Structural optimization of finite deformation elastoplasticity using continuum-based shape design sensitivity formulation

A continuum-based shape design sensitivity formulation and optimization method is proposed for finite deformation elastoplasticity. In response analysis, the multiplicative decomposition of the deformation gradient into elastic and plastic parts is used for the hyperelasticity-based elastoplastic constitutive model with respect to the intermediate configuration. In design sensitivity analysis, the shape variation at the undeformed configuration is taken using a design velocity concept and then is transformed to the current configuration to recover the updated Lagrangian formulation. The design sensitivity equation of the direct differentiation method is solved at each time step without iteration. The effect of using different reference frames for response analysis and sensitivity analysis is discussed in detail. The path-dependency of the sensitivity is due to the evolutions of the intermediate configuration and the internal plastic variables. A numerical example is shown to confirm the accuracy and efficiency of the proposed computational method using a vehicle bumper optimization.