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The universal algorithm based on complex hypersingular integral equation to solve plane elasticity problems

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Abstract

The effective numerical algorithm to solve a wide range of plane elasticity problems is presented. The method is based on the use of the complex hypersingular boundary integral equation (CHBIE) for blockyFootnote 1 systems and bodies with cracks and holes. The BEM technique is employed to solve this equation. The unknown functions (displacement discontinuities (DD) or tractions) are approximated by Lagrange polynomials of the arbitrary degree. For the tip elements the asymptotics for the DD are taken into account. The boundaries of the blocks, cracks and holes are approximated by the arcs of the circles and the straight elements. In this case all the integrals (hypersingular, singular and regular) involved in this equation are evaluated in a closed form. Numerical results are given and compared either to the ones obtained by the other authors or to analytical solutions.

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Notes

  1. The terminology refers to multiregions of interacting elastic bodies with generalized interfaces ranging from fixed to having displacement discontinuities. The terminology derives from Linkov (1983) and was associated with the hypersingular formulation in Linkov and Mogilevskaya (1991).

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Authors and Affiliations

  1. Department of Mathematics, Kuzbass Technical University, Vesennia 28, 650026, Kemerovo, Russia

    S. G. Mogilevskaya

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  1. S. G. Mogilevskaya
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Communicated by T. Cruse, 22 January 1996

This work was supported by the International Science Foundation (Grants R3X000, R3X300) funded by George Soros. The part of this work was performed when the author was a visiting research fellow at the University of Minnesota. I am especially grateful to Prof. A. Linkov of the Institute of Problems of Mechanical Engineering (Russian Academy of Science) for the fruitful discussion and Prof. T. Cruse of the University of Vanderbilt for much communication on the contents of this paper.

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Mogilevskaya, S.G. The universal algorithm based on complex hypersingular integral equation to solve plane elasticity problems. Computational Mechanics 18, 127–138 (1996). https://doi.org/10.1007/BF00350531

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