Topology and shape optimization including elastoplastic material behavior

Abstract

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 material topology optimization determining the basic layout is extended to elastoplasticity. Afterwards the shape of the boundaries is optimized by shape optimization also considering 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 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. Topology optimization problems are solved by optimality criteria (OC) methods, shape optimization problems by mathematical programming (MP) methods, i.e. SQP-algorithm. In topology optimization a geometrically adaptive optimization procedure is additionally applied in order to increase the numerical efficiency and to avoid artificial stress singularities. The numerical procedures are verified by a 2D design problem under plane stress conditions.