Shape-design sensitivity analysis and optimization of nonlinear static/dynamic structures with contact/impact

A nonlinear shape design sensitivity analysis (DSA) and optimization for static/dynamic structures with contact/impact are proposed based on continuum approaches. The material nonlinearity includes hyper-elasticity, rate-independent elasto-plasticity, and finite deformation elasto-plasticity with multiplicative decomposition of the deformation gradient. The geometric nonlinearity is considered using material and spatial description of the deformation. For boundary nonlinearity, the multi-body frictional contact/impact constraint is formulated using the penalty method. Transient dynamics increases those nonlinearities significantly, and both implicit and explicit time integration are used for analysis and DSA.; The response analysis is carried out using the meshless method (RKPM) where the modified kernel functions that are constructed by enforcing reproducing conditions so that the kernel estimates of the displacement variables exactly reproduce certain classes of polynomials are used. The special feature of RKPM is discussed compared to the finite element method. The design sensitivity equation always uses the same tangent stiffness operator as response analysis, and thus no iteration is required to solve the design sensitivity equation. For the path-independent problem (or potential problem), the design sensitivity equation is solved only one time at the final converged load step, whereas the design sensitivity equation is solved at each converged load step for the path-dependent problem and the material derivatives of path-dependent parameters are updated.; Proposed approach is quite accurate and efficient to compute sensitivity information compared to the finite difference method. The accurate sensitivity information also reduces the number of design iterations during the design optimization procedure. The accuracy and efficiency of he proposed approach are shown through numerical examples including door seal, windshield blade, ring contact, plate punch, block impact, bumper impact, and sheet metal stamping problems.