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Mathematics and Mechanics

Russian Academy of Sciences
 Founded
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IssuesArchive of Issues2017-6pp.486-491

Archive of Issues

Total articles in the database: 1813
In Russian (): 1014
In English (J. Appl. Math. Mech.): 799

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S.M. Aizikovich, S.S. Volkov and B.I. Mitrin, "The solution of a certain class of dual integral equations with the right-hand side in the form of a Fourier series and its application to the solution of contact problems for inhomogeneous media," J. Appl. Math. Mech. 81 (6), 486-491 (2017)
Year 2017 Volume 81 Issue 6 Pages 486-491
DOI 10.1016/j.jappmathmech.2018.03.018
Title The solution of a certain class of dual integral equations with the right-hand side in the form of a Fourier series and its application to the solution of contact problems for inhomogeneous media
Author(s) S.M. Aizikovich (Don State Technical University, Rostov-on-Don, Russia, saizikovich@gmail.com)
S.S. Volkov (Don State Technical University, Rostov-on-Don, Russia)
B.I. Mitrin (Don State Technical University, Rostov-on-Don, Russia, bmitrin@dstu.edu.ru)
Abstract Using the bilateral asymptotic method, a semi-analytical solution of a dual integral equation with its right-hand side in the form of a Fourier series is constructed. This equation arises in the solution of a number of contact problems of elasticity theory for bodies with inhomogeneous coatings. The efficiency of the method is illustrated in the example of the solution of the plane contact problem on bending of a beam lying on a functionally graded strip with arbitrary variation of the elastic moduli with depth. It is assumed that the strip is perfectly bonded to an elastic half-plane. Numerical results are presented for a strip whose Young's modulus varies harmonically with depth. In this case, Young's modulus of the substrate is 100 times greater than at the lower boundary of the coating.
Keywords functionally graded
Received 19 November 2015
Link to Fulltext https://www.sciencedirect.com/science/article/pii/S0021892818300285
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