Mathematical programming methods for deformation analysis at plastic collapse

Abstract

A variety of alternative mathematical programming procedures for first-order elastoplastic analysis at the collapse-load level for discrete structures described by piecewise-linear elastic-perfectly plastic constitutive laws are formulated and then assessed with respect to their relative computational merit. An iterative Linear Programming, three Quadratic Programming and two Restricted Basis Linear Programming procedures are developed in detail. In addition, Parametric Linear Complementarity and Parametric Quadratic Programming methods are briefly discussed. The governing relations for analysis and the various formulations are initially developed for a trusslike structure, and are then shown to apply, without formal alteration, to a broad range of frameworks and continua discretized into finite elements. The unbounded nature of deformations at plastic collapse of elastic-perfectly plastic structures is considered, as is the possibility that there may be a multiplicity of (bounded) deformation responses to a single load path prior to plastic collapse, and several devices to overcome related difficulties are illustrated. Two example structures are each analyzed by six of the procedures presented.