Finite element analysis of elastic-plastic plane stress problems based upon Tresca yield criterion

A finite element technique for the elastic-plastic analysis of two dimensional structures subjected to conditions of plane stress and monotonically increasing loads is presented. The complete load deformation history as well as the propagation of the yield zones in the structure up to plastic collapse are studied. The material is assumed to be elastic-perfectly plastic and yielding is governed by Tresca yield condition. Plastic stress-strain relations for the sides and corners of Tresca yield condition are derived in terms of the components of the stresses and strains along a fixed reference coordinate system and the direction of the principal stress. The load is applied in small increments and the principal stress direction for each plastic element during a load increment is determined by an interpolation technique which leads to stresses that satisfy the yield condition. Numerical examples are given to illustrate the accuracy of the results obtained by the proposed method.