ws 04 buckling

WS4-1

NAS400, Workshop 4, August 2011Copyright 2011 MSC.Software Corporation

WORKSHOP 4

BUCKLING OF A COMPOSITE PLATE


● Workshop Objectives• Linear buckling analysis

• Post-buckling analysis

● Software Version• Patran 2010.2.3

• MD Nastran 2011

● Required• No Supporting file is required

● Problem Description• The simulation is to use 3D solid finite elements. The elements are

uniformly spaced along the length of the beam (i.e. a mesh 100 elements wide and four elements deep).


• Problem Description– A nine-layer composite square plate (10 in. X 10 in.) is subjected to

uniaxial compressive edge load (400 lbf/in). The edges of the plate are simply supported in bending, but free to move in-plane. The thicknesses and the fiber orientations of the layers are given below. Calculate the bifurcation buckling load, and the post-buckling behavior of the plate.

– Due to symmetrical geometry, lamination sequence, and orientations, only a quarter of the model is modeled here, using a 10X10 quad4 mesh.

The material properties for all the layers are as follows:

E11 = 40.E6 psi ; E22 = 1.E6 psi

NU12 = 0.25

G12 = G13 = 0.6E6 psi

G23 = 0.5E6 psi


● Suggested Exercise Steps1. Create a New Database.

2. Create a 5x5 inch surface in the XY Plane.

3. Mesh the model with 10x10 mesh of Quad4 elements.

4. Create the Orthotropic Lamina Material.

5. Create the Laminate Composite Material.

6. Define the Element Properties.

7. Create Displacement Constraint.

8. Create Edge Load Force.

9. Set Up and Run the Buckling Analysis.

10. Access the Bifurcation Buckling Results.

11. Post Process Buckling Mode.

12. Apply a Small Transverse Load.

13. Set Up and Run the Implicit Nonlinear Analysis.

14. Access the Nonlinear Results.

15. Post Process Stress Results.

16. Create Graph.

17. Quit Patran.


Create a new database called comp_plate.db.

a. Pull down File > New.

b. Enter comp_plate as the file name.

c. Click OK.

d. Make sure MD Nastran is set as the Analysis Code.

e. Click OK.

Step 1. Create a New Database

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a

b ce


Step 2. Create Surface in the XY Plane

Geometry: Use the XYZ method to create a 4 x 1 surface.

a. Under the Geometry tab, click on XYZ in the Surfaces group.

b. Enter <5 5 0> for the Vector Coordinate List.

c. Click Apply.

b

c

a


Step 3. Create Mesh of Quad4 Elements

Mesh the plate.

a. Under the Meshing tab, click on Surface in the Meshers group.

b. Click the Surface List panel.

c. Pick the surface.

d. Enter 0.5 as Value for Global Edge Length

e. Click Apply.

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b

d

e

c

This is what the mesh should look like after clicking Apply.


Step 4. Create the Orthotropic Lamina Material

Create the orthotropic lamina material properties.

a. Under the Properties tab, click on 2D in the Orthotropic group.

b. Enter lamina_mat1 as the Material Name.

c. Click Input Properties.

d. Select Linear Elastic as the Constitutive Model.

e. Enter 40E6 for Elastic Modulus 11.

f. Enter 1E6 for Elastic Modulus 22.

g. Enter 0.25 for Poisson Ratio 12.

h. Enter 0.6E6 for Shear Modulus 12.

i. Enter 0.5E6 for Shear Modulus 23.

j. Enter 0.6E6 for Shear Modulus 13.

k. Click OK.

l. Click Apply.

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Step 5. Create the Laminate Composite Material

Create the laminate composite material

a. Under the Properties tab, click on Laminate in the Composite group.

b. Enter laminated_composite as the Material Name.

c. Enter 9 as value for Insert.

d. Click on Insert.

e. Select lamina_mat1 for all the rows.

f. Enter 0.01 as Thicknesses for rows 1, 3, 5, 7 and 9.

g. Enter 0.0125 as Thicknesses for rows 2, 4, 6, and 8.

h. Enter 0 as Orientations for rows 1, 3, 5, 7, and 9.

i. Enter 90 for Orientations for rows 2, 4, 6, and 8.

j. Click Apply.

