ADAPTIVE TOPOLOGY OPTIMIZATION OF ELASTOPLASTIC STRUCTURES

Material topology optimization is applied to determine the basic layou t of a structure. The nonlinear structural response, e.g. buckling or plasticity, must be considered in order to generate a reliable design by structural optimization. In the present paper adaptive material top ology optimization is extended to elastoplasticity. The objective of t he design problem is to maximize the structural ductility which is def ined by the integral of the strain energy over a given range of a pres cribed displacement. The mass in the design space is prescribed. The d esign variables are the densities of the finite elements. The optimiza tion problem is solved by a gradient based OC algorithm. An elastoplas tic von Mises material with linear, isotropic work-hardening/softening for small strains is used. A geometrically adaptive optimization proc edure is applied in order to avoid artificial stress singularities and to increase the numerical efficiency of the optimization process. The geometric parametrization of the design model is adapted during the o ptimization process. Elastoplastic structural analysis is outlined. An efficient algorithm is introduced to determine the gradient of the du ctility with respect to the densities of the finite elements. The over all optimization procedure is presented and verified with design probl ems for plane stress conditions.