Failure Prediction in a Laminated Composite Shell

In the tree, select .

Load the material properties and material strengths from a file.

Global Definitions

Parameters 1

In the window, under click .

In the window for , locate the section.

Layered Material: [90/-45/45/0]

Browse to the model’s Application Libraries folder and double-click the file failure_prediction_in_a_laminated_composite_shell_materialproperties.txt.

Material 1 (mat1)

In the window, right-click and choose .

Add a node and assign appropriate thickness and rotation angles to each ply.

Right-click and choose .

In the window for , locate the section.


Layer	Material	Rotation (deg)	Thickness	Mesh elements
Layer 1	Material 1 (mat1)	90	th	1

Click three times.


Layer	Material	Rotation (deg)	Thickness	Mesh elements
Layer 2	Material 1 (mat1)	-45	th	1
Layer 3	Material 1 (mat1)	45	th	1
Layer 4	Material 1 (mat1)	0	th	1

In the text field, type Layered Material: [90/-45/45/0].

Locate the section. Click in the upper-right corner of the section.

Click to expand the section. In the text field, type 0.4.

Work Plane 1 (wp1)>Plane Geometry

button in the toolbar.

Locate the section. Click in the upper-right corner of the section.

Click in the upper-right corner of the section.

Geometry 1

Work Plane 1 (wp1)

In the toolbar, click

In the window, click .

Work Plane 1 (wp1)>Square 1 (sq1)

In the toolbar, click

In the window for , locate the section.

In the text field, type 1e-2.

Layered Material Link 1 (llmat1)

button in the toolbar.

Materials

In the window, under right-click and choose .

Shell (shell)

Activate .

Layered Linear Elastic Material 1

button in the toolbar.

In the dialog box, in the tree, select the check box for the node .

Click .

Set the discretization for the displacement field to in order to resemble the benchmark example.

In the window for , click to expand the section.

From the list, choose .

Right-click and choose .

Safety 2, 3, 4, 5, 6, 7

Select Boundary 1 only.

In the window for , locate the section.

From the list, choose .

Global Definitions

Material 1 (mat1)

In the window, under click .

In the window for , locate the section.

Layered Linear Elastic Material 1


Property	Variable	Value	Unit	Property group
Young’s modulus	{Evector1, Evector2, Evector3}	{E1, E2, E3}	Pa	Orthotropic
Poisson’s ratio	{nuvector1, nuvector2, nuvector3}	{nu12, nu23, nu13}	1	Orthotropic
Shear modulus	{Gvector1, Gvector2, Gvector3}	{G, G, G}	N/m²	Orthotropic
Density	rho	1500	kg/m³	Basic

Shell (shell)

In the window, under click .

Safety: Tsai-Wu Orthotropic Criterion

In the toolbar, click

and choose .

In the window for , type Safety: Tsai-Wu Orthotropic Criterion in the text field.

Locate the section. From the list, choose .

Create six similar nodes by duplicating the node. Replace the failure criterion according to the table below:


Name	Failure Criterion
Safety 2	Tsai-Hill
Safety 3	Hoffman
Safety 4	Modified Tsai-Hill
Safety 5	Azzi-Tsai-Hill
Safety 6	Norris
Safety 7	Tsai-Wu anisotropic

Global Definitions

Material 1 (mat1)

Enter the material properties for the Tsai-Wu anisotropic criterion as shown in Equation 1 and Equation 2.

In the window, under click .

In the window for , locate the section.

Prescribed Displacement/Rotation 1


Property	Variable	Value	Unit	Property group
Tensile strengths	{sigmats1, sigmats2, sigmats3}	{Sigmats1, Sigmats2, Sigmats3}	Pa	Orthotropic strength parameters, Voigt notation
Compressive strengths	{sigmacs1, sigmacs2, sigmacs3}	{Sigmacs1, Sigmacs2, Sigmacs3}	Pa	Orthotropic strength parameters, Voigt notation
Shear strengths	{sigmass1, sigmass2, sigmass3}	{Sigmass23, Sigmass13, Sigmass12}	Pa	Orthotropic strength parameters, Voigt notation
Second rank tensor, Voigt notation	{F_s1, F_s2, F_s3, F_s4, F_s5, F_s6}	{1/Sigmats1-1/Sigmacs1, 1/Sigmats2-1/Sigmacs2, 1/Sigmats3-1/Sigmacs3, 0, 0, 0}	1/Pa	Anisotropic strength parameters, Voigt notation
Fourth rank tensor, Voigt notation	{F_f11, F_f12, F_f22, F_f13, F_f23, F_f33, F_f14, F_f24, F_f34, F_f44, F_f15, F_f25, F_f35, F_f45, F_f55, F_f16, F_f26, F_f36, F_f46, F_f56, F_f66} ; F_fij = F_fji	{1/(Sigmats1Sigmacs1), -0.5sqrt(1/((Sigmats1Sigmacs1)(Sigmats2Sigmacs2))), 1/(Sigmats2Sigmacs2), -0.5sqrt(1/((Sigmats1Sigmacs1)(Sigmats3Sigmacs3))), -0.5sqrt(1/((Sigmats2Sigmacs2)(Sigmats3Sigmacs3))), 1/(Sigmats3*Sigmacs3), 0, 0, 0, 1/Sigmass23^2, 0, 0, 0, 0, 1/Sigmass13^2, 0, 0, 0, 0, 0, 1/Sigmass12^2}	m²·s^4/kg²	Anisotropic strength parameters, Voigt notation

Shell (shell)

Fixed Constraint 1

In the toolbar, click

and choose .

