Bracket — Static Analysis

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Bracket — Static 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.

This is the most fundamental model in the suite, and includes the definition of material properties and boundary conditions. After the solution is computed, you learn how to analyze results and check the reaction forces.

Model Definition

The model used in this guide is a bracket made of steel. This type of bracket can be used to install an actuator that is mounted on a pin placed between the two holes in the bracket arms. The geometry is shown in Figure 1.

Figure 1: Bracket geometry.

In this analysis, the mounting bolts are assumed to be fixed and securely bonded to the bracket. One of the arms is loaded upward and the other downward. The loads are applied as a pressure on the inner surfaces of the holes, and their intensity is P0 cos(α), where α is the angle from the direction of the load resultants. Figure 2 below shows the loads applied to the bracket.

Figure 2: Load distribution in the bracket arms.

Figure 3 shows the von Mises stress distribution together with an exaggerated (automatically scaled) picture of the deformation. The high stress values are located in the vicinity of the mounting bolts and at the transition between the plates.

Figure 3: Von Mises stress distribution in the bracket under bending load in z-axis direction.

In Figure 4 you can see that the bracket base remains fixed while only the arms are deformed. The maximum total displacement is about 0.2 mm, which is in agreement with the assumption of small deformations.

Figure 4: Total displacement.

Figure 5 shows the principal stresses in the bracket. The largest principal stress is shown with red arrows, the intermediate principal stress with green arrows, and the smallest principal stress with blue arrows.

Figure 5: Principal stress in the bracket left arm.

In Table 1 you can see the reaction force in the x, y, and z directions in each bolt. In all directions the sum is zero, which is a good check, since in this model there are no resultant forces. The slight asymmetry can be attributed to the mesh not being perfectly symmetric.

Table 1: Reaction force in bolt.
	Reaction force, x direction (N)	Reaction force, y direction (N)	Reaction force, z direction (N)
Bolt 1	451	307	2535
Bolt 2	-451	73	-1703
Bolt 3	452	-307	-2534
Bolt 4	-451	-73	1702

Structural_Mechanics_Module/Tutorials/bracket_static

Modeling Instructions

From the menu, choose .

In the window, click

.

1

In the window, The first step to build a model is to open COMSOL and then specify the type of analysis you want to do - in this case, a stationary, solid mechanics analysis.

2

3

In the tree, select .

4

5

6

In the tree, select .

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Global Definitions

It is good modeling practice to gather the constants and parameters in one place so that you can change them easily. Using parameters will also improve the readability of your input data.

1

In the window, under click .

2

In the window for , locate the section.

3

In the table, enter the following settings:


Name	Expression	Value	Description
P0	2.5[MPa]	2.5E6 Pa	Peak load intensity
YC	-300[mm]	-0.3 m	Y-coordinate of hole center

The next step is to create your geometry, which also can be imported from an external program. COMSOL Multiphysics supports a multitude of CAD programs and file formats. In this example, import a file in the COMSOL Multiphysics geometry file format (.mphbin).

Import 1 (imp1)

1

In the toolbar, click

.

2

In the window for , locate the section.

3

From the list, choose .

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5

Browse to the model’s Application Libraries folder and double-click the file bracket.mphbin.

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It is possible to create a free tetrahedral mesh covering the whole component. Such a strategy is however not efficient for the large flat regions. For this reason, you will partition the geometry, so that you can create a better mesh.

1

In the toolbar, click

.

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In the window for , locate the section.

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Find the subsection. Click .

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In the dialog box, type Partition Block in the text field.

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In the window for , locate the section.

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In the text field, type 0.025.

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In the text field, type 0.13.

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In the text field, type 0.04.

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Locate the section. In the text field, type -0.11.

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In the text field, type -0.12.

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In the text field, type 0.025.

13

.

Mirror 1 (mir1)

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In the toolbar, click

and choose .

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In the window for , locate the section.

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From the list, choose .

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Select the check box.

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Locate the section. Find the subsection. From the list, choose .

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.

Mirror 2 (mir2)

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In the toolbar, click

and choose .

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In the window for , locate the section.

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From the list, choose .

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Select the check box.

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Locate the section. In the text field, type 1.

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In the text field, type 0.

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Locate the section. Find the subsection. From the list, choose .

8

.

