1. Can Bottom Snap-through
MSC.Patran 2005 r2
MSC.Marc 2005 r2
Estimated Time for Completion: ~35min
Experience Level: Lower

2. Topics Covered Topics covered in Modeling Topic covered in Analysis
Importing Geometry file with FEA data.
Neutral format (.out)
Creating Material Properties using Fields option.
Specify the input data that represent the stress-strain relationship.
Verifying Element Normal
Shell element layers are dependent on the element direction
Topic covered in Analysis
Applying Large Displacement/Large Strains Analysis.
Applying Modified Rik’s/Ramm Method
Topics covered in Review
Creating XY plots
Load vs. Displacement plot
Strain Energy vs. Time plot
Animations
Increment based animation
Time based animation

3. Problem Description
This example demonstrates the nonlinear analysis of the bottom of a 3D aluminum container under given internal pressure. The configuration of the bottom and the critical pressure leads to a snap-through problem.
Pressure

4. Simplifying the problem
Problem Description
Given Parameters
Aluminum can
Dimensions
Thickness of the shell=0.025 in
Diameter of the can= 2.61 in
Material properties
Young’s Modulus=11E6 psi
Poisson’s ratio=0.3
Simplifying the problem
To apply the axisymmetric condition, the rotation at the center of the bottom is fixed

5. Goal Find the critical pressure leading the snap-through phenomenon.
Find the location and value of the maximum stress during the loading and unloading processes.
Plot the Load vs. Displacement, and Strain Energy vs. time.

6. Expected Results Deformation Increasing Pressure Time 0.01.0
Decreasing Pressure
Time 1.02.0
Snap-through

7. Create Database file and Import Geometry
Create a New Database file called ‘can_snapthrough.db’
Use Marc as the analysis Code
Import the Neutral Geometry file called ‘canbottom.out’, and Node and element information will be imported.
Imported elements and nodes

8. Elements Verify the Shell Element Normal
This is required to know the layer information.
The top layer of the element is numbered as Layer 1.
Layer 5
Layer 1

9. Boudary Condtions Displacement Constraints Pressure Fixed_x Fixed_sym
This will fixed the displacements of the cut surface, however in-plane motion of the surface should be allowed.
Fixed_sym
This will symplify the problem. Unexpected buckling shape will be eliminated.
Pressure
Pressure_in
Loading condition
Pressure_zero
Unloading condition
Fixed_sym
Pressure_in
Pressure_zero

10. Fields Stress-strain curve
Plastic material property is defined as a table.

11. Materials Elastic model Plastic model Aluminum
Elastic Modulus: 11e6 psi
Possion’s ratio: 0.3
Plastic model
Use the stress-strain curve defined in the previous slide.

12. Properties Element Properties 2D Thin Shell Material: Aluminum
Thickness 0.025in

13. Load Cases Loading Name: LoadPressure Apply following three BCs/Load
Fixed_sym
Fixed_x
Pressure_in
Unloading
Name: UnloadingPressure
Pressure_zero
LoadPressure
UnloadPressure

14. Analysis Two Load Steps Solving Options Loading Name: PressureStep
Load Case selected: LoadPressure
Unloading
Name: UnloadingStep
Load Case selected: UnloadPressure
Solving Options
Large Displacement/Large Strain
Loads Follow Deformations
Adaptive Arc Length method
Use Modifed Riks/Ramm method
Use default options for all others
Required nodal results
Displacement, Rotation, Reaction Force, and External Force

15. Review Results Select the reference information
Reference nodes to review the displacement and stress results
Reference increment to compare the results based on time (load factor) and increment (solving step)
Reference increments for
Loading and unloading results:
Select the increment results with the time increasing.
Reference node for
the displacement axis
Reference nodes for
the von-Mises stress

16. Load applied vs. displacement Curve
Results
Load applied vs. displacement Curve
Snap-through information can be found by plotting the results with the increasing time.
The critical load leads the snap-through is about 370 psi at time=0.74 (=500psi x 0.74)
loading
unloading
Snap-through
At time=0.74
Based on the increasing time(load)
Based on the increment(solving step)

17. Plastic Strain Energy vs. Time
Results
Plastic Strain Energy vs. Time
Plastic Strain Energy is dramatically increased at the critical load (or time)
It does not changed during the unloading step. So there is only elastic deformation in the step.
Snap-through
loading
unloading
Based on the increasing time(load)
Based on the increment(solving step)

18. Results Elastic Strain Energy vs. Time Elastic Deformation
Snap-through
loading
unloading
Based on the increasing time(load)
Based on the increment(solving step)

19. von Mises Stress vs. Time
Results
von Mises Stress vs. Time
Use the reference nodes for the von Mises Stress.
Maximum von Mises occurs after the loading step and it is about 0.1 MPa
Locate the maximum stress by plotting on the geometry (Next slide)
Snap-through
Maximum stress
Plastic Deformation
loading
unloading

20. Results (Stress: von Mises)
Stress at layer 1 (inside)
Stress at layer 5 (Outside)
Max=0.101 psi
Max=0.104 psi

21. Animation (based on the increments)

22. Animation (based on the Time: Actual motion)

23. Further Analysis (Optional)
Remove the axisymmetric condition (fixed rotation) from the node at the cetner. Find the difference from the current analysis.
For further simplification, use line elements and the axisymmetric condition and compare the results to the one with shell elements.