Numerical Treatment of Hypersingular Integral Equations with Application to Crack Mechanics

Details Numerical Treatment of Hypersingular Integral Equations with Application to Crack Mechanics Numerical Treatment of Hypersingular Integral Equations with Application to Crack Mechanics

2003-07-10

arxiv.org/abs/math-ph/0307025v1

Physics

Mathematical Physics

4 PAGES, Proceedings of the 3-rd Russian Conference on Elasticity, 2003,Rostov-on-Don, Russia

Scientific paper

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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