Topology optimization using difference-based equivalent static loads

Topology optimization of crash-related problems usually involves a huge number of design variables as well as nonlinearities in geometry, material, and contact. The Equivalent Static Load (ESL) method provides an approach to solve such problems. This method has recently been extended under the name Difference-based Equivalent Static Load (DiESL) method to employ a set of Finite Element models, each describing the deformed geometry at an individual time step. Only sizing optimization problems were considered so far. In this paper, the DiESL method is extended to topology optimization utilizing a Solid Isotropic Material with Penalization approach (SIMP). The method is tested using an example of a rigid pole colliding with a simple beam, where the intrusion of the pole is minimized. The initial velocity of the pole is varied in order to examine the influence of inertia effects on the optimized structures. It is shown that the results differ significantly depending on the chosen initial velocity and, consequently, that they exhibit inertia effects. This cannot be seen in the results derived by the standard ESL method. Consequently, the results of the DiESL method’s show a considerable improvement compared to those of the standard ESL method.