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Construction of Solutions for the First Elasticity Problem for Noncircular Domain

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Abstract

Here we present a method for constructing the solution a simply connected domain with a given smooth boundary by an approximate solution of the Fredholm equation. Consider the problem in the following formulation: given the dislocations at the boundary, one can find the necessary analytical functions with the given values at the boundary of the region. Here we give a mathematically correct base of the method and construct certain examples. In order to approximately construct the analytic functions in a finite simply connected domain we solve a system of Fredholm equations.

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  1. Lobachevskiy Institute of Mathematics and Mechanics, Kazan Federal University, Kremlevskaya st., 35, Kazan, Russia, 420008

    P. N. Ivanshin

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  1. P. N. Ivanshin
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Correspondence to P. N. Ivanshin.

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Ivanshin, P.N. Construction of Solutions for the First Elasticity Problem for Noncircular Domain. Int. J. Appl. Comput. Math 7, 181 (2021). https://doi.org/10.1007/s40819-021-01121-3

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  • DOI: https://doi.org/10.1007/s40819-021-01121-3

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