Abstract
We consider the pressure of a plate on a halfspace with a round cylindrical cavity. The surface of the cavity is reinforced by elastic elements that are modeled by very general operators. The problem is reduced to a Fredholm integral equation of second kind. A detailed study is made of the case of reinforcement described by the Winkler law. An approximate solution is obtained in the form of the asymptotics with respect to the radii of the plate and the cavity. One table.
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V. Z. Parton and P. I. Perlin,Methods of the Mathematical Theory of Elasticity [in Russian], Nauka, Moscow (1981).
P. Ya. Malits, “The contact problem for a half-space with a reinforced cavity,”Dinam. Sist., No. 3, 39–45 (1984).
M. V. Fedoryuk,The Saddle-point Method [in Russian], Nauka, Moscow (1977).
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Translated fromDinamicheskie Sistemy, No. 6, 1987, pp. 80–85.
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Malits, P.Y. An axially symmetric contact problem for a half-space with an elastically reinforced cylindrical cavity. J Math Sci 57, 3417–3420 (1991). https://doi.org/10.1007/BF01880209
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DOI: https://doi.org/10.1007/BF01880209