Mechanics of Solids (about journal) Mechanics of Solids
A Journal of Russian Academy of Sciences
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IssuesArchive of Issues2021-7pp.1379-1387

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A.O. Vatulyan and D.K. Plotnikov, "On a Study of the Contact Problem for an Inhomogeneous Elastic Strip," Mech. Solids. 56 (7), 1379-1387 (2021)
Year 2021 Volume 56 Number 7 Pages 1379-1387
DOI 10.3103/S0025654421070268
Title On a Study of the Contact Problem for an Inhomogeneous Elastic Strip
Author(s) A.O. Vatulyan (Shern Federal University, Rostov-on-Don, 344006 Russia; Southern Mathematical Institute, Branch of Vladikavkaz Scientific Center, Russian Academy of Sciences, Vladikavkaz, 362027 Russia, vatulyan@aaanet.ru)
D.K. Plotnikov (Shern Federal University, Rostov-on-Don, 344006 Russia; Southern Mathematical Institute, Branch of Vladikavkaz Scientific Center, Russian Academy of Sciences, Vladikavkaz, 362027 Russia, dustheap@mail.ru)
Abstract In this paper, we study the contact problem for an inhomogeneous elastic strip and a stamp with a smooth base in a flat formulation. A system of differential equations with variable coefficients for the transformants of the components of the displacement vector and the stress tensor is constructed using the Fourier transform. The kernel symbol of the integral equation is constructed using the shooting method. An asymptotic analysis of the kernel symbol is performed at small and large values of the transformation parameter. A computational scheme based on the boundary element method for constructing a solution to the integral equation of a contact problem with an unknown contact area is presented. The results of solving the contact problem for various inhomogeneity laws are presented.
Keywords contact problem, inhomogeneous strip, asymptotic analysis, boundary element method
Received 02 February 2021Revised 18 March 2021Accepted 25 March 2021
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