COMSOL 6.4 - Failure Prediction in a Layered Shell

In the tree, select > .

In the tree, select > .

In the tree, select > .

In the tree, select > .

Load the text file containing the material properties and material strengths.

Global Definitions

Parameters 1

In the window, under click .

In the window for , locate the section.

Set up three rotated coordinate systems.

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

Definitions

Rotated System 2 (sys2)

In the toolbar, click

and choose .

In the window for , locate the section.

Find the subsection. In the α text field, type pi/2.

Rotated System 3 (sys3)

Right-click and choose .

In the window for , locate the section.

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

Rotated System 4 (sys4)

Right-click and choose .

In the window for , locate the section.

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

Geometry 1

Work Plane 1 (wp1)

In the toolbar, click

In the window for , click

Work Plane 1 (wp1) > Plane Geometry

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.

Click the

button in the toolbar.

Materials

Material 1 (mat1)

In the window, under right-click and choose .

Ply 1

Activate option from button.

Click the

button in the toolbar.

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

The layered shell is modeled using four separate shell interfaces located on the same boundary (mesh surface), sharing the degrees of freedom. The stacking of the shells is done using a option in a feature. With this option the constraints and loads are transferred to the actual midplane of the shells without modeling it.

As the same degrees of freedom are to be shared by all shell interfaces, set the displacement field to and the displacement of the shell normals to for Shell 2, Shell 3, and Shell 4.

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

The results given in the benchmark example are at the midplane of each shell layer. Set the to zero for all shells.

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

In the text field, type shell1.

Click to expand the section. In the z text field, type 0.

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

In the window, under > click .

In the window for , locate the section.

In the d0 text field, type th.

From the list, choose .

In the zreloffset text field, type -3.

Choose the transversely isotropic solid model for the linear elastic material and assign as .

In the window, click .

In the window for , locate the section.

From the list, choose .

Select the checkbox.

Shell Local System 1

In the window, click .

In the window for , locate the section.

From the list, choose .

Ply 2

In the window, under click .

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

Locate the section. From the list, choose .

Locate the section. In the z text field, type 0.

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

In the text field, type ar.

In the window, under > click .

In the window for , locate the section.

In the d0 text field, type th.

From the list, choose .

In the zreloffset text field, type -1.

Choose the transversely isotropic solid model for the linear elastic material and assign as .

In the window, click .

In the window for , locate the section.

From the list, choose .

Select the checkbox.

Shell Local System 1

In the window, click .

In the window for , locate the section.

From the list, choose .

Ply 3

In the window, under click .

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

Locate the section. From the list, choose .

Locate the section. In the z text field, type 0.

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

In the text field, type ar.

In the window, under > click .

In the window for , locate the section.

In the d0 text field, type th.

From the list, choose .

In the zreloffset text field, type 1.

Choose the transversely isotropic solid model for the linear elastic material and assign as .

In the window, click .

In the window for , locate the section.

From the list, choose .

Select the checkbox.

Shell Local System 1

In the window, click .

In the window for , locate the section.

From the list, choose .

Ply 4

In the window, under click .

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

Locate the section. From the list, choose .

Locate the section. In the z text field, type 0.

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

In the text field, type ar.

In the window, under > click .

In the window for , locate the section.

In the d0 text field, type th.

From the list, choose .

In the zreloffset text field, type 3.

Choose the transversely isotropic solid model for the linear elastic material.

In the window, click .

In the window for , locate the section.

From the list, choose .

Select the checkbox.

Materials

Material 1 (mat1)

Select the material properties for the transversely isotropic material from Table 1.

In the window, under > click .

In the window for , locate the section.


Property	Variable	Value	Unit	Property group
Young’s modulus	{Evect1, Evect2}	{E1, E2}	Pa	Transversely isotropic
Poisson’s ratio	{nuvect1, nuvect2}	{nu12, nu23}	1	Transversely isotropic
Shear modulus	{Gvect1}	G	N/m²	Transversely isotropic
Density	rho	1500	kg/m³	Basic

Ply 1 (shell1)

Safety: Tsai–Wu Orthotropic, Plane Stress Criterion

In the window, under > click .

In the toolbar, click

and choose .

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

Locate the section. From the list, choose .

Select the checkbox.

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

Create six similar nodes by duplicating the node, and replace the failure criterion as given in the table below:


Name	Failure Criterion
Safety 2	Hoffman
Safety 3	Tsai-Hill with Plane Stress option
Safety 4	Azzi-Tsai-Hill
Safety 5	Norris
Safety 6	Tsai-Wu anisotropic

Select all nodes under > , and right-click to . Then, go to under , , and and right-click to .

Materials

Material 1 (mat1)

In the window, under > click .

