Application of Topological Optimization Techniques to Structural Crashworthiness

Abstract

The topological optimization of components to maximize crash energy absorption for a given volume is considered. The crash analysis is performed using a DYNA3D finite element analysis. The original solid elements are replaced by ones with holes, the hole size being characterized by a so-called density (measure of the reduced volume). A homogenization method is used to find elastic moduli as a function of this density. Simpler approximations were developed to find plastic moduli and yield stress as functions of density. Optimality criteria were derived from an optimization statement using densities as the design variables. A resizing algorithm was constructed so that the optimality criteria are approximately satisfied. A novel feature is the introduction of an objective function based on strain energies weighted at specified times. Each different choice of weighting factors leads to a different structure, allowing a range of design possibilities to be explored. The method was applied to an automotive body rear rail. The original design and a new design of equal volume with holes were compared for energy absorption.

Generic Topology Optimization Based on Local State Features

“…Early research on topology optimization for crashworthiness was conducted in the late nineties by Mayer et al for maximizing crash energy absorption based on a homogenization approach of a piecewise linear elasticplastic material model [117]. In their work, optimality criteria are derived based on an objective function that weights the strain energies at specified times.…”

Evaluating the Potential for Secondary Mass Savings in Vehicle Lightweighting

“…Various engineering and design approaches can be used to reduce mass, including materials substitution, , novel processing techniques, and design optimization. , A number of authors have noted that all of these mass saving approaches are challenging to implement because it is difficult to estimate their impact on costs ,, and on load path management. − An additional challenge emerges from the nature of the vehicle development process, which is time-constrained and in which subsystems are designed concurrently. As such, to maximize mass savings it is necessary to have sound estimates of the impact of any mass solution, and those estimates must be available early, before key design details are locked in.…”