Topology and shape optimization including elastoplastic material behavior

摘要

In order to generate a reliable design, the nonlinear structural response, e.g., buckling or plasticity, has to be considered in topology and shape optimization. ^In the present study, a material topology optimization that determines the basic layout is extended to elastoplasticity. ^The shape of the boundaries is optimized by a shape optimization that also considers the nonlinear material behavior. ^An elastoplastic von Mises material model with linear, isotropic hardening/softening for small strains is used. ^The objective of the design problem is to maximize the structural ductility defined by the strain energy over a given range of a prescribed displacement. ^With respect to the specific features of topology and shape optimization, e.g., the number of optimization variables or the local-global influence of optimization variables on the structural response, different numerical methods are applied to solve the respective optimization problem. ^In topology optimization the gradient of the ductility is determined by the variational adjoint approach. ^In shape optimization the derivatives of the state variables with respect to the optimization variables are evaluated analytically by a variational direct approach. ^The numerical procedures are verified by a 2D design problem under plane stress conditions. ^(Author)