EXACT SOLUTION OF THE TWO-DIMENSIONAL WIENER-HOPF INTEGRAL EQUATION IN MIXED PROBLEMS FOR ANISOTROPIC MEDIA
V.A. Babeshko, O.V. Evdokimova, O.M. Babeshko, V.S. Evdokimov
Kuban State University, Krasnodar, Russia
Keywords: contact problem, Wiener-Hopf integral equation, wedge-shaped domain, block element, factorization
Abstract
An exact solution to the two-dimensional Wiener-Hopf integral equation is obtained for the first time. This solution is used to solve mixed problems in acute-angled wedge-shaped domains. Mixed problems are considered for an arbitrary multilayer anisotropic composite. The block element method is employed in combination with topological and factorization approaches. The constructed solution has an integral representation that can be utilized in standard software packages for evaluating integrals in the study of anisotropic composites. The solution contains singular sets where it becomes infinite, which complicates the direct numerical solution of such mixed problems. An exact solution to the two-dimensional Wiener-Hopf integral equation is equivalent to solving the mixed problem in a wedge-shaped domain with an angle of 90°. This result may be used together with topological methods to solve these equations in arbitrary acute-angled wedge-shaped domains. A theory of contact problems for wedge-shaped punches with an acute angle is developed.
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