COMSOL 6.4 - Connecting Layered Shells with Solids and Shells

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Connecting Layered Shells with Solids and Shells

The interface is used to model thick to moderately thin composite laminates. These composite laminates are often connected with solid or sufficiently thin structures in different configurations to represent a realistic structure. These solid and thin structures are in general accurately and efficiently modeled using and interfaces respectively.

This tutorial and verification model illustrates how to connect layered shell elements with solid and shell elements in cladding or side-by-side configuration using built-in coupling features. In this example, the results of the layered shell-solid-shell structure is compared with the reference model built using solid elements.


	Read more about the Composite Materials Module in the COMSOL blog, Introduction to the Composite Materials Module.

Model Definition

The model (Figure 1) consists of two set of geometries; model geometry and reference geometry. The model geometry consists of layered shell, solid, and shell elements whereas the reference geometry is modeled with only solid elements.

Figure 1: The model and reference geometry showing different structural members in different parts of the geometry.

layered Shell-Structure Couplings

The model geometry has three sections. The middle section is modeled as a layered shell elements, while side supports are modeled using solid and shell elements as shown in Figure 1. The model geometry is made up of solid blocks and surfaces whereas the reference geometry is made up of only solid blocks. The connection between the layered shell and other structural elements are defined as below:

•

Boundaries of the interface shared with the interface, the connection is set up using multiphysics coupling.

•

Boundaries of the interface side-by-side with the interface, the connection is set up using the multiphysics coupling.

•

Boundaries of the interface parallel with the interface, the connection is set up using multiphysics coupling.

•

Edges of the interface side-by-side with the interface, the connection is set up using the multiphysics coupling.

Figure 2: Different connections of layered shell with other structural members on different sides are as follows:(A) layered shell-solid cladding (B) layered shell-solid transition (C) layered shell-shell cladding (D) layered shell-shell transition.

In the layered shell–solid transition coupling, only the bottom layer of layered shell is connected to the solid, whereas the top layer free. A similar connection is achieved in the reference model by disconnecting the degrees of freedom using an node in the interface.

Stacking Sequence

In the model geometry, layered shell and shell members consist of two layers where each layer (ply) has a thickness of 10 mm with [0/45] stacking sequence.

Material Properties

In the model geometry, layered shell and shell elements are made up of AS4/APC carbon–thermoplastic composite material. The AS4/APC carbon–thermoplastic is a built-in material in the material library. The transversely isotropic material properties (Young’s modulus, shear modulus, and Poisson’s ratio) are given in Table 1.

Table 1: Material properties of a lamina.
Material property	Value
ρ	1570 kg/m3
{E11, E22}	{138, 8.7} GPa
G12	5 GPa
{υ12, υ23}	{0.28, 0.45}

The solid elements in the model geometry are made up of structural steel. The stacking sequence and materials in the reference geometry are used as per the model geometry specifications.

Boundary conditions

•

Boundary load of 10 kN is applied at the top surface of the middle plate modeled using layered shell.

•

Fixed constraints is used on the outermost boundaries of four support members modeled using solid and shell members.

Results and Discussion

von Mises stress distribution for the given applied load is shown in Figure 3. The stress distribution in the model geometry matches quite well with the same in the reference geometry. The total displacement in both setups are shown in Figure 4 which also matches quite closely with each other. This shows the accuracy of different types of elements and connections used in the model geometry.

Figure 3: The comparison of von Mises stress distribution in both structural models.

The distribution of von Mises stress in the bottom and top layer of composite laminate modeled using layered shell and solid elements are shown in Figure 5 and Figure 6, respectively.

The distribution of von Mises stress at the common edge between layered shell and different structural elements is also compared with the reference model. Figure 7 through Figure 10 illustrate such a comparison with a good overall qualitative and quantitative match.

Figure 4: The comparison of total displacement distribution in both structural models.

Figure 5: The comparison of von Mises stress distribution in the bottom layer of both structural models.

Figure 6: The comparison of von Mises stress distribution in the top layer of both structural models.

Figure 7: von Mises stress along the common edge for layered shell-solid cladding coupling.

Figure 8: von Mises stress along the common edge for layered shell-shell cladding coupling.

Figure 9: von Mises stress along the common edge for layered shell-shell transition coupling.

Figure 10: von Mises stress along the common edge for layered shell-solid transition coupling.

Notes About the COMSOL Implementation

•

Modeling a composite laminate as a layered shell requires a surface geometry, in general referred to as a base surface, and a node which adds an extra dimension (1D) to the base surface geometry in the surface normal direction. You can use the functionality to model several layers stacked on top of each other having different thicknesses, material properties, and fiber orientations. You can optionally specify the interface materials between the layers, and control the number of through-thickness mesh elements for each layer.

