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A Journal of Russian Academy of Sciences
 Founded
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IssuesArchive of Issues2016-3pp.334-338

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V.V. Vasil'ev and S.A. Lurie, "Generalized Solution of the Problem on a Circular Membrane Loaded by a Lumped Force," Mech. Solids. 51 (3), 334-338 (2016)
Year 2016 Volume 51 Number 3 Pages 334-338
DOI 10.3103/S0025654416030109
Title Generalized Solution of the Problem on a Circular Membrane Loaded by a Lumped Force
Author(s) V.V. Vasil'ev (Ishlinsky Institute for Problems in Mechanics, Russian Academy of Sciences, pr. Vernadskogo 101, str. 1, Moscow, 119526 Russia, vvvas@dol.ru)
S.A. Lurie (Ishlinsky Institute for Problems in Mechanics, Russian Academy of Sciences, pr. Vernadskogo 101, str. 1, Moscow, 119526 Russia; Institute of Applied Mechanics, Russian Academy of Sciences, Leninskii pr. 32A, Moscow, 117334 Russia, lurie@ccas.ru)
Abstract The solution of the problem on a circular membrane loaded at the center by a lumped force is a classical example of a singular solution of equations of mathematical physics. In this paper, the problem is solved by using relations of the generalized theory of elasticity, which contain a structural parameter and permit obtaining a regular solution. An experiment for determining the structural parameter in the problem of bending of a membrane is described.
Keywords singular solution, nonclassical theories of elasticity, elastic membrane
References
1.  S. G. Mikhlin, Linear Partial Differential Equations (Vysshaya Shkola, Moscow, 1977) [in Russian].
2.  V. V. Vasil'ev and S. A. Lurie, "Generalized Theory of Elasticity," Izv. Ross. Akad. Nauk. Mekh. Tverd. Tela, No. 4, 16-27 (2015) [Mech. Solids (Engl. Transl.) 50 (4), 379-388 (2015)].
3.  G. A. Korn and T. M. Korn, Mathematical Handbook for Scientists and Engineers (McGraw-Hill, New York, 1968; Nauka, Moscow, 1973).
4.  M. Abramowitz and I. Stegun (Editors), Handbook of Mathematical Functions, with Formulas, Graphs, and Mathematical Tables (Gov. Print off., Wasgington, 1964; Nauka, Moscow, 1979).
