Evolutionary Structural Topology Optimization for Crashworthiness Structure 2020-01-0630
Gradient-based topology optimization method is hardly used for crashworthiness structures due to sophisticated nonlinear behaviors (geometric nonlinearity, material nonlinearity and boundary nonlinearity) of structures during collision and high computational cost. Equivalent static loads method (ESLM) is one of methods for nonlinear dynamic response optimization, but this method ignore the nonlinearity of materials. Thus, this article presents a topology optimization method of continuum structure for crashworthiness structure. ESLM is introduced to simplify the dynamic impact process to a series of nonlinear static finite element analysis. Therefore a dynamic response optimization is transformed into a nonlinear static response optimization with multiple load cases, so as to reduce the expensive computational cost in explicit dynamic analysis. Elements in design domain are treated as design variables, a SIMP-like material interpolation scheme is used to interpret the solid and void elements so that avoid singularity of stiffness matrix and re-meshing. Sensitivity numbers are derived with high efficiency adjoint variable method, the optimization process is stabilized by mesh-independency filter technique and normalization of sensitivity numbers. Design variables are updated by bi-directional evolutionary structural optimization (BESO) with its adaptive addition and removal scheme and gradually evolve to the optimal design. Several 2D and 3D examples are used to demonstrate the effectiveness of the proposed method. The results show that the optimal designs could satisfy loads throughout the whole dynamic history, instead of just satisfying the maximum load.
Yunkai Gao, Chao Ma, Linli Tian
Tongji University, Wuhan University of Technology