Topology optimization of structures in transient impacts with Coulomb friction

This paper demonstrates gradient driven density-based topology optimization of transient impact problems with friction. The sensitivities are obtained using the semi-discrete adjoint approach in which the temporal components are obtained by the "differentiate then discretize" whereas the spatial part is determined discretely. In this work, the sensitivity analysis method is extended to a mixed formulation involving both displacements, velocities, accelerations, and contact forces. The proposed formulation allows to account for frictional impacts during the structural optimization process. A first simple example demonstrates the effects of including frictional impacts into the transient design problem. As a second example, a drop test is considered and a casing for protecting a falling object during a frictional impact, is designed. Solid-void designs are obtained by application of the robust design formulation combined with a parameter continuation scheme.