Numerical Treatment of Hypersingular Integral Equations with Application to Crack Mechanics
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.
- Publication:
-
arXiv e-prints
- Pub Date:
- July 2003
- DOI:
- 10.48550/arXiv.math-ph/0307025
- arXiv:
- arXiv:math-ph/0307025
- Bibcode:
- 2003math.ph...7025I
- Keywords:
-
- Mathematical Physics;
- Mathematics - Mathematical Physics;
- Mathematics - Numerical Analysis
- E-Print:
- 4 PAGES, Proceedings of the 3-rd Russian Conference on Elasticity, 2003,Rostov-on-Don, Russia