We consider the minimum weight design of suitably discretized elastoplastic
structures subjected to variable repeated loads and constraints on the amo
unt of residual (or permanent) deflections. The optimization problem is for
mulated on the basis of the classical lower bound theorem of shakedown, sup
plemented by appropriate constraints on deflections obtained from existing
bounding results. The primary purpose of the paper is to show that, even fo
r large size structures, this important and challenging problem can be mode
led and solved directly as a mathematical programming problem within the in
dustry standard modeling framework GAMS. Examples concerning truss-like str
uctures are presented for illustrative purposes.