Design sensitivity analysis and optimization of nonlinear transient dynamics

A shape design sensitivity analysis (DSA) and optimization of structural tr ansient dynamics are proposed for the finite deformation elastoplastic mate rials under impact with a rigid surface. A shape variation of the structure is considered using the material derivative approach in continuum mechanic s. Hyperelasticity based multiplicatively decomposed elastoplasticity is us ed for the constitutive model. The implicit Newmark time integration scheme is used for the structural dynamics. The design sensitivity equation is so lved at each converged time step with the same tangent stiffness matrix as response analysis without iteration. The cost of sensitivity computation is more efficient than the cost of response analysis for the implicit time in tegration method. The efficiency and the accuracy of the proposed method ar e shown through the design optimization of a vehicle bumper.