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

This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
Published online: 
30.11.2022
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Language: 
Russian
Heading: 
Mechanics
Article type: 
Article
UDC: 
539.3
DOI: 
10.18500/1816-9791-2022-22-4-479-493
EDN: 
JDIVGD

Contact problem for functionally graded orthotropic strip

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

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.

Key words: 
contact problem
functionally graded strip
orthotropic material
asymptotic analysis
boundary element method
Acknowledgments: 
This work was partially supported by the Russian Science Foundation (project No. 22-11-00265).
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Received: 
06.06.2022
Accepted: 
05.08.2022
Published: 
30.11.2022
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