A note on truss design for stress and displacement constraints by optimality criteria methods

Abstract

One of the difficulties with the optimization of large structural systems by optimality criteria (OC) methods, in which stress constraints are stated in terms of relative displacements, is the need to evaluate a large number of Lagrangians. An improved OC method, which does not require Lagrangians for stress constraints, is outlined in this note in the context of problems with stress constraints and a single displacement constraint. Whilst general formulae giving continuum-type optimality criteria for elastic systems are available (e.g. Rozvany 1989), the criteria for trusses are confirmed here by a simple derivation and verified on a ten-bar truss, for which the proposed technique and a dual programming method are shown to give a twelve-digit agreement.