Topology optimization of transient nonlinear structures—A comparative assessment of methods

Topology optimization considering transient nonlinear behavior of mechanical structures, e.g. automotive crash, remains a challenge in both the implementation as well as computational effort. In recent years, efficient optimization algorithms and increased computer technology has begun to allow the development of methodologies to examine optimal topology of structures undergoing such behavior. Here, the topology optimization methodologies are categorized by the abstraction of the loads, from fully transient nonlinear structural-mechanical analysis to multiple static replacement loads to a single static replacement load. Several methods are investigated for varying loading conditions and degrees of nonlinear behavior: 1) the use of the algorithms based on hybrid cellular automata with full transient nonlinear finite-element analyses; 2) multiple static replacement loads with updates via transient nonlinear finite-element analysis; 3) multiple static replacement loads without updates; 4) single static replacement load. These will be introduced in the following. Each method has limits to its validity and application. To assess this, representative validation cases showing typical behavior of automotive components in an automotive crash have been used here.