Select Point 1 only.

In the toolbar, click

and choose .

Select Point 2 only.

In the window for , locate the section.

Select the check box.

Apply a total tensile load of 15 N as an edge load.

Edge Load 1

In the toolbar, click

and choose .

Select Edge 4 only.

In the window for , locate the section.

From the list, choose .

Specify the Ftot vector as


Ftotal	x
0	y
0	z

Mesh 1

Use a single quadrilateral element.

Free Quad 1

In the toolbar, click

and choose .

Select Boundary 1 only.

Distribution 1

Right-click and choose .

In the window for , locate the section.

From the list, choose .

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

Generation of default plots is switched off in order to show how to create different plots to analyze the layered material.

Study 1

In the window, click .

In the window for , locate the section.

Clear the check box.

In the toolbar, click

Results

In the window, expand the node.

Layered Material 1

In the window, expand the node.

Right-click and choose .

In the window for , locate the section.

In the text field, type 10.

Add a local z-coordinate as a parameter in order to compute failure indices, safety factors and stresses in different plies.

Parameters

In the toolbar, click

In the window for , locate the section.

Select the check box in the result node to enable automatic reevaluation of evaluation groups when the model is resolved.


Name	Expression	Value	Description
zl	0.5*th	2.5E-5	Local z-coordinate

Use an instead of to compute the failure indices, safety factors, and stresses.

In the window, click .

In the window for , locate the section.

Select the check box.

Failure Indices

In the toolbar, click

In the window for , type Failure Indices in the text field.

Locate the section. From the list, choose .

Locate the section. Select the check box.

Point Evaluation 1

Right-click and choose .

To compute the failure indices at the midplane of each ply, load the expressions from a file.

Select Point 4 only.

In the window for , locate the section.

From the list, choose .

In the text field, type zl.

Locate the section. Click

Browse to the model’s Application Libraries folder and double-click the file failure_prediction_in_a_laminated_composite_shell_failure_indices.txt.

In the toolbar, click

Failure Indices

In the window, click .

Failure Indices in Ply 1

In the toolbar, click

In the window for , type Failure Indices in Ply 1 in the text field.

Safety Factors

In the toolbar, click

In the window for , type Safety Factors in the text field.

Locate the section. From the list, choose .

Locate the section. Select the check box.

Point Evaluation 1

Right-click and choose .

To compute the safety factors at the midplane of each ply, load the expressions from a file.

Select Point 4 only.

In the window for , locate the section.

From the list, choose .

In the text field, type zl.

Locate the section. Click

Browse to the model’s Application Libraries folder and double-click the file failure_prediction_in_a_laminated_composite_shell_safety_factors.txt.

In the toolbar, click

Safety Factors

In the window, click .

Safety Factors in Ply 1

In the toolbar, click

In the window for , type Safety Factors in Ply 1 in the text field.

Stresses

In the toolbar, click

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

Locate the section. From the list, choose .

Locate the section. Select the check box.

Point Evaluation 1

Right-click and choose .

To compute the stresses at the midplane of each ply, load the expressions from a file.

Select Point 4 only.

In the window for , locate the section.

From the list, choose .

In the text field, type zl.

Locate the section. Click

Browse to the model’s Application Libraries folder and double-click the file failure_prediction_in_a_laminated_composite_shell_stresses.txt.

In the toolbar, click

Stresses

In the window, click .

Stresses in Ply 1

In the toolbar, click

In the window for , type Stresses in Ply 1 in the text field.

To compute the failure indices, safety factors, and stresses at the midplane of the remaining plies, change the zl value in the node to 1.5*th, 2.5*th, 3.5*th for the second, third, and fourth ply, respectively, and create a new table for each point evaluation.

To visualize von Mises stress at the midplane of each ply, use four different plots and shift them in the z direction for better visualization. As the stresses are constant within a ply with very small numerical fluctuations, use the operator to get uniform color in each ply.

von Mises Stress (Ply)

In the toolbar, click

and choose .

In the window for , type von Mises Stress (Ply) in the text field.

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

In the text area, type Layered Material Slice: von Mises Stress (MPa).

Locate the section. From the list, choose .

Ply 1

Right-click and choose .

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

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

Locate the section. In the text field, type round(shell.mises).

From the list, choose .

Locate the section. From the list, choose .

In the text field, type -0.75.

Deformation 1

Right-click and choose .

In the window for , locate the section.

Select the check box.

In the associated text field, type 1.

Locate the section. In the text field, type w-1.5e-3.

Ply 2, 3, 4

Create three similar nodes by duplicating the node above, and replacing the local z-coordinate according to the following table. Replace the color table in the subsequent nodes, and replace the Z-component field in the corresponding node with the following choices in the table:


Name	Local z-coordinates	Choice of color table	Z component field expression
Ply 2	-0.25	Cyclic	w-0.5e-3
Ply 3	0.25	Disco	w+0.5e-3
Ply 4	0.75	Thermal	w+1.5e-3