Block Element Method for Solving Integrated Equations of Contact Problems in V-Shaped Regions
V. A. Babeshko1, O. V. Evdokimova1, O. M. Babeshko2, A. G. Fedorenko2
1Southern Scientific Center of the Russian Academy of Sciences, Rostov-on-Don, 344006, Russia
2Kuban State University, Krasnodar, 350040, Russia
Keywords: контактные задачи, интегральные уравнения, клиновидная область, блочный элемент, факторизация, приближенные решения, сингулярные особенности, contact problems, integral equations, V-shaped region, block element, factorization, approximate solutions, singular properties
Abstract
This paper describes the block element method for spatial integral equations with a difference kernel in boundary-value problems of continuum mechanics and mathematical physics. The basis of the proposed method is the Wiener-Hopf method, whose generalization for a spatial case is called integral factorization method. The block element method is applied to solve problems in regions with piecewise smooth boundaries containing corner points. The developed method was used to solve the contact problem for a V-shaped stamp occupying the first quadrant. This paper describes in detail the methods of obtaining various characteristics of the solution constructed by reversing the system of one-dimensional linear integral equations typical for dynamics and static contact problems for stamps in the form of a strip.
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