Can Bottom Snapthrough MSC Patran 2005 r 2

Can Bottom Snap-through MSC. Patran 2005 r 2 MSC. Marc 2005 r 2 Estimated Time for Completion: ~35 min Experience Level: Lower

Topics Covered • Topics covered in Modeling • 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 2

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

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=11 E 6 psi • Poisson’s ratio=0. 3 • Simplifying the problem • To apply the axisymmetric condition, the rotation at the center of the bottom is fixed 4

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. 5

Expected Results • Deformation Increasing Pressure Time 0. 0 1. 0 Decreasing Pressure Time 1. 0 2. 0 Snap-through 6

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 7

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 8 Layer 1

Boudary Condtions • Displacement Constraints Fixed_x • Fixed_x • This will fixed the displacements of the cut Fixed_sym 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_in • Pressure_in • Loading condition Pressure_zero • Pressure_zero • Unloading condition 9

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

Materials • Elastic model • Aluminum • Elastic Modulus: 11 e 6 psi • Possion’s ratio: 0. 3 • Plastic model • Use the stress-strain curve defined in the previous slide. 11

Properties • Element Properties • 2 D Thin Shell • Material: Aluminum • Thickness 0. 025 in 12

Load Cases • Loading • Name: Load. Pressure • Apply following three BCs/Load • Fixed_sym • Fixed_x Load. Pressure • Pressure_in • Unloading • Name: Unloading. Pressure • Apply following three BCs/Load • Fixed_sym • Fixed_x • Pressure_zero Unload. Pressure 13

Analysis • Two Load Steps • Loading • Name: Pressure. Step • Load Case selected: Load. Pressure • Unloading • Name: Unloading. Step • Load Case selected: Unload. Pressure • 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 14

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 node for the displacement axis Reference nodes for the von-Mises stress Reference increments for Loading and unloading results: Select the increment results with the time increasing. 15

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 (=500 psi x 0. 74) Snap-through At time=0. 74 loading unloading Based on the increasing time(load) Based on the increment(solving step) 16

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) 17

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

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 19

Results (Stress: von Mises) • Stress at layer 1 (inside) • Stress at layer 5 (Outside) Max=0. 101 psi Max=0. 104 psi 20

Animation (based on the increments) 21

Animation (based on the Time: Actual motion) 22

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. 23