Constitutive Relations and Solution Schemes in Plastic Analysis

Several methods based on a finite element stiffness formulation developed in the last few years to obtain solutions to elastic-plastic problems involving small deformations are reviewed in this paper. Various yield conditions, i.e., von Mises, Tresca, and Approximate Tresca, that have frequently been employed in the development of the plastic stress-strain relations in the incremental form, are presented. Specific attention is drawn to the successful use of the Tresca yield condition. Two solution techniques, i.e., direct stiffness method and quadratic programming technique, are compared in terms of their computational efficiency. Iterative and interpolative schemes that are utilized in an incremental plastic analysis to satisfy the yield condition are given. Comparisons of solutions using constant strain and linear strain triangular elements are presented indicating the advantages of one over the other. A joint application of the substructuring and mesh-refinement schemes in elastic-plastic finite element analysis is demonstrated.