Bi-Directional Evolutionary Structural Optimization for Crashworthiness Structures

Gradient based topology optimization method is difficult used to optimization of crashworthiness structures due to the expensive computational cost of sensitivity analysis and complex nonlinear behaviors (geometric nonlinearity, material nonlinearity and contact nonlinearity) of structures during a collision. Equivalent static loads (ESLs) method is one of the methods for nonlinear dynamic response optimization. However, this method ignores the material nonlinearity. Thus this paper proposes an improved topology optimization method for crashworthiness structure based on a modified ESLs method. A new calculation of ESLs considering material nonlinearity is proposed. The improved ESLs method is employed to transform the nonlinear dynamic response optimization into a nonlinear static response optimization with multiple load cases. Each element in the design domain is assigned with a design variable. A solid isotropic material with penalization (SIMP)-like material interpolation scheme is used to avoid singularity of the global stiffness matrix and re-meshing. Sensitivity analysis is implemented with the adjoint variable method. The optimization process is stabilized by mesh-independent filter and normalization of sensitivity numbers. Design variables are updated by bi-directional evolutionary structural optimization (BESO) with its material addition and removal scheme. Two examples are used to validate the proposed method. The results show that the optimization processes have no significant oscillations. Optimal designs have higher absorbed energy per unit volume. Thus they can support the external loads sufficiently throughout the entire time domain instead of satisfying the maximum loads at certain time steps only.