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A new method for evaluating singular integrals in stress analysis of solids by the direct boundary element method. (English) Zbl 0576.65129
Problems in stress analysis of elastic and elasto-plastic solids can be formulated in terms of integral equations defined on the boundary. For an approximate solution the boundary is divided into elements, leading to the boundary element method (BEM), where the integral equations are replaced by a system of linear algebraic equations with matrix elements derived by evaluating (singular) integrals over the elements. In this paper triangle polar co-ordinates are used to reduce the order of singularity of the boundary integrals by one degree and to carry out the integration over mappings of the boundary elements onto plane squares. The method is extended to the cubature of singular integrals over three- dimensional internal cells. The analytical investigations, which are explained in detail, are illustrated by numerical examples. The paper is of interest for engineers using BEM for solving stress problems in solids.
Reviewer: S.Christiansen
MSC:
65R20Integral equations (numerical methods)
65N35Spectral, collocation and related methods (BVP of PDE)
74B99Elastic materials
74C99Plastic materials, etc.
45E05Integral equations with kernels of Cauchy type