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b

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hi

jIf you end up with an extra row, just click on it and hit the Delete Selected Rows

button.


Step 6. Define the Element Properties

Define the element properties.

a. Under the Properties tab, click on Shell in the 2D Properties group.

b. Enter composite_plate as the Property Set Name.

c. Select Laminate as Options.

d. Click Input Properties.

e. Click Mat Prop Name icon to bring up the Materials list.

f. Select laminated_composite.

g. Click OK.

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b

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a. Click Select Application Region.

b. Select Surface 1.

c. Click Add.

d. Click OK.

e. Click Apply. c

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a

Step 6. Define the Element Properties (Cont.)

b


Step 7. Create Displacement Constraint

Create the Displacement Boundary

conditions.

a. Under the Loads/BCs tab, click on Displacement Constraint in the Nodal group.

b. Enter Edge_Support as the New Set Name.

c. Click Input Data.

d. Enter < , , 0 > as the Translations.

e. Click OK.

f. Click Select Application Region.

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b

c

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a. Select Geometry.

b. Click inside the Select Geometry Entities panel.

c. Use Curve or Edge picking icon.

d. Pick the left and bottom edges of surface.

e. Click Add.

f. Click OK.

g. Click Apply.

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b

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Step 7. Create Displacement Constraint (Cont.)

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a. Enter Symmetry_X as the New Set Name.

b. Click Input Data.

c. Enter <0, , > as the Translations.

d. Enter < , 0, 0> as the Rotations.

e. Click OK.

f. Open Select Application Region.

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bf

c

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a. Pick the right edge of surface.

b. Click Add.

c. Click OK.

d. Click Apply.

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c


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a. Enter Symmetry_Y as the New Set Name.

b. Open Input Data.

c. Enter < ,0, > as the Translations.

d. Enter <0, ,0> as the Rotations.

e. Click OK.

f. Open Select Application Region. d

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c


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bf


a. Pick the top edge of surface.

b. Click Add.

c. Click OK.

d. Click Apply.

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The 2000 lb. of total load applied on the edge with a length of 5 in. is equivalent to 400 lbf/in.

Step 8. Create Edge Load Force

Create the Force for the edge load.

a. Under the Loads/BCs tab, click on Total Load in the Element Uniform group.

b. Enter Edge_Load as the New Set Name.

c. Select 2D as Target Element Type.

d. Click Input Data.

e. Enter < 2000, > as the Edge Load.

f. Click OK.

g. Click Select Application Region.

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b

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a. Pick the left edge.

b. Click Add.

c. Click OK.

d. Click Apply.

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b

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Step 8. Create Edge Load Force (Cont.)

d


Step 9. Set Up and Run the Buckling Analysis

Run analysis

a. Under the Analysis tab, click on Entire Model in the Analyze group.

b. Enter bifurcation_buck as the Job Name.

c. Open Solution Type.

d. Select Buckling as Solution Type.

e. Click OK.

f. Click Apply.

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e

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b

c

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Read (Attach) results.

a. Under the Analysis tab, click on XDB in the Access Results group.

b. Click on Select Results File.

c. Select bifurcation_buck.xdb.

d. Click OK.

e. Click Apply.

Step 10: Access the Bifurcation Buckling Results

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Step 11. Post Process Buckling Mode

Post process buckling mode

a. Under the Results tab, click on Fringe/Deformation in the Quick Plot group.

b. Select Default, A1:Mode 1 under Select Result Cases.

c. Select Eigenvectors, Translational under Select Fringe Result.

d. Select Eigenvectors, Translational under Select Deformation Result.

e. Click Apply.

f. Click the Iso 3 View.

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Buckling Load (Estimated): 360.6 lbf/in (=0.90146*400)

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Step 12. Apply a Small Transverse Load

Create an (small) out-of-plane Force at the center.

a. Under the Loads/BCs tab, click on Force in the Nodal group.

b. Enter Fz_Center as the New Set Name.

c. Click Input Data.

d. Enter < , , 0.1 > as the Force.

e. Click OK.

f. Click Select Application Region.