In the window for , locate the section.

Apply a nodal tensile load of 15 N as an edge load. The load is shared by all shell midplanes, hence it is divided by 4 in order to keep a total value of 15 N.


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}	{Fs11, Fs22, Fs33, 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	{Ff11, Ff12, Ff22, Ff13, Ff23, Ff33, 0, 0, 0, Ff44, 0, 0, 0, 0, Ff55, 0, 0, 0, 0, 0, Ff66}	m²·s4/kg²	Anisotropic strength parameters, Voigt notation

Ply 1 (shell1)

Fixed Constraint 1

In the toolbar, click

and choose .

Select Point 1 only.

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/4	x
0	y
0	z

Now select and nodes under , and right-click to . Then go to , , and ; and right-click to .

Ply 2 (shell2)

To enforce a fixed x direction translation on Node 2, apply the displacement -u0 in the x direction to Point 2 of shell2, and the displacement u0 in the x direction to the same point of shell3. Also add a node under shell2 for the additional degree of freedom u0.

In the window, under click .

Prescribed Displacement/Rotation 1

In the toolbar, click

and choose .

Select Point 2 only.

In the window for , locate the section.

From the list, choose .

In the u 0 x text field, type -u0.

Click the

button in the toolbar.

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

Global Equations 1 (ODE1)

In the toolbar, click

and choose .

In the window for , locate the section.


Name	f(u,ut,utt,t) (1)	Initial value (u_0) (1)	Initial value (ut_0) (1/s)	Description
u0		0	0

Locate the section. Click

In the dialog, type displacement in the text field.

In the tree, select > .

Prescribed Displacement/Rotation 1

Ply 3 (shell3)

In the toolbar, click

and choose .

Select Point 2 only.

In the window for , locate the section.

From the list, choose .

In the u 0 x text field, type u0.

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.

Switch off the generation of default plots.

Study 1

In the window, click .

In the window for , locate the section.

Clear the checkbox.

In the toolbar, click

Set default units for result presentation.

Results

Preferred Units 1

In the toolbar, click

and choose .

In the window for , locate the section.

In the dialog, select > in the tree.

In the window for , locate the section.


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

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

Cut Point 3D 1

In the window, expand the > node.

Right-click > and choose .

In the window for , locate the section.

In the text field, type 0.5e-2.

In the text field, type 0.

In the window, click .

In the window for , locate the section.

Select the checkbox.

Failure Indices in Ply 1

In the toolbar, click

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

Locate the section. From the list, choose .

Locate the section. Select the checkbox.

Point Evaluation 1

Right-click and choose .

In the window for , locate the section.


Expression	Unit	Description
shell1.emm1.sf1.f_im	1	Tsai-Wu orthotropic failure index, middle, plane stress
shell1.emm1.sf2.f_im	1	Hoffman failure index, middle
shell1.emm1.sf3.f_im	1	Tsai-Hill failure index, middle, plane stress
shell1.emm1.sf4.f_im	1	Azzi-Tsai-Hill failure index, middle
shell1.emm1.sf5.f_im	1	Norris failure index, middle
shell1.emm1.sf6.f_im	1	Tsai-Wu anisotropic failure index, middle

In the toolbar, click

Evaluation Group 2, 3, 4

Create three similar evaluation groups by duplicating the node, and replace the word shell1 in the by shell2, shell3, and shell4 in nodes in respective evaluation groups. Rename evaluation group nodes appropriately.

Select evaluation groups corresponding to the failure indices, and right click on to create a group.

Failure Indices

In the window, under click .

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

Safety Factors in Ply 1

In the toolbar, click

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

Locate the section. From the list, choose .

Locate the section. Select the checkbox.

Point Evaluation 1

Right-click and choose .

In the window for , locate the section.


Expression	Unit	Description
shell1.emm1.sf1.s_fm	1	Tsai-Wu orthotropic safety factor, middle, plane stress
shell1.emm1.sf2.s_fm	1	Hoffman safety factor, middle
shell1.emm1.sf3.s_fm	1	Tsai-Hill safety factor, middle, plane stress
shell1.emm1.sf4.s_fm	1	Azzi-Tsai-Hill safety factor, middle
shell1.emm1.sf5.s_fm	1	Norris safety factor, middle
shell1.emm1.sf6.s_fm	1	Tsai-Wu anisotropic failure index, middle

In the toolbar, click

Evaluation Group 6, 7, 8

Select evaluation groups corresponding to the safety factors, and right click on to create a group.

Safety Factors

In the window, under click .

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

Stresses in Ply 1

In the toolbar, click

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

Locate the section. From the list, choose .

Locate the section. Select the checkbox.

Point Evaluation 1

Right-click and choose .

In the window for , locate the section.