Bracket — Shell Analysis

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Bracket — Shell Analysis

The various examples based on a bracket geometry form a suite of tutorials which summarizes the fundamentals when modeling structural mechanics problems in COMSOL Multiphysics and the Structural Mechanics Module.

In this example you study the stress in a bracket subjected to external loads. The thin parts with constant thickness are modeled using the Shell interface, and the transition regions where 3D effects are important are modeled using the Solid Mechanics interface. This example also shows how to connect shell elements with solid elements.

For thin geometries, it can be more efficient to use shell elements than solid elements, thus saving computational time and memory. The Shell interface in the Structural Mechanics Module can be used to model structures approximated by thin and thick shells. There is also a similar Plate interface for 2D problems. The thickness of the shell or plate is taken into account in the equations instead of being explicitly modeled in the geometry.

It is recommended that you review the Introduction to the Structural Mechanics Module, which includes background information and discusses the bracket_basic.mph model relevant to this example.

Model Definition

The model is described in the section “The Fundamentals: A Static Linear Analysis” in the Introduction to the Structural Mechanics Module.

The parts of the geometry modeled with shells are highlighted in Figure 1 and the parts modeled with solids are highlighted in Figure 2.

Figure 1: Shell domains in the bracket geometry.

Figure 2: Solid domains in the bracket geometry.

The load is applied along the edge at the bracket holes.

Results and Discussion

The Shell interface generates a default plot which indicates the physical location of top and bottom surfaces. Especially when working with offsets, as in the current example, this is an excellent tool for checking that the input data is correct. This plot is shown in Figure 3.

Figure 3: The shell geometry plot. Red indicates top surface and blue indicates bottom surface.

In another default plot, the thickness is indicated by color contours, and the directions of the shell local coordinate systems are shown. This plot is shown in Figure 4.

Figure 4: Plot of thickness and local directions. The Red-Green-Blue convention is used for ordering of the coordinate axes.

Figure 5 shows the first principal strain on a in both the solid domains and at the top and bottom shell surfaces. When using the Shell dataset, the shell is represented by two surface plots, one on each side of the physical shell.

As can be seen, the continuity over the transition between the shell and the solid is very good.

Figure 5: First principal strain distribution in the solid and at the top and bottom of the shell.

Notes About the COMSOL Implementation

You can specify an offset in the shell definition if the meshed surface is not the same as the midsurface of the real geometry. This is used here, since the external geometrical boundaries are immediately available.

The multiphysics coupling is used for connecting shell edges to solid boundaries.

Structural_Mechanics_Module/Tutorials/bracket_shell

From the menu, choose .

Browse to the model’s Application Libraries folder and double-click the file bracket_static.mph.

Component 1 (comp1)

Start by removing the results from the loaded model.

1

In the window, expand the node.

Study 1/Solution 1 (sol1)

1

In the window, expand the node.

2

Right-click and choose .

3

Right-click and choose .

Add a Shell interface to the model.

1

In the toolbar, click

to open the window.

2

Go to the window.

3

In the tree, select .

4

Click in the window toolbar.

5

In the toolbar, click

to close the window.

Add a number of selections.

1

In the toolbar, click

.

2

In the window for , type Solid in the text field.

3

Select Domains 2, 3, 7, and 8 only.

4

button in the toolbar.

1

In the toolbar, click

.

2

In the window for , type Shell in the text field.

3

Locate the section. From the list, choose .

4

Select Boundaries 1, 32, 37, 50, and 86 only.

Solid Mechanics (solid)

1

In the window, under click .

2

In the window for , locate the section.

3

From the list, choose .

Disable not used boundary conditions from the Solid Mechanics interface. Both the loads and constraints will be applied to the shell part. This is just to clean up the Model Builder tree. Since these nodes now have an empty selection, they would not influence the analysis if kept.

4

In the window, expand the node.

Boundary Load 1, Fixed Constraint 1

1

In the window, under , Ctrl-click to select and .

2

Right-click and choose .

Not Used; Applied in Shell Interface

1

In the window for , type Not Used; Applied in Shell Interface in the text field.

2

Right-click and choose .

Add settings to the Shell interface. Since the mesh is placed on the outer boundary, the location of the midsurface is described by an offset.

1

In the window, under click .

2

In the window for , locate the section.

3

From the list, choose .

Thickness and Offset 1

1

In the window, under click .

2

In the window for , locate the section.

3

In the d text field, type 8[mm].

4

From the list, choose .

5

In the zreloffset text field, type -1.

6

button in the toolbar.

Fixed Constraint 1

1

In the toolbar, click

and choose .

2

In the window for , locate the section.

3

From the list, choose .

1

In the toolbar, click

and choose .

2

In the window for , locate the section.

3

From the list, choose .

4

Select Edges 4 and 188 only.

5

Locate the section. From the list, choose .

In order to use the local edge system, you need to know the orientation of the edges and the positive shell normal orientation. The orientation of the shell normal can be displayed by enabling physics symbols, and then moving to the node. The line orientation arrows are controlled from the node.

6

In the window, click .

7

In the window for , locate the section.

8

Select the check box.

1

In the window, expand the node, then click .

2

In the window for , locate the section.

3

Select the check box.

1

In the window, under click .

2

In the window for , locate the section.

3

Specify the FA vector as


0	xl
load(P0*sign(X),Y-YC,Z)	yl
0	zl

Add the connection between the shells and the solids.

Solid-Thin Structure Connection 1 (sshc1)

1

In the toolbar, click

and choose .

2

In the window for , locate the section.

3

Select the check box.

4

Select Boundaries 9, 11, 13, 14, 30, 34, 58, 62, 80, 81, 83, and 84 only.

5

From the list, choose .

The current material is attached only to the domains. A separate material definition is needed for the boundaries where the Shell interface is active.

Structural steel 1 (mat2)

1

In the window, expand the node.

2

Right-click and choose .

3

In the window for , locate the section.

4

From the list, choose .

5

From the list, choose .

Run the analysis.

In the toolbar, click

.

The first default plot for the Shell interface shows the von Mises stress on top and bottom surfaces. Create a combined stress plot with the results from both interfaces by copying the default stress plot for the solid.

1

In the window, expand the node.

2

Right-click and choose .

1

In the window, right-click and choose .

2

In the window for , click to expand the section.

3

From the list, choose .

4

Locate the section. From the list, choose .

1

In the window, click .

2

In the window for , click to expand the section.

3

Select the check box.

4

In the text field, type 0.

5

In the text field, type 7e7.

6

In the toolbar, click

.

The second default plot shows the shell geometry, with the top surface colored in blue-green and the bottom surface colored in white.

Shell Geometry (shell)

1

In the window, click .

2

In the toolbar, click

.

3

button in the toolbar.

The third default plot shows the shell thickness and the orientation of the local coordinate system.

Thickness and Orientation (shell)

1

In the window, click .

2

In the toolbar, click

.

Create a plot of the maximum principal stresses.

Principal Strain

1

In the window, right-click and choose .

2

In the window for , type Principal Strain in the text field.

1

In the window, expand the node, then click .

2

In the window for , locate the section.

3

In the text field, type shell.ep1.

4

Locate the section. In the text field, type 2.0E-4.

1

In the window, click .

2

In the window for , locate the section.

3

In the text field, type solid.ep1.

4

button in the toolbar.

5

In the toolbar, click

.