Topology optimization of nonlinear structures under displacement loading

This paper presents topology optimization of geometrically and materially nonlinear structures under displacement loading. A revised bi-directional evolutionary optimization (BESO) method is used. The objective of the optimization problem is to maximize the structural stiffness within the limit of prescribed design displacement. The corresponding sensitivity number is derived using the adjoint method. The original BESO technique has been extended and modified to improve the robustness of the method. The revised BESO method includes a filter scheme, an improved sensitivity analysis using the sensitivity history and a new procedure for removing and adding material. The results show that the developed BESO method provides convergent and mesh-independent solutions for linear optimization problems. When the BESO method is applied to nonlinear structures, much improved designs can be efficiently obtained although the solution may oscillate between designs of two different deformation modes. Detailed comparison shows that the nonlinear designs are always better than the linear ones in terms of total energy. The optimization method proposed in this paper can be directly applied to the design of energy absorption devices and structures.