Submodeling Analysis of a Shaft

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Submodeling Analysis of a Shaft

Submodeling can be used when it is not possible to resolve all details of a complex geometry in a global model.

You can cope with this type of problems with a technique known as submodeling. First you solve the complete model with a mesh which is sufficient to capture the stiffness of the structure. In a second analysis you create a local model (submodel) of the region around the stress concentration with a fine mesh, and solve it using the displacements from the global model as boundary conditions.

There are some underlying assumptions when using submodels:

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The global model is accurate enough to give correct displacements on the boundary to the submodel.

•

The improvements introduced in the submodel are so small that they do not introduce significant changes in stiffness on the global level. Given this, it could still be possible to introduce a nonlinear material locally in the submodel.

In this example this technique is applied to perform an accurate stress evaluation in a structural mechanics model, but the same approach is applicable to many physical problems. The example geometry as such is not so complicated, so there is nothing to gain from a submodeling in this case. The purpose of the example is to show the technique.

Model Definition

The geometry consists of a shaft with a sudden change in diameter. At the location of the diameter change, there is a fillet with a small radius. In the fillet, stress concentrations will appear. There is also a central hole through the shaft. The geometry and mesh are shown in Figure 1.

The shaft is fixed at the thick end. On the thin end, a tensile force of 300 N and a shear force of 100 N are applied.

Figure 1: The full model.

As submodel, a region around the fillet at side giving the highest stress is chosen. The cuts where the boundary conditions are applied on the submodel should preferably be placed at locations where the stress field is fairly smooth.

The geometry and mesh of the submodel are shown in Figure 2. As can be seen, the fillet has a very good mesh resolution since the purpose is to obtain results with high accuracy there.

Figure 2: The submodel.

The general stress distribution is shown in Figure 3. Since the load is unsymmetrical (there is both an axial and a bending component), the highest stress occurs at the side with positive Z coordinate.

The cut through the model in Figure 4 displays that the stresses are not well resolved. There are significant jumps between the neighboring elements.

In the corresponding figures from the submodel, Figure 5 and Figure 6, the stress field is smooth and well resolved.

The computed peak stress for the global model is about 9% different compared to that in the submodel, which is expected given the coarse mesh in the global model.

Figure 3: Stress distribution in the global model.

Figure 4: Stress within the full model (cut view).

Figure 5: Stress distribution in the submodel.

Figure 6: Stress within the submodel (cut view).

As a verification, it is a good habit to always check the stress state at the cuts where the submodel has displacements prescribed by the results in the global model. Such a comparison is shown in Figure 7. The results have an almost perfect match, which strongly indicates that the submodel has been set up correctly.

Figure 7: Stress distribution over one of the cuts. Global model (left) and submodel (right) are compared.

Notes About the COMSOL Implementation

Two different components are used within the same mph file. In the global model, a general extrusion feature is introduced in order to describe the mapping of results from the global model to the submodel. The prescribed displacements on the cut boundaries in the submodel reference the displacements in the global model through this mapping.

In this example, there are no volume forces. If there were, such forces must be applied also on the submodel.

COMSOL_Multiphysics/Structural_Mechanics/shaft_submodeling

Modeling Instructions

From the menu, choose .

In the window, click

.

1

In the window, click

.

2

In the tree, select .

3

4

5

In the tree, select .

6

In the window, under right-click and choose .

Create the geometry. To simplify this step, insert a prepared geometry sequence.

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In the window for , locate the section.

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From the list, choose .

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In the toolbar, click and choose .

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

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In the toolbar, click

.

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In the text field, type Full Geometry.

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In the window, click .

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In the window for , type Full model in the text field.

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In the window, under click .

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In the window for , locate the section.

3

From the list, choose .

Full Geometry 1 (pi1)

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In the toolbar, click

and choose .

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In the window for , click

.

3

Click to expand the section. In the table, enter the following settings:


Name	Keep	Physics	Contribute to
Boundary Load	√	√	None
Fixed Constrained	√	√	None

The geometry sequence contains two selections, these will be used later to apply loads and constraints.