Partition Objects 1 (par1)

1

In the toolbar, click

and choose .

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Select the object only.

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In the window for , locate the section.

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Find the subsection. Select the

toggle button.

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From the list, choose .

6

.

Form Union (fin)

1

In the toolbar, click

.

2

button in the toolbar.

Here you want to define an expression for the load applied to the load-carrying holes. Assume the load distribution to be defined by a trigonometric function.

Analytic 1 (an1)

1

In the toolbar, click

and choose .

2

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

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Locate the section. In the text field, type F*cos(atan2(py,abs(px))).

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In the text field, type F, py, px.

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Locate the section. In the text field, type Pa, m, m.

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In the text field, type Pa.

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In the toolbar, click

.

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In the window for , type Bolt 1 in the text field.

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button in the toolbar.

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Locate the section. From the list, choose .

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Select Boundary 41 only.

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Select the check box.

7

Repeat the steps above to add three more explicit selections, with the following properties:


Default node label	New node label	Select this boundary
Explicit 2	Bolt 2	43
Explicit 3	Bolt 3	55
Explicit 4	Bolt 4	57

1

In the toolbar, click

.

2

In the window for , type Bolt Holes in the text field.

3

Locate the section. From the list, choose .

4

Locate the Color section. On Windows, select the eighth color in the first row of the palette (orange). On other platforms, choose Color 8 from the Color list.

5

Locate the section. Under , click

.

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In the dialog box, in the list, choose , , , and .

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Create selections for the two holes carrying the load.

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In the toolbar, click

.

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In the window for , type Left Pin Hole in the text field.

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Locate the section. From the list, choose .

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Select Boundary 4 only.

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Select the check box.

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Locate the Color section. On Windows, select the ninth color in the first row of the palette (green). On other platforms, choose Color 9 from the Color list.

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In the toolbar, click

.

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In the window for , type Right Pin Hole in the text field.

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Locate the section. From the list, choose .

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Select Boundary 75 only.

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Select the check box.

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Locate the Color section. On Windows, select the second color in the second row of the palette (a red color). On other platforms, choose Color 12 from the Color list.

Add a selection to be used during mesh generation.

1

In the toolbar, click

.

2

In the window for , type Pin Holes in the text field.

3

Locate the section. From the list, choose .

4

Locate the section. Under , click

.

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In the dialog box, in the list, choose and .

6

Bolt Hole Edges

1

In the toolbar, click

.

2

In the window for , type Bolt Hole Edges in the text field.

3

Locate the section. From the list, choose .

4

Locate the section. From the list, choose .

5

Locate the section. Under , click

.

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In the dialog box, select in the list.

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8

button in the toolbar.

COMSOL Multiphysics is equipped with built-in material properties for a number of common materials. Here, choose structural steel. The material is automatically assigned to all domains.

1

In the toolbar, click

to open the window.

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Go to the window.

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In the tree, select .

4

Click in the window toolbar.

5

In the toolbar, click

to close the window.

Solid Mechanics (solid)

By default, the Solid Mechanics interface assumes that the participating material models are linear elastic, which is appropriate for this example. All that is left to do is to define the constraints and loads.

Fixed Constraint 1

1

In the window, under right-click and choose .

2

In the window for , locate the section.

3

From the list, choose .

Boundary Load 1

Apply a boundary load to the bracket holes. The predefined boundary system is used for orienting the load in the normal direction. Note how boolean expressions like Z>0 can be used to limit the part of the hole where the load is active. Also, the sign of the X-coordinate is used to flip where the load is applied.

1

In the toolbar, click

and choose .

2

In the window for , locate the section.

3

From the list, choose .

4

Locate the section. From the list, choose .

5

Locate the section. Specify the FA vector as


0	t1
0	t2
load(-P0,Y-YC,Z)(sign(X)Z>0)	n

Start by creating an edge mesh around the bolt holes to make sure that they are properly resolved.

1

In the toolbar, click

and choose .

2

In the window for , locate the section.

3

From the list, choose .

1

Right-click and choose .

2

In the window for , locate the section.

3

In the text field, type 8.

Create a mesh which is swept through the thin flat parts, and then use a free tetrahedral mesh in the parts with a more complex geometry. Note that the transition between the two types of elements is automatic.

1

In the toolbar, click

.

2

In the window for , locate the section.

