Geodesic
Contact problem for functionally graded orthotropic strip
Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 22 (2022) no. 4, pp. 479-493

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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. 
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     author = {A. O. Vatulyan and D. K. Plotnikov},
     title = {Contact problem for functionally graded orthotropic strip},
     journal = {Izvestiya of Saratov University. Mathematics. Mechanics. Informatics},
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A. O. Vatulyan; D. K. Plotnikov. Contact problem for functionally graded orthotropic strip. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 22 (2022) no. 4, pp. 479-493. http://geodesic.mathdoc.fr/item/ISU_2022_22_4_a5/