A Finite Element Method for Problems in Perfect Plasticity Using Discontinuous Trial Functions

摘要

A finite element method of displacement type for problems in perfect plasticity is proposed. For simplicity, a stationary problem corresponding to Henky's law is considered. The quasi-static rate problem corresponding to the Prandtl-Reuss' flow rule does not present any serious difficulties and leads to a problem of Henky type at each incremental step. The proposed method is analyzed, considering a polygonal bounded region in the plane. For a given triangulation, a set of piece wise polynomial functions with no continuity requirement on interelement boundaries is defined. The convergence of the method is proved. A numerical example in one-dimensional space is presented. The error between the exact solution and the solution of the discrete problems is tabulated, and the results are discussed.