•

The third direction for the selected coordinate system in the , , or represents the normal direction of the or physics. This is also the direction in which the layer stacking is interpreted from bottom to top, and therefore, it is crucial to know it during modeling. There are two ways to achieve this:

-

Using physics symbols: Go to the physics settings, find the section, and select the checkbox. Then go to the material feature, for instance, , to see the normal direction represented by green arrows in the geometry.

-

Using result templates: When a solution dataset is available, use the result template to plot the normal direction.

•

From a constitutive model point of view, you can either use the Layerwise (LW) theory based interface or the Equivalent Single Layer (ESL) theory based node in the interface.

•

The multiphysics coupling is used to model cladding between a interface and a , , or interface. In the section, shared and parallel boundaries options are provided to connect boundaries of different structural physics interfaces.¨

•

The multiphysics coupling is used to couple side-by-side structural connection between a interface and a or interface. This is a layered multiphysics coupling and in the section, it is possible to select only few layers for the connection.

•

The built-in material library contains data for fiber and matrix constituents as well as for unidirectional and bidirectional laminae.

Composite_Materials_Module/Tutorials/layered_shell_structure_connection

Modeling Instructions

From the menu, choose .

In the window, click

.

1

In the window, click

.

2

In the tree, select > , > , and > .

3

Right-click and choose .

4

5

In the tree, select > .

6

Layered Shell (lshell)

In the window, under right-click and choose .

Global Definitions

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
F	10[kN]	10000 N	Total load

1

In the toolbar, click and choose .

2

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

3

In the toolbar, click

.

4

button in the toolbar.

Complete geometry instructions can be found in the Appendix — Geometry Modeling Instructions section.

1

In the window, under right-click and choose .

2

In the window for , locate the section.

3

From the list, choose .

4

5

In the dialog, type 4,6 in the text field.

6

7

In the window for , locate the section.

8

In the table, enter the following settings:


Name	Expression	Unit	Description
misesTop_solid	solid.mises	N/m²	von Mises stress

1

In the window, right-click and choose .

2

In the window for , locate the section.

3

From the list, choose .

4

5

In the dialog, type 3,5 in the text field.

6

7

In the window for , locate the section.

8

In the table, enter the following settings:


Name	Expression	Unit	Description
misesBot_solid	solid.mises	N/m²	von Mises stress

1

Right-click and choose .

2

In the window for , locate the section.

3

In the table, enter the following settings:


Name	Expression	Unit	Description
misesTop_lshell	lshell.atxd1(lshell.d,mean(lshell.mises))		von Mises stress

Add required materials and layered material first.

1

In the toolbar, click

to open the window.

2

Go to the window.

3

In the tree, select > .

4

Right-click and choose .

5

In the tree, select > > .

6

Right-click and choose .

7

In the toolbar, click

to close the window.

Global Definitions

Layered Material 1 (lmat1)

1

In the window, under right-click and choose .

2

In the window for , locate the section.

3

In the table, enter the following settings:


Layer	Material	Rotation	Value	Thickness	Mesh elements
Layer 1	Unidirectional fiber lamina: AS4/APC2 carbon/PEEK thermoplastic [fiber volume fraction 58%] (mat2)	0.0	0 rad	1e-2[m]	1

4

5

In the table, enter the following settings:


Layer	Material	Rotation	Value	Thickness	Mesh elements
Layer 2	Unidirectional fiber lamina: AS4/APC2 carbon/PEEK thermoplastic [fiber volume fraction 58%] (mat2)	45	0.7854 rad	1e-2[m]	1

Layered Material Link 1 (llmat1)

1

In the window, under right-click and choose > .

2

In the window for , locate the section.

3

4

5

In the dialog, type 11-13, 25, 37, 69 in the text field.

6

7

In the window for , locate the section.

8

From the list, choose .

Material Link 1 (matlnk1)

1

Right-click and choose > .

2

In the window for , locate the section.

3

4

In the dialog, type 3-6, 8, 9, 11, 12 in the text field.

5

6

In the window for , locate the section.

7

From the list, choose .

Material Link 2 (matlnk2)

1

Right-click and choose > .

2

In the window for , locate the section.

3

4

In the dialog, type 1, 2, 7, 10 in the text field.

5

Set linear elastic material in all physics interfaces to orthotropic. The isotropic properties of is automatically converted to orthotropic properties.

Set the discretization of interface to quadratic Lagrange in order to have a proper structural connection with other interfaces having quadratic Lagrange discretization.