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b

c

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a. Click Reset Graphics and change to Front View.

b. Select FEM.

c. Click inside the Select Nodes panel.

d. Pick the center node.

e. Click Add.

f. Click OK.

g. Click Apply.

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Step 12. Apply a Small Transverse Load

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Step 13. Set Up and Run the Implicit Nonlinear Analysis

Set up the non-linear Analysis job.

a. Under the Analysis tab, click on Entire Model in the Analyze group.

b. Enter post_buck as the Job Name.

c. Open Solution Type.

d. Select Implicit Nonlinear as Solution Type.

e. Click on Solution Parameters.

f. Check SOL400 Run, and uncheck Assumed Strain

g. Click on Results Output Format

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a. Select MASTER/DBALL

b. Select Print

c. Click OK.

d. Click OK.

e. Click OK.

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Step 13. Set Up and Run the Implicit Nonlinear Analysis (Cont.)

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a. Click on Subcases.

b. Click on Default under Available Subcases.

c. Click on Subcase Parameters.

d. Select Large Displacement/Large Strains.

e. Click on Load Increment Parameters.

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a. Select Fixed.

b. Enter 100 as Number of Increments.

c. Click OK.

d. Click on Iteration Parameters.

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a. Select Pure Full Newton as Matrix Update Method.

b. Select Displacement Error.

c. Select Load Error.

d. Select Work Error.

e. Select Vector Component Method.

f. Enter 4 as Max # of Bisections.

g. Click OK.

h. Click OK.

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The load is bisected when the solution diverges until the limit

(max # of bisections) is reached..

The load is bisected when the solution diverges until the limit

(max # of bisections) is reached..


a. Select Output Requests.

b. Click on Standard Output.

c. Change the form type to Advanced.

d. Change the Intermediate Output Option to Yes.

e. Click OK.

f. Click OK.

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a. Click Apply

b. Click Cancel.

c. Click Apply.

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Read (Attach) results.

a. Under the Analysis tab, click on MASTER/DBALL in the Access Results group.

b. Click on Select Results File.

c. Select post_buck.MASTER.

d. Click OK.

e. Click Apply.

Step 14: Access the Nonlinear Results

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c

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Step 15. Post Process Stress Results

Post-process stress results.

a. Under the Results tab, click on Fringe/Deformation in the Quick Plot group.

b. Select the last result case.

c. Select Stress Tensor for Fringe Result.

d. Select Displacements, Translational for deformation.

e. Select Layer 1 for Position.

f. Click on the Deform Attributes icon.

g. Select True Scale.

h. Unselect Show Undeformed.

i. Click Apply.

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Step 15. Post Process Stress Results (Cont.)


Step 16. Create Graph

Create Normal Deflection vs. Load curve.

a. Under the Results tab, select Graph in the Result Plots group.

b. Select all the Non-linear (A2:…) result cases.

c. Select Displacements, Translational.

d. Select Z Component.

e. Select Percent of Load.

f. Click on the Target Entities icon.

g. Pick the center node.

h. Click Apply.

fSee the notes on the next page to help clarify the Create/Graph Select Result Cases

options, needed for step b, below.

b

c

d

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a


Step 16. Create Graph (Cont.)

Then, you can click and drag or click and shift-click to select the Result Cases

to plot (b), as shown here.

In order to expand the List Box to show all the Result Cases, click on the leftmost small icon (a), which should result in a List Box like this:

When first attempting to ‘Graph’, the Select Result Cases window

might look like this:

a

b


This deflection vs. Load Curve predicted by MD Nastran agrees well with that obtained by Noor and Hartley (“Nonlinear Shell Analysis via Mixed Isoparametric Elements”, Computers and Structures, Vol. 7, 1977, pp. 615-626).

Step 16. Create Graph (Cont.)

The ideal amount of normal force to apply is unknown… it needs to be large enough to force an instability, but small enough to have little effect on the ‘suddenness’ of the instability… feel free to experiment with smaller values if you have time and see the effect on this curve.


Step 17. Quit Patran

ws 04 buckling

Documents

implicit nonlinear

open solution

quick plot

bifurcation

small transverse

create displacement

click input

laminate composite