Closed-Form Solutions of the Nonlinear Partial Differential Equations Governing the Stress-Field in a Rigid, Perfectly-Plastic Body

Abstract

In this paper closed-form solutions for the evaluation of the stress-field in a rigid perfectly-plastic body under plane-stress or plane-strain conditions are estimated. The two nonlinear partial differential systems describing the problem under consideration consist of the stress equilibrium equations and the appropriate yield condition, the Von Mises–Hencky conditions. The above systems are decoupled, and second-order nonlinear partial differential equations of the Monge type are formulated. Appropriate handling of analytical treatments leads to closed-form general solutions of the last equations. Finally, the effectiveness and the potentialities of the method are demonstrated through an application concerning a finite plate bi-axially loaded under plane-strain conditions.