A solution technique for indirect boundary integral equation in planar elasto-plastic problems

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A scheme for solving planar elasto-plastic problems using the indirect boundary element approach is presented. The area integrals over the plastic region contains singularities of the order of ( 1 r). The usual approach in evaluating these integrals is to extract the singularity contribution analytically and evaluate the Cauchy's principal value numerically. In the present paper the area integrals which assume a linear plastic strain distribution are evaluated analytically over triangular cells. The form of analytical expressions is such that the singularity contribution comes out automatically without the usual need of neglecting the cell (area) containing the singularity. It should be pointed out that the region over which the plastic strain is assumed linear, need not be a triangle. This is especially useful when the general form of the elasto-plastic boundary is known a priori, e.g. axisymmetric problems. Good accuracies have been obtained for number of problems. Two examples are included, namely the elasto-plastic deformation of a circular disc with a hole and a square. The circular disc is especially illustrative of the power of the method as the problem is solved in Cartesian coordinates. © 1983.

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International Journal of Solids and Structures