Can Bottom Snap-through

Estimated Time for Completion: ~35minExperience Level: Lower

MSC.Patran 2005 r2MSC.Marc 2005 r2

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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

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• 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.

Problem Description

Pressure

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• 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

Problem Description

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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.

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Expected Results

• Deformation

Increasing Pressure Time 0.01.0

Decreasing Pressure Time 1.02.0

Snap-through

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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

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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 1Layer 5

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Boudary Condtions

• Displacement Constraints• Fixed_x

• 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

Fixed_x

Pressure_in

Pressure_zero

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Fields

• Stress-strain curve• Plastic material

property is defined as a table.

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Materials

• Elastic model• Aluminum• Elastic Modulus: 11e6 psi

• Possion’s ratio: 0.3

• Plastic model• Use the stress-strain

curve defined in the previous slide.

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Properties

• Element Properties• 2D Thin Shell

• Material: Aluminum

• Thickness 0.025in

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Load Cases

• Loading• Name: LoadPressure

• Apply following three BCs/Load

• Fixed_sym

• Fixed_x

• Pressure_in

• Unloading

• Name: UnloadingPressure

• Apply following three BCs/Load• Fixed_sym

• Fixed_x

• Pressure_zero

LoadPressure

UnloadPressure

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Analysis

• Two Load Steps• 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

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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 forthe displacement axis

Reference nodes forthe von-Mises stress

Reference increments forLoading and unloading results:

Select the increment resultswith the time increasing.

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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-throughAt time=0.74

Based on the increasing time(load)

Based on the increment(solving step)

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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)

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Results

• Elastic Strain Energy vs. Time

Snap-through

loading unloading

Based on the increasing time(load)

Based on the increment(solving step)

Elastic Deformation

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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

Plastic Deformation

Maximumstress

loading unloading

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Results (Stress: von Mises)

• Stress at layer 1 (inside)

• Stress at layer 5 (Outside)

Max=0.101 psi

Max=0.104 psi

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Animation (based on the increments)

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Animation (based on the Time: Actual motion)

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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.