Topology optimization for nonlinear dynamic problem with multiple materials and material-dependent boundary condition

This article develops a new optimization scheme for geometrically nonlinear dynamic topology optimization considering multiple materials and material-dependent boundary conditions. In the framework of convectional topology optimization procedures, some major issues must be addressed regarding complicated analysis and optimization formulations for these difficult conditions, as well as the unstable elements. To rigorously resolve these issues, this article develops a new patch stacking method based on our previous contribution (the element connectivity parameterization method (ECP) and the element stacking method). Compared with existing multi-material topology optimization schemes, the two differences in the present scheme are the stacking of multiple patches of the ECP method on the same discretization pixel, and the selection of one patch or no patch among them. To show the potential usage and limitations of the developed optimization method, several topology optimization examples with the above conditions are solved.