Elastic-plastic torsion as a problem in non-linear programming

Abstract

For a simply connected region, it is shown that the problem of determining the elastic-plastic stress function is equivalent to that of minimizing the complementary energy subject to the inequality constraints required by the yield condition. A method is proposed for approximating this minimum in which the cross section is approximated by a finite number of triangles and a linear stress function is assumed for each triangle. This approximate problem is then solved by means of a recently available computer program for solving nonlinear constrained minimization problems.