Abstract
We propose a method of approximate solution of problems of elasticity theory for a half-space with protuberances based on the use of jump conditions in the stresses and displacements at a thin elastic element. The problem of determining the stresses reduces to a system of two-dimensional integral equations of Newtonian potential type for determining the contact stresses between the protuberances and the half-space. We consider the case when the elastic characteristics of the material of the protuberances are different from the material of the half-space.
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Literature cited
V. M. Aleksandrov and S. M. Mkhitaryan,Contact Problems for Bodies with Thin Coatings and Layers [in Russian], Nauka, Moscow (1983).
G. S. Kit and M. V. Khai,The Potential Method in in Three-dimensional Problems of Thermoelasticity of Bodies with Cracks [in Russian], Naukova Dumka, Kiev (1989).
A. I. Lur'e,Theory of Elasticity [in Russian], Fizmatgiz, Moscow (1970).
Ya. S. Podstrigach, “Conditions on the jump of stresses and displacements at a thinwalled elastic inclusion in a continuum,”Dokl. Akad. Nauk Ukr. SSR, Ser. A, No. 12, 30–32 (1982).
G. Ya. Popov,Concentration of Elastic Stresses Near Slabs, Cuts, Thin Inclusions, and Reinforcements [in Russian], Nauka, Moscow (1982).
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Translated fromMatematicheskie Metody i Fiziko-Mekhanicheskie Polya, Issue 35, 1992, pp. 156–160.
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Kit, G.S., Khai, M.V. & Grilitskii, N.D. On the use of jump conditions at a thin inclusion in solving problems of elasticity theory for a half-space with protuberances. J Math Sci 67, 2968–2972 (1993). https://doi.org/10.1007/BF01095879
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DOI: https://doi.org/10.1007/BF01095879