Contact problem for functionally graded orthotropic strip
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 tra...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Saratov State University
2022-11-01
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| Series: | Известия Саратовского университета. Новая серия. Серия Математика. Механика. Информатика |
| Subjects: | |
| Online Access: | https://mmi.sgu.ru/sites/mmi.sgu.ru/files/text-pdf/2022/11/479-493-vatulyan-plotnikov.pdf |
| Summary: | 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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| ISSN: | 1816-9791 2541-9005 |