By using the Mellin integral transformation, we obtain the solutions of basic two-dimensional problems for an elastic wedge. It is shown that, in the case of boundary conditions symmetric under the inversion transformation, some components of the solutions of plane strain problems and the solutions of antiplane strain problems for a wedge also have the inversion symmetry.
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References
K. L. Johnson, Contact Mechanics, Cambridge Univ. Press, Cambridge (1987).
K. M. Nekyslykh and V. I. Ostryk, “Wedging of an elastic wedge,” Visn. Kyiv. Nats. Univ. im. T. Shevchenka. Ser. Fiz.-Mat. Nauk., Issue 3, 91–96 (2009).
V. I. Ostryk, Contact Mechanics [in Ukrainian], Kyiv. Univ., Kiev (2015).
V. I. Ostryk and O. M. Shchokotova, “Sliding contact of a punch with elastic wedge,” Fiz.-Khim. Mekh. Mater., 47, No. 4, 82–91 (2011); English translation:Mater. Sci., 47, No. 4, 514–526 (2012).
YA. S. Uflyand, Integral Transformations in Problems of the Elasticity Theory [in Russian], Nauka, Leningrad (1967).
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Translated from Matematychni Metody ta Fizyko-Mekhanichni Polya, Vol. 60, No. 4, pp. 90–110, October–December, 2017.
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Ostrik, V.I. Inversion Symmetry of the Solutions of Basic Boundary-Value Problems of Two-Dimensional Elasticity Theory for a Wedge. J Math Sci 247, 108–138 (2020). https://doi.org/10.1007/s10958-020-04792-3
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DOI: https://doi.org/10.1007/s10958-020-04792-3