Topology optimization of structures with geometrical nonlinearities

In this paper, the stiffness optimization problem is investigated for structures with geometrical nonlinearities. The mean compliance of the structure is chosen as the objective function and its sensitivities are derived using the adjoint method. The optimal problem is formulated using a microstructure-based design domain method and is solved iteratively by a sequential convex approximation method. Three numerical examples are presented to show the applications of the proposed method and the results demonstrate that the geometrically nonlinear finite element analysis is indispensable to the optimization process of large displacement structures.