Material Parameterization in Topology Optimization for Crashworthiness Designs

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Material Parameterization in Topology
Optimization for Crashworthiness Designs

• Punit Bandi
• First Year Graduate Student
• Aerospace and Mechanical Engineering Department
• University of Notre Dame

Advisor Dr. John E. Renaud Aerospace and
Mechanical Engineering Department University of
Notre Dame
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Introduction

• Topology Optimization
• Iterative process for obtaining the best
  arrangement of a limited volume of structural
  material within a given design domain
• Elimination and redistribution of material
  throughout the domain
• Crash Event
• Structural behavior during transient loading
• Plastic material behavior during Topology
  Optimization

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Internal Energy Density

• Elastic Strain Energy
• Inelastic Strain Energy

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Material Parameterization

• Homogenization approach
• Based on composite material models
• Density approach
• One design variable each material element
• Material can assume intermediate property values
  by defining an interpolation function
• CrasHCA uses relative density (xi) as design
  variable
• xi 0 (void) and xi 1 (solid)

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Material Parameterization (Cont)

• Density and other material properties are mapped
  to relative density as

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Motivation

• To minimize the maximum stresses in the
  structure, IED should be evenly distributed among
  various elements (CAs)
• This work shows the nature of variation in IED as
  design variable xi varies
• To obtain a smooth convergence of HCA algorithm
  IED should vary monotonically wrt xi

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Test Model

• FEA is performed using LS-Dyna Implicit on an
  isotropic cubic material element of
• Steel
  Aluminum 6063
• ?0 7800 Kg/m3 ?0 2700
  Kg/m3
• E0 207 GPa E0 70 GPa
  
• ?0 0.29 ?0
  0.33
• sy0 253 MPa sy0 241
  Mpa
• Plastic 8 point Eh 7
  GPa
• stress-strain curve

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Results
Material yields quickly i.e. at high x as
penalization q is increased
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Results (Cont)
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Results of Neals work
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Conclusions

• Monotonic nature of the variation of IED with x
  has been confirmed
• The affect of penalization parameters p and q on
  material yielding has been studied
• Same kind of analysis can be done for Topology
  Optimization with shell elements with thickness
  as design variables

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Thank You
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Stresses in the block
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Results (Cont)
3x3x3 block
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Results (Cont)
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Results (Kishore)
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Points to be discussed

• Reasons for different behavior of curve in
  different conditions.
• Our main concerns for doing this exercise.
• How does it affects our crasHCA code.
• Does the model for this exercise is similar to
  what we have in crasHCA.
• Why Neals plot show such high values of IE as
  any try to achieve such high values causes
  unrealistic deformations (in my model)

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Points to be discussed

• Is taking different sets of values for p and q
  changes the final topology if not then is there
  any effect on the rate of convergence.

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Possible Reason

• High forces for relatively low values of
  densities gives high values of IE (LS-Dyna
  numerically) but the deformations involved are
  unrealistic.
• Example 3x3x3 block with force 4x5x106 N for
  density x0.05 gives IE 1.37x1010J while the
  simulations shows

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Unreal Deformations
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crasHCA runs for material parameterization

• Run1 p1, q1/3
• Run2 p1, q1/2
• Run3 p1, q2/3
• Run4 p1, q1
• Run5 p2, q2
• Run6 p3, q3

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Run1 Summary

• Total of iterations 58

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Run4 Summary

• Total of Iterations 38

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Final Topologies Comparison
P1,q1/3
P1,q1