Energy Management through Topology Optimization of Microstructure of Functionally Graded Materials under Dynamic Loading

A numerical algorithm is proposed to design microstructure of a two-phase functionally graded material under dynamic loading. In order to direct energy propagation through the desired regions in the domain, we introduced a regularized Heaviside function in our objective functional, namely the time-averaged sum of the elastic strain energy and the kinetic energy. To generate a well-posed topology optimization, we used homogenization via a solid isotropic material with penalization (SIMP) model. We proposed our solution methodology based on the adjoint sensitivity analysis and by implementation of a gradient based optimization method. The overall volume fraction plots are presented to demonstrate the performance of our algorithm. The resulting optimal layouts for energy focusing case are compared to the ones for the case with no energydirectionality.

Keywords:

Topology optimization , Functionally graded material , Energy management , Adjoint sensitivity analysis , Material design