Finite Element Analysis of Elastic-plastic Plane Stress Problem - Winnicki, I.; Kleiber, M.; Kwieciński, M. (Engineering Transactions, 1975)
The finite element method Is applied to the statical analysis of an elastic-perfectly plastic material in plane stress. The in-plane system is split up into triangular elements for which linear shape function is prescribed. Basic relationships are formulated for the elastic-plastic material in the matrix form. The procedure to build up an elastic-plastic stiffness matrix is shown for the Huber-Mises-Hencky material in the three-dimensional situation as well as in both plane stress and plane strain. In the numerical calculations an ideally plastic material is assumed, however, the derived relationships are valid for strain-hardening material. Basic algorithms are described for the solution of the non-linear system of equations obtained. The method of tangential stiffness is presented together with the method of initial nodal forces and its modification. the initial stress method. In the course of numerical analysis was investigated the possibility of the unloading process to occur in particular elements while the whole system undergoes loading program. The algorithm is given and a numerical example is solved.