An effective topology optimization method for crashworthiness of thin-walled structures using the equivalent linear static loads

Abstract

The equivalent static loads method for nonlinear dynamic response structural optimization may be failed in large deformation crash conditions, due to topology optimization with the equivalent static loads mostly beyond the linear range and causing numerical defects such as high compliance of elements. To overcome the above disadvantage, an advanced structural topology optimization method for crashworthiness considering crash-reduced large deformation and plastic buckling is proposed using newly defined equivalent linear static loads. The equivalent linear static loads can adaptively scale to guarantee that the topology optimization is performed within linear range. At each cycle, the crash simulation is performed and the nonlinear nodal displacement vector at the time step with the maximum strain energy is scaled by an adaptive displacement-scaling factor. The equivalent linear static loads that are generated by multiplying the linear stiffness matrix and the scaled nodal displacement vector will be incorporated into topology optimization, which can guarantee the topology optimization to remain in linear range and further solve the numerical instability problems. The process is repeated until the convergence criteria are satisfied. The effectiveness of the proposed method is evaluated by solving a crashworthiness topology optimization of a crash box considering crash-induced plastic buckling to determine the location and profile of crash triggers. The results show that the proposed method can effectively solve the large deformation crashworthiness topology optimization of thin-walled structures and provides a feasible strategy for crash triggers design in crash box.