Some numerical methods for limit analysis in continuum mechanics

Abstract

Abstract A class of nonlinear optimization problems arises in various fields of continuum physics with a common mathematical structure. The problems are governed by a linear partial differential equation subjected to a quadratic inequality constraint. A linear objective function is minimized or maximized over the set of feasible solutions. The problem is approximated in a finite dimensional space in the form of a special nonlinear programming problem. Several techniques for solving the structured nonlinear programming problem are presented and compared with computational results for a sample problem in plasticity.