3

From the list, choose .

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Select Domains 1, 4–6, and 9 only.

5

Click to expand the section. Select Boundaries 1, 33, 37, 50, and 72 only.

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Right-click and choose .

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In the window for , locate the section.

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Click the button.

4

Locate the section. Select the check box.

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

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.

Free Tetrahedral 1

In the toolbar, click

.

1

Right-click and choose .

2

In the window for , locate the section.

3

From the list, choose .

4

.

The steps below show how to visualize the load distribution in the current geometry before computing the solution.

In the toolbar, click

.

Note that the Study node automatically defines a solver sequence for the simulation based on the selected physics (Solid Mechanics) and study type (Stationary).

Boundary Loads (solid)

1

In the window, expand the node, then click .

2

In the toolbar, click

.

Now, solve the model.

In the toolbar, click

.

The default plot shows the von Mises stress distribution, together with an exaggerated (automatically scaled) picture of the deformation.

1

In the window, expand the node, then click .

2

In the window for , locate the section.

3

From the list, choose .

Boundary Load 1

1

In the window, expand the node.

2

Right-click and choose .

Boundary Load 1

1

In the window, right-click and choose .

2

In the window for , locate the section.

3

From the list, choose .

4

Select the check box.

5

In the associated text field, type 1E-8.

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Click to expand the section. From the list, choose .

7

Clear the check box.

8

Clear the check box.

9

Clear the check box.

Color Expression

1

In the window, expand the node, then click .

2

In the window for , locate the section.

3

Clear the check box.

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button in the toolbar.

5

button in the toolbar.

Add a plot group to display the displacement of the bracket.

Total Displacement

1

In the toolbar, click

and choose .

2

In the window for , type Total Displacement in the text field.

1

Right-click and choose .

2

In the window for , locate the section.

3

From the list, choose .

4

Locate the section. From the list, choose .

1

Right-click and choose .

2

In the window for , locate the section.

3

From the list, choose .

4

Locate the section. From the list, choose .

5

Locate the section. In the text field, type 2.

Total Displacement

1

In the window, click .

2

In the window for , locate the section.

3

From the list, choose .

4

In the toolbar, click

.

Create another plot to display the principal stresses.

Principal Stress

1

In the toolbar, click

and choose .

2

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

Principal Stress Volume 1

1

In the toolbar, click

and choose .

2

In the window for , locate the section.

3

Find the subsection. In the text field, type 30.

4

Find the subsection. In the text field, type 60.

5

Find the subsection. In the text field, type 15.

6

Locate the section. From the list, choose .

7

In the toolbar, click

.

A final check is to compute the total reaction force along the x-, y-, and z-directions. Use a surface integration over the constrained boundaries.

Evaluation Group: Reactions

1

In the toolbar, click

.

2

In the window for , type Evaluation Group: Reactions in the text field.

1

Right-click and choose .

2

In the window for , type Bolt 1 in the text field.

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Locate the section. From the list, choose .

4

Click in the upper-right corner of the section. From the menu, choose .

5

Locate the section. In the table, enter the following settings:


Expression	Unit	Description
solid.RFx	N	Bolt 1, X
solid.RFy	N	Bolt 1, Y
solid.RFz	N	Bolt 1, Z

1

Right-click and choose .

2

In the window for , type Bolt 2 in the text field.

3

Locate the section. From the list, choose .

4

Locate the section. In the table, enter the following settings:


Expression	Unit	Description
solid.RFx	N	Bolt 2, X
solid.RFy	N	Bolt 2, Y
solid.RFz	N	Bolt 2, Z

1

Right-click and choose .

2

In the window for , type Bolt 3 in the text field.

3

Locate the section. From the list, choose .

4

Locate the section. In the table, enter the following settings:


Expression	Unit	Description
solid.RFx	N	Bolt 3, X
solid.RFy	N	Bolt 3, Y
solid.RFz	N	Bolt 3, Z

1

Right-click and choose .

2

In the window for , type Bolt 4 in the text field.

3

Locate the section. From the list, choose .

4

Locate the section. In the table, enter the following settings:


Expression	Unit	Description
solid.RFx	N	Bolt 4, X
solid.RFy	N	Bolt 4, Y
solid.RFz	N	Bolt 4, Z

5

In the toolbar, click

.