Topology and shape optimization for elastoplastic structural response

It is a common practice to base both, material topology optimization as wel l as a subsequent shape optimization on linear elastic response. However, i n order to obtain a realistic design, it might be essential to base the opt imization on a more realistic physical behavior, i.e. to consider geometric ally or/and materially nonlinear effects. In the present paper, 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 in the elastopla stic range while the mass in the design space is prescribed. With respect t o the specific features of either topology or shape optimization, for examp le the number of optimization variables or their local-global influence on the structural response, different methods are applied. For topology optimi zation problems, the gradient of the ductility is determined by the variati onal adjoint approach. In shape optimization, the derivatives of the state variables with respect to the optimization variables are evaluated analytic ally by a variational direct approach. The topology optimization problem is solved by an optimality criteria (OC) method and the shape optimization pr oblem by a mathematical programming (MP) method. In topology optimization, a geometrically adaptive procedure is additionally applied in order to incr ease the efficiency and to avoid artificial stress singularities. The proce dures are verified by 2D design problems under plane stress conditions. (C) 2001 Elsevier Science B.V. All rights reserved.