Topology optimization of nonlinear structures for energy absorption

This paper presents a method for topology optimization of both geometrically and materially nonlinear structures for energy absorption. The optimization problem is formulated by using the element as design variables. The element sensitivity number is derived from using the adjoint method to address two principle design parameters, namely absorbed energy per unity volume and absorbed energy ratio. Filter techniques are used to smooth sensitivities in space and to eliminate unnecessary structural details below a certain length-scale. The bi-directional evolutionary optimization (BESO) technique is used to search for the optimal design in the whole design domain by gradually removing and adding material. Several examples are presented to verify the proposed method.