Handling bifurcations in the optimal design of transient dynamic problems

This paper presents a methodology to tackle some of the difficulties encountered in the optimal design of transient dynamic problems. For this class of problems, the structural responses can be discontinuous due to numerous bifurcations. This characteristic makes gradient-based or response surface optimization techniques difficult to implement. This work (in progress) proposes an approach to define regions of the design space where the dynamic behavior is homogeneous and hence does not produce discontinuities. This is done by isolating points that correspond to unwanted bifurcations within boundaries that are defined explicitly in terms of the design variables. Using this method, a designer can obtain an optimal design with a prescribed dynamic behavior. The approach is applied to the design of a tube impacting a rigid wall. In addition, as the transient dynamic behavior is very sensitive to small variations of the design, reliability-based optimization is considered.