An Algorithm for Evaluating the Boundary Integral Equations in Planar Elasto-Plastic Bodies.

Abstract

A numerical algorithm is developed for solving the boundary integral equations for two dimensional isotropic elasto-plastic bodies. The differential equations of the boundary value problem are converted into a set of integral equations using Fourier transforms and a body force analogy for plastic strains. The unknown function in the boundary integral is approximated by a combination of Fourier series and a piecewise linear function. The piecewise linear representation is used in those regions of the boundary where it is anticipated that the unknown function has high gradients. The contribution of the singularities in the influence functions of the line integrals and the area integrals are evaluated numerically. The plastic strains are assumed to vary linearly in small regions of the plastic zone. The incremental theory of plasticity in conjunction with the von Mises yield criterion and the associated Pr and tl-Reuss flow rule is used to determine the plastic strains. Numerical examples are solved to demonstrate the effectiveness of the algorithm for problems with corners, discontinuous loadings and multiple boundaries.