Comparison of Different Formulations of a Front Hood Free Sizing Optimization Problem Using the ESL-Method

Abstract

Topology and free sizing optimization are very important tools in the design phase to compute optimized design proposals. However, they are only well established for optimization problems based on linear analysis. In contrast, in the nonlinear analysis area -- in particular in crash analysis - such kind of optimization cannot be applied due to the unavailability of gradients. A workaround is to create linear auxiliary load cases, which approximate the nonlinear load case at different time steps and which can then be used in optimization based on linear statics analysis. The ESL (Equivalent Static Load) method provides a procedure to create such auxiliary load cases in a well-defined way. A general drawback of such an approach is that responses in the nonlinear system and the related requirements are not defined in the linear statics system. Hence, a formulation must be derived translating the nonlinear requirements to the linear statics system. This is sometimes very difficult and is also the reason why very often the strain energy is used as objective function even if this does not reflect the real objective in the optimization task.