1

In the toolbar, click

to open the window.

2

Go to the window.

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In the tree, select .

4

Right-click and choose .

5

In the toolbar, click

to close the window.

The material is now defined as global material so that both the full model and the submodel can use the same material definition, defined at one location only in the model tree.

Material Link 1 (matlnk1)

In the window, under right-click and choose .

Solid Mechanics (solid)

Fixed Constraint 1

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In the window, under right-click and choose .

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In the window for , locate the section.

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From the list, choose .

Boundary Load 1

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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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Locate the section. From the list, choose .

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Specify the Ftot vector as


-300	x
0	y
-100	z

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In the window, under click .

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In the window for , locate the section.

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From the list, choose .

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.

5

button in the toolbar.

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In the window, click .

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In the window for , type Full model in the text field.

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In the toolbar, click

.

Stress - Full model

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In the window for , type Stress - Full model in the text field.

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Locate the section. Select the check box.

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In the window, expand the node, then click .

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In the window for , click to expand the section.

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From the list, choose .

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From the list, choose .

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In the toolbar, click

.

6

button in the toolbar.

1

In the window, expand the node.

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Right-click and choose .

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In the window for , locate the section.

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From the list, choose .

Cut Plane Stress -Full model

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In the toolbar, click

.

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In the window for , type Cut Plane Stress -Full model in the text field.

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Locate the section. Select the check box.

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Right-click and choose .

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In the window for , locate the section.

3

In the text field, type solid.mises.

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

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From the list, choose .

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In the toolbar, click

.

7

In the window, expand the node.

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In the window, expand the node, then click .

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In the window for , locate the section.

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In the text field, type 25.8.

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In the text field, type 34.2.

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In the text field, type 1.5.

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In the text field, type 7.5.

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In the window, right-click the root node and choose .

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

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In the window, under right-click and choose .

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In the window for , type Submodel Cut in the text field.

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Locate the section. From the list, choose .

Cylinder 1 (cyl1)

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In the toolbar, click

.

2

In the window for , locate the section.

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In the text field, type 7.

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In the text field, type 8.

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Locate the section. In the text field, type 26.

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Locate the section. From the list, choose .

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In the toolbar, click

.

2

In the window for , locate the section.

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In the text field, type 10.

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In the text field, type 14.

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In the text field, type 10.

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Locate the section. In the text field, type 26.

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In the text field, type -7.

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In the toolbar, click

and choose .

2

In the window for , type Submodel Cut in the text field.

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Click in the window and then press Ctrl+A to select both objects.

4

Locate the section. Select the check box.

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From the list, choose .

1

In the window, under click .

2

In the window for , locate the section.

3

From the list, choose .

Full Geometry 1 (pi1)

In the toolbar, click

and choose .

Submodel Cut 1 (pi2)

1

In the toolbar, click

and choose .

2

In the window for , click

.

3

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


Name	Keep	Physics	Contribute to
Submodel Cut	√	√	None

Intersection 1 (int1)

1

In the toolbar, click

and choose .

2

Click in the window and then press Ctrl+A to select both objects.

3

In the window for , click

.

The submodel geometry is now built. In order to create a structured mesh, you need to partition the geometry following the xz-plane.

Work Plane 1 (wp1)

1

In the toolbar, click

.

2

In the window for , locate the section.

3

From the list, choose .

Partition Objects 1 (par1)

1

In the toolbar, click

and choose .

2

Select the object only.

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In the window for , locate the section.

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From the list, choose .

Mesh Control Domains 1 (mcd1)

1

In the toolbar, click

and choose .

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On the object , select Domains 1 and 2 only.

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In the toolbar, click

.

4

button in the toolbar.

Material Link 2 (matlnk2)

In the window, under right-click and choose .

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 .

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Find the subsection. In the table, select the check box for .

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Click in the window toolbar.

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In the toolbar, click

to close the window.

Definitions (comp1)

In the window, under click .

General Extrusion 1 (genext1)

1

In the toolbar, click

and choose .

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Select Domain 1 only.

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In the window for , locate the section.

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In the text field, type X.

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In the text field, type Y.

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In the text field, type Z.

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Locate the section. From the list, choose .

You have now created the nonlocal coupling which will be used for mapping the solution from the full model to the submodel.

Solid Mechanics 2 (solid2)

In the window, under click .

Prescribed Displacement 1

1

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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Locate the section. Select the check box.

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In the u 0 x text field, type comp1.genext1(comp1.u).

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Select the check box.

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In the u 0 y text field, type comp1.genext1(comp1.v).

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Select the check box.

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In the u 0 z text field, type comp1.genext1(comp1.w).

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In the toolbar, click

and choose .

2

Select Boundary 2 only.

1

Right-click and choose .

2

Select Edges 1 and 3 only.

3

In the window for , locate the section.

4

From the list, choose .

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In the text field, type 6.

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In the text field, type 3.

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Select the check box.

1

In the window, right-click and choose .

2

Select Edge 13 only.

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In the window for , locate the section.

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From the list, choose .

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In the text field, type 6.

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In the text field, type 3.

1

Right-click and choose .

2

Select Edge 15 only.

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In the window for , locate the section.

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In the text field, type 6.

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Right-click and choose .

2

Select Edge 10 only.

3

In the window for , locate the section.

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From the list, choose .

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In the text field, type 10.

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In the text field, type 2.

In the toolbar, click

.

1

Right-click and choose .

2

In the window for , locate the section.

3

In the text field, type 12.

4

.

5

In the window, right-click and choose .

6

button in the toolbar.

1

In the toolbar, click

to open the window.

2

Go to the window.

3

Find the subsection. In the tree, select .

4

Find the subsection. In the table, clear the check box for .

5

Click in the window toolbar.

6

In the window, click the root node.

7

In the toolbar, click

to close the window.

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

Step 1: Stationary

1

In the window, under click .

2

In the window for , click to expand the section.

3

Find the subsection. From the list, choose .

4

From the list, choose .

5

From the list, choose .

6

In the toolbar, click

.

Stress - Submodel

1

In the window for , type Stress - Submodel in the text field.

2

Locate the section. Select the check box.

1

In the window, expand the node, then click .

2

In the window for , locate the section.

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From the list, choose .

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From the list, choose .

5

In the toolbar, click

.

6

button in the toolbar.

1

In the toolbar, click

.

2

In the window for , locate the section.

3

From the list, choose .

4

Locate the section. From the list, choose .

Cut Plane Stress - Submodel

1

In the toolbar, click

.

2

In the window for , type Cut Plane Stress - Submodel in the text field.

3

Locate the section. Select the check box.

4

Locate the section. From the list, choose .

1

Right-click and choose .

2

In the window for , locate the section.

3

In the text field, type solid2.mises.

4

Locate the section. From the list, choose .

5

From the list, choose .

6

In the toolbar, click

.

7

button in the toolbar.

Now verify that the differences in stress between the full model and the submodel are small where the displacements are mapped.

1

In the toolbar, click

.

2

In the window for , locate the section.

3

In the text field, type 26.

Stress comparison

1

In the toolbar, click

.

2

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

3

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. In the text field, type solid.mises.

5

Locate the section. From the list, choose .

6

From the list, choose .

7

In the toolbar, click

.

8

In the toolbar, click

and choose .

1

In the window for , locate the section.

2

From the list, choose .

3

Select Boundary 1 only.

4

Locate the section. From the list, choose .

1

In the window, right-click and choose .

2

In the window for , locate the section.

3

From the list, choose .

4

Locate the section. In the text field, type solid2.mises.

5

Locate the section. From the list, choose .

6

From the list, choose .

7

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

1

Right-click and choose .

2

In the window for , locate the section.

3

In the text field, type 11.

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In the text field, type 0.

5

Locate the section. Select the check box.

6

In the associated text field, type 1.

7

In the toolbar, click

.

8

button in the toolbar.

The solution is computed, follow the steps below if you want to save and reuse the model in the future.

Step 1: Stationary

1

In the window, under click .

2

In the window for , locate the section.

3

In the table, clear the check box for .