Indirect identification of yield limits by mathematical programming

Abstract

An elastic-perfectly plastic discretized structure subjected to given proportional loads, undergoes displacements, some of which are measured; on the basis of these experimental data assumed as exact (unaffected by measurement errors) the yield limits are sought, whereas the elastic and geometric properties are known. This special problem of identification (or inverse problem in structural elasto-plasticity), under suitable hypotheses of piecewise linear yield surfaces and no local unstressing under increasing loads is shown to be amenable to the minimization of a convex quadratic function under linear and (nonconvex) complementarity constraints. Various alternative solution procedures are proposed. Among these the most promising method from the computational standpoint, consists of two phases: (1) minimizing, under linear constraints only, a nonconvex quadratic function of the plastic strains and of the parameters to identify (thus enforcing by penalization the fulfilment of complementarity); (II) checking the optimality of the solution (and moving from a possible local minimum to the global one) by a procedure based on recent results from quadratic complementarity theory. The mathematical programming method developed for the indirect identification of yield limits is tested by means of examples with encouraging results.