Solid Mechanics (solid)

1

In the window, under click .

2

In the window for , click to expand the section.

3

From the list, choose .

Linear Elastic Material 1

1

In the window, under > click .

2

In the window for , locate the section.

3

From the list, choose .

Linear Elastic Material 2

1

In the toolbar, click

and choose .

2

In the window for , locate the section.

3

From the list, choose .

4

Locate the section. Click

.

5

In the dialog, type 4, 6, 9, 12 in the text field.

6

Definitions (comp1)

Rotated System 2 (sys2)

1

In the toolbar, click

and choose .

2

In the window for , locate the section.

3

Find the subsection. In the α text field, type pi/4.

Solid Mechanics (solid)

Linear Elastic Material 2

1

In the window, under > click .

2

In the window for , locate the section.

3

From the list, choose .

The solid domains form a geometric union. To disconnect two adjacent domains, add an feature. To see the feature you first need to enable the .

4

button in the toolbar.

5

In the dialog, in the tree, select the checkbox for the node > .

6

Auxiliary Slit 1

1

In the toolbar, click

and choose .

2

In the window for , locate the section.

3

4

In the dialog, type 57 in the text field.

5

In any node in the Model Builder, you can add comments to explain the settings. Right click on the node to select the option to add the comment.

Boundary Load 1

1

In the toolbar, click

and choose .

2

Select Boundaries 20 and 33 only.

3

In the window for , locate the section.

4

From the list, choose .

5

Specify the Ftot vector as


0	x
0	y
F	z

Fixed Constraint 1

1

In the toolbar, click

and choose .

2

In the window for , locate the section.

3

4

In the dialog, type 1, 6, 43, 45, 48, 60, 82, 83 in the text field.

5

Layered Shell (lshell)

1

In the window, under click .

2

In the window for , locate the section.

3

4

5

In the dialog, type 11-13, 25 in the text field.

6

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. From the list, choose .

6

Specify the Ftot vector as


0	x
0	y
F	z

1

In the window, under click .

2

In the window for , locate the section.

3

4

5

In the dialog, type 37, 69 in the text field.

6

Add to shell interface and set it to orthotropic.

Linear Elastic Material, Layered 1

1

In the toolbar, click

and choose .

2

In the window for , locate the section.

3

From the list, choose .

4

Locate the section. Click

.

5

In the dialog, type 37, 69 in the text field.

6

Fixed Constraint 1

1

In the toolbar, click

and choose .

2

Select Edges 68 and 163 only.

Add different layered shell-structure multiphysics couplings for appropriate selections.

Layered Shell–Structure Cladding 1 (lssc1)

1

In the toolbar, click

and choose > .

2

In the window for , locate the section.

3

From the list, choose .

Layered Shell–Structure Transition 1 (lsst1)

1

In the toolbar, click

and choose > .

2

For this coupling only first layer is connected, so deselect the second layer. To get proper solid boundary selection activate the manual control of solid selections.

3

In the window for , locate the section.

4

Clear the checkbox.

5

In the table, clear the checkbox for .

6

Locate the section. Click

.

7

8

In the dialog, type 74 in the text field.

9

10

In the window for , locate the section.

11

Select the checkbox.

12

Locate the section. Click

.

13

14

In the dialog, type 39, 41 in the text field.

15

Layered Shell–Structure Cladding 2 (lssc2)

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. Click to select the

toggle button.

6

Select Boundary 25 only.

7

Locate the section. Click to select the

toggle button.

8

Select Boundary 69 only.

9

Locate the section. From the list, choose .

10

From the list, choose .

Layered Shell–Structure Transition 2 (lsst2)

1

In the toolbar, click

and choose > .

2

In the window for , locate the section.

3

From the list, choose .

4

Locate the section. Click

.

5

Select Edge 69 only.

1

In the toolbar, click

and choose .

2

In the window for , locate the section.

3

4

In the dialog, type 11, 13, 25, 37, 69 in the text field.

5

In the toolbar, click

.

1

In the window, click .

2

In the window for , locate the section.

3

Click the button.

4

Locate the section. In the text field, type 0.03.

5

In the text field, type 9.0E-4.

6

In the text field, type 1.3.

7

In the text field, type 0.2.

8

In the text field, type 1.

9

Switch off the generation of default plots, since for this study new custom plots are needed.

1

In the window, click .

2

In the window for , locate the section.

3

Clear the checkbox.

4

In the toolbar, click

.

Set default units for result presentation.

Preferred Units 1

1

In the toolbar, click

and choose .

2

In the window for , locate the section.

3

4

In the dialog, select > in the tree.

5

6

In the window for , locate the section.

7

In the table, enter the following settings:


Quantity	Unit	Preferred unit
Displacement	m	mm

8

9

In the dialog, select > in the tree.

10

11

In the window for , locate the section.

12

In the table, enter the following settings:


Quantity	Unit	Preferred unit
Stress tensor	N/m^2	MPa

13

Select the checkbox.

14

As generation of default plots are switched off, create custom datasets and plots.

Layered Material 1

In the toolbar, click

and choose .

Layered Material: Bottom Layer

1

In the toolbar, click

and choose .

2

In the window for , locate the section.

3

Find the subsection. Clear the checkbox.

4

In the table, clear the checkbox for .

5

In the text field, type Layered Material: Bottom Layer.

Layered Material: Top Layer

1

In the toolbar, click

and choose .

2

In the window for , type Layered Material: Top Layer in the text field.

3

Locate the section. Find the subsection. Clear the checkbox.

4

In the table, clear the checkbox for .

5

In the window, collapse the > node.

1

In the toolbar, click

.

2

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

1

Right-click and choose .

2

In the window for , locate the section.

3

In the text field, type solid.mises.

4

Locate the section. From the list, choose .

5

Click to expand the section. Select the checkbox.

6

In the text field, type 10.

Right-click and 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 lshell.mises.

5

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

6

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 u3.

4

In the text field, type v3.

5

In the text field, type w3.

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 shell.mises.

5

Locate the section. From the list, choose .

6

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 u2.

4

In the text field, type v2.

5

In the text field, type w2.

In the window, under click .

Table Annotation 1

1

In the toolbar, click

and choose .

2

In the window for , locate the section.

3

From the list, choose .

4

In the table, enter the following settings:


x-coordinate	y-coordinate	z-coordinate	Annotation
1.5	1.5	0	Layered Shell-Solid-Shell
1.5	4	0	Solid (Reference)

5

Locate the section. Clear the checkbox.

1

In the window, collapse the > node.

2

In the window, click .

3

In the toolbar, click

.

4

button in the toolbar.

1

Right-click and choose .

2

In the window for , type Displacement 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 solid.disp.

4

Locate the section. Clear the checkbox.

5

Locate the section. From the list, choose .

1

In the window, click .

2

In the window for , locate the section.

3

In the text field, type lshell.disp.

1

In the window, click .

2

In the window for , locate the section.

3

In the text field, type shell.disp.

1

In the window, collapse the > node.

2

In the window, click .

3

In the toolbar, click

.

Stress: Layered Shell, Bottom Layer

1

In the toolbar, click

.

2

In the window for , type Stress: Layered Shell, Bottom Layer in the text field.

1

Right-click and choose .

2

In the window for , locate the section.

3

In the text field, type misesBot_solid.

4

Locate the section. Select the checkbox.

5

In the text field, type 10.

6

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 lshell.mises.

5

Locate the section. From the list, choose .

6

Locate the section. From the list, choose .

Stress: Layered Shell, Bottom Layer

1

In the window, collapse the > node.

2

In the window, click .

3

In the toolbar, click

.

Stress: Layered Shell, Top Layer

1

Right-click and choose .

2

In the window for , type Stress: Layered Shell, Top Layer 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 misesTop_solid.

1

In the window, click .

2

In the window for , locate the section.

3

From the list, choose .

Stress: Layered Shell, Top Layer

1

In the window, collapse the > node.

2

In the window, click .

3

In the toolbar, click

.

Stress, Layered Shell-Solid Cladding

1

In the toolbar, click

.

2

In the window for , type Stress, Layered Shell-Solid Cladding in the text field.

3

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

4

Locate the section.

5

Select the checkbox. In the associated text field, type Y-coordinate (m).

6

Select the checkbox. In the associated text field, type von Mises stress (MPa).

1

Right-click and choose .

2

In the window for , locate the section.

3

4

In the dialog, type 17, 19, 21 in the text field.

5

6

In the window for , locate the section.

7

In the text field, type misesTop_lshell.

8

Click to expand the section. Select the checkbox.

9

From the list, choose .

10

In the table, enter the following settings:


Legends
Layered Shell

1

Right-click and choose .

2

In the window for , locate the section.

3

4

5

In the dialog, type 30 in the text field.

6

7

In the window for , locate the section.

8

In the text field, type solid.mises.

9

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

10

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


Legends
Solid (Reference)

Stress, Layered Shell-Solid Cladding

1

In the window, collapse the > node.

2

In the window, click .

3

In the toolbar, click

.

Stress, Layered Shell-Shell Cladding

1

Right-click and choose .

2

In the window for , type Stress, Layered Shell-Shell Cladding in the text field.

1

In the window, expand the node, then click .

2

In the window for , locate the section.

3

4

Select Edge 151 only.

1

In the window, click .

2

In the window for , locate the section.

3

4

Select Edge 156 only.

5

Locate the section. From the list, choose .

Stress, Layered Shell-Shell Cladding

1

In the window, collapse the > node.

2

In the window, click .

3

In the toolbar, click

.

Stress, Layered Shell-Shell Transition

1

Right-click and choose .

2

In the window for , type Stress, Layered Shell-Shell Transition in the text field.

3

Locate the section. In the text field, type X-coordinate (m).

1

In the window, expand the node, then click .

2

In the window for , locate the section.

3

4

Select Edges 18, 42, 69, and 108 only.

1

In the window, click .

2

In the window for , locate the section.

3

4

5

In the dialog, type 31, 56, 92, 124 in the text field.

6

7

In the window for , locate the section.

8

From the list, choose .

Stress, Layered Shell-Shell Transition

1

In the window, collapse the > node.

2

In the window, click .

3

In the toolbar, click

.

Stress, Layered Shell-Solid Transition

1

Right-click and choose .

2

In the window for , type Stress, Layered Shell-Solid Transition in the text field.

1

In the window, expand the node, then click .

2

In the window for , locate the section.

3

4

Select Edges 23, 48, 74, and 112 only.

1

In the window, click .

2

In the window for , locate the section.

3

In the text field, type misesTop_solid.

4

Locate the section. Click

.

5

6

In the dialog, type 40, 66, 101, 132 in the text field.

7

Stress, Layered Shell-Solid Transition

1

In the window, collapse the > node.

2

In the window, click .

3

In the toolbar, click

.

Appendix — Geometry Modeling Instructions

From the menu, choose .

In the window, click

.

1

In the window, click

.

2

Work Plane 1 (wp1)

1

In the toolbar, click

.

2

In the window for , locate the section.

3

Clear the checkbox.

4

Work Plane 1 (wp1) > Rectangle 1 (r1)

1

In the toolbar, click

.

2

In the window for , locate the section.

3

In the text field, type 0.4.

4

In the text field, type 0.5.

5

Locate the section. In the text field, type 0.3.

6

In the text field, type -0.5.

Work Plane 1 (wp1) > Rotate 1 (rot1)

1

In the toolbar, click

and choose .

2

Select the object only.

3

In the window for , locate the section.

4

Select the checkbox.

5

Locate the section. In the text field, type 90 180 270.

6

Locate the section. In the text field, type 0.5.

7

In the text field, type 0.5.

8

In the toolbar, click

.

Extrude 1 (ext1)

1

In the window, right-click and choose .

2

In the window for , locate the section.

3

From the list, choose .

4

On the object , select Boundary 1 only.

5

On the object , select Boundary 1 only.

6

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


Distances (m)
0.2

7

Select the checkbox.

8

1

In the toolbar, click

and choose .

2

Select the object only.

3

In the window for , locate the section.

4

In the text field, type 0.1.

5

1

In the toolbar, click

and choose .

2

Select the object only.

3

In the window for , locate the section.

4

In the text field, type -0.02.

5

Work Plane 2 (wp2)

In the toolbar, click

.

Work Plane 2 (wp2) > Plane Geometry

In the window, click .

Work Plane 2 (wp2) > Rectangle 1 (r1)

1

In the toolbar, click

.

2

In the window for , locate the section.

3

In the text field, type 1.4.

4

In the text field, type 1.

5

Locate the section. In the text field, type -0.2.

Work Plane 2 (wp2) > Rectangle 2 (r2)

1

In the toolbar, click

.

2

In the window for , locate the section.

3

In the text field, type 0.2.

4

In the text field, type 1.

5

Locate the section. In the text field, type -0.2.

1

In the window, right-click and choose > .

2

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

3

In the window for , locate the section.

4

Select the checkbox.

5

Locate the section. In the text field, type 2.5.

6

Extrude 2 (ext2)

1

In the toolbar, click

.

2

button in the toolbar.

3

Select the object only.

4

In the window for , locate the section.

5

From the list, choose .

6

On the object , select Boundary 1 only.

7

On the object , select Boundaries 1 and 2 only.

8

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


Distances (m)
0.01
0.02

9

Extrude 3 (ext3)

1

In the toolbar, click

.

2

In the window for , locate the section.

3

From the list, choose .

4

On the object , select Boundary 1 only.

5

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


Distances (m)
0.01
0.02

Form Union (fin)

In the toolbar, click

.