm) for the section of the hanger.

Main Menu > Preprocessor > Modeling > Create > Areas > Circle > Solid Circle

Figure 11. Define the circular area for the hanger.

Apply the option "Overlap Areas" (Figure 12):

Main Menu > Preprocessor > Modeling > Operate > Booleans > Overlap Areas

And click "Pick All".

Figure 12.

Figure 12. "Overlap Areas" operation.

Number the keypoints from "Utility Menu – PlotCtrls – Numbering".

Now, create the keypoint at the center of the circular area (Figure 13).

Main Menu > Preprocessor > Modeling > Create > Keypoints > KP at center > 3 keypoints

With this option, select keypoints 29, 30 and 32. It is observed that keypoint 33 is created.

Figure 13. Create a keypoint at the center of the circular area.

Now, create two new keypoints (34 and 35) that will define the line for the extrusion. The coordinates are indicated in Figure 14.

Main Menu > Preprocessor > Modeling > Create > Keypoints > In Active CS

Figure 14. Create Keypoints 34 and 35.

Then, create two lines as indicated in Figure 15.

Main Menu > Preprocessor > Modeling > Create > Lines > Lines > Straight Line

Figure 15. Create two lines.

These two lines are displayed in Figure 16. In the same figure, "Line Fillet" operation is applied for the curvature.

Main Menu > Preprocessor > Modeling > Create > Lines > Line Fillet

Figure 16.

Figure 16. "Line Fillet" operation.

The radius of curvature is 8 mm (Figure 17).

Figure 17. Radius of curvature: 8 mm.

After that, extrude the circular area along the line, as indicated in Figure 18.

Main Menu > Preprocessor > Modeling > Operate > Extrude > Areas > Along Lines

Select the circular area, "OK" and then the lines for the direction of the extrusion, and "OK".

Figure 18. Sweep Areas along Lines.

Next, extrude the plate.

Main Menu > Preprocessor > Modeling > Operate > Extrude > Areas > Along Normal

Select the rectangular and the circular areas (Figure 19).

The length of extrusion is 2 mm.

Figure 19.

Figure 19. "Extrude" operation.

Add the volumes 1 and 4, as indicated in Figure 20.

Main Menu > Preprocessor > Modeling > Operate > Booleans > Add > Volumes

Figure 20.

Figure 20. "Add Volumes" operation.

Move the working plane at keypoint 76 (Figure 21).

Utility Menu > WorkPlane > Offset WP to > Keypoints

Figure 21. Move the working plane at keypoint 76.

Now, rotate the working plane as indicated in Figure 22 (90º).

Utility Menu > WorkPlane > Offset WP by Increments

Figure 22. Rotate the working plane.

Divide the volume by the working plane (Figure 23).

Main Menu > Preprocessor > Modeling > Operate > Booleans > Divide > Volu by WrkPlane

And select volume 5.

Figure 23. Divide the volume 5 by working plane.

Repeat the same operation to divide the volume in four parts. Figures 24 to 27 show the process.

Figure 24. Move the working plane at keypoint 77.

Figure 25. Rotate the working plane (X axis).

Figure 26. Divide the volume 4 by working plane.

Figure 27. Divide the volume 1 by working plane.

Now, apply the operation "Area Fillet" to join the plate and the cylinder. There are four parts.

Main Menu > Preprocessor > Modeling > Create > Areas > Area Fillet

Number the areas (Utility Menu – PlotCtrls – Numbering). Figure 28 displays this operation for the areas A47 and A62.

Figure 28.

Figure 28. "Area Fillet" operation (Areas A47 and A62).

Figure 29 displays the "Area Fillet" operation for the areas A50 and A56.

Figure 29.

Figure 29. "Area Fillet" operation (Areas A50 and A56).

Figure 30 displays the "Area Fillet" operation for the areas A67 and A48.

Figure 30.

Figure 30. "Area Fillet" operation (Areas A67 and A48).

Figure 31 displays the "Area Fillet" operation for the areas A55 and A49.

Figure 31.

Figure 31. "Area Fillet" operation (Areas A55 and A49).

To avoid the coincidence of some geometric entities, apply "Merge Items".

Main Menu > Preprocessor > Numbering Ctrls > Merge Items

And select "All", as indicated in Figure 32.

Figure 32.

Figure 32. "Merge Items" operation.

Now, create the new areas between the hanger and the plate:

Utility Menu > Select > Entities

Define the parameters indicated in Figure 33.

Figure 33. Select areas (X coordinates).

Select the areas in Y direction (Figure 34).

Figure 34. Select areas (Y coordinates).

And select the areas in Z direction (Figure 35).

Figure 35. Select areas (Z coordinates).

After that, create the areas by lines, as indicated in Figure 36.

Main Menu > Preprocessor > Modeling > Create > Areas > Arbitrary > By Lines

Figure 36. Create areas by lines.

Figures 37 to 39 show the same process for the other parts.

Figure 37. Create areas by lines.

Figure 38. Create areas by lines.

Figure 39. Create areas by lines.

Finally, create the volumes by areas.

Main Menu > Preprocessor > Modeling > Create > Volumes > Arbitrary > By Areas

Figures 40 to 43 display the process for the new volumes, using the option "Box".

Figure 40. New volume by areas.

Figure 41. New volume by areas.

Figure 42. New volume by areas.

Figure 43. New volume by areas.

And select all the geometric entities.

Utility Menu > Select > Everything

Now, mesh the model (Figure 44).

Main Menu > Preprocessor > Meshing > Size Cntrls > ManualSize > Global > Size

The element size is 2 mm.

Figure 44. Element size: 2 mm.

Finish the meshing process (Figure 45).

Main Menu > Preprocessor > Meshing > Mesh > Volumes > Free

Click "Pick All".

Figure 45.

Figure 45. "Mesh Volumes" operation.

LOADS AND BOUNDARY CONDITIONS

The wall hanger is fixed at the four holes (Figure 46).

Main Menu > Preprocessor > Loads > Define Loads > Apply > Structural > Displacement > On Areas

Select the four lateral areas that define the cylindrical holes and restrict all degrees of freedom (All DOF).

Figure 46.

Figure 46. "All DOF" at the cylindrical holes.

Figure 47 displays the model with the boundary conditions and the window "Apply PRES on Areas". As a first approach, apply a pressure of 1000000 Pa at the top part of the hanger.

Main Menu > Preprocessor > Loads > Define Loads > Apply > Structural > Pressure > On Areas

Figure 47. Apply the pressure.

SOLUTION

Solve the problem:

Main Menu > Solution > Solve > Current LS

"Solution is done!".

Evaluate the value of the reactions, that are listed in Figure 48.

Main Menu > General Postproc > List Results > Reaction Solu

Select "All items".

Figure 48. List of reactions.

The total value of the reaction has to be 2000 N. So, define a new value for the pressure, as indicated in Figure 49. There is no need to delete the previously defined pressure, since ANSYS considers the new value.

Figure 49. New value for the pressure.