Optimal plastic limit and shake-down design of bar structures with constraints on plastic deformation

Abstract

Optimal plastic design methods of discretized bar structures are presented where the objective function is the volume of the structure and the permanent deformations are controlled by introducing a constraint on the complementary strain energy of the residual internal forces. Single- and multiparameter loadings are considered and in the latter case the constraint on shakedown is also included in the optimal design procedure. Alternative formulations of the problems, where the complementary strain energy of residual forces is minimized at a given volume of the structure, are also presented. The proposed design methods are nonlinear and their solutions lead to nonlinear mathematical programming. Iterative solution techniques can also be efficiently applied. This is illustrated by an example.