Izvestiya of Saratov University.

Mathematics. Mechanics. Informatics

ISSN 1816-9791 (Print)
ISSN 2541-9005 (Online)

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Vatulyan A. O., Plotnikov D. K. Contact problem for functionally graded orthotropic strip. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2022, vol. 22, iss. 4, pp. 479-493. DOI: 10.18500/1816-9791-2022-22-4-479-493, EDN: JDIVGD

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Contact problem for functionally graded orthotropic strip

Vatulyan Alexander Ovanesovitsch, Southern Federal University
Plotnikov Dmitry K., Southern Mathematical Institute, Vladikavkaz Scientific Center of the Russian Academy of Sciences

Within the framework of plane elasticity, the equilibrium problem for an inhomogeneous orthotropic elastic strip under the action of a stamp with a smooth base is investigated. Based on the Fourier transform, a canonical system of differential equations with variable coefficients with respect to transformants of the displacement vector and stress tensor components is constructed. A connection between the vertical displacement and the normal boundary stress is constructed, with which an integral equation of the first kind with a difference kernel is formulated. Using the shooting method, the kernel symbol for the integral equation of the contact problem is constructed numerically. Based on the Vishik – Lyusternik method, an asymptotic analysis of the kernel symbol for large values of the transformation parameter is carried out. A computational scheme for solving an integral equation with an unknown contact area is~constructed. The solution of the contact problem for different laws of strip inhomogeneity is presented.

This work was partially supported by the Russian Science Foundation (project No. 22-11-00265).
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