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Multiobjective Optimization

In this crashworthiness optimization example more than one criteria will be considered as objective function. Hence the solution is not unique, but will result in a Pareto optimal front. The same model is considere here using a single objective approach.

The problem is of a simplified vehicle moving at a constant velocity and crashing into a pole.

 vehicle_crash1.png vehicle_des_var2.png 
Fig. 1(a): Deformed vehicle after 50 ms Fig. 1(b): Design variables with part numbers

The problem illustrates the following features:

  • A multiobjective optimization using metamodels (Pareto optimal solutions)
  • Dealing with an infeasible design formulation
  • Use of composite functions
  • Trade-off study
  • Use of the LS-DYNA result interface

The criteria of interest are the following:

  • Head injury coefficient (HIC) of a selected point (15ms)
  • Component Mass of the structural components (bumper, front, hood and underside)
  • Intrusion computed using the relative motion of two points

Design variables:

  • The hood, front and underside (parts 3, 4 and 5 in Fig. 1(b)) are grouped under a single design variable: thood
  • The bumper (part 2 in Fig. 1(b)) is identified as another design variable: tbumper

Design Formulation

The design formulation is as follows:

  • Minimize the Mass and Intrusion subject to HIC (15ms) < 250. The intrusion is measured as the distance between the nodes 167 and 432 (for the location of the nodes see Fig. 1).

Problem Solution

⇒ Solution with LS-OPT