Optimum design of rigidworkhardening structures with constraints on deformation

Abstract

The problem of optimum design of rigid-plastic discrete structures is studied adopting as the design criterion the workhardening adaptation concept, the latter being meant in a narrow sense. According to this, a safe structure is one not only able to adapt to statically or dynamically variable loads inside a given domain, but also strong enough for some deformation parameters (such as displacement, strain and plastic strain intensity components) to be not greater than given upper limits. This control over deformation is made possible by starting two bounding theorems based on a perturbation procedure of the bounding technique of shakedown theory. In spite of some simplifying hypotheses (linear cost function and plastic resistances, piecewise linear yield surface and workhardening law, linear strain-rate sensitivity, etc) the optimization problem is a nonlinear one of mathematical programming. The Kuhn-Tucker conditions are discussed. A simple application is given and future developments are considered.