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Numerical Treatment of Hypersingular Integral Equations with Application to Crack Mechanics

G. Iovane·M. A. Sumbatyan
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Abstract

In this paper we present a treatment of hypersingular integrals and integral equations. It is shown the equivalence of different definitions of hypersingular integrals. Then we construct explicit analytical solution to a characteristic equation and prove convergence of the collocation method to this solution. Further, we expand these results to full hypersingular kernels, and give a demonstration of the developed method to some problems of crack mechanics including crack problem for porous elastic materials, in the framework of Cowin-Nunziato model.

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BibTeXRIS

G. Iovane, M. A. Sumbatyan. 2003-07-10. Numerical Treatment of Hypersingular Integral Equations with Application to Crack Mechanics. https://arxiv.org/abs/math-ph/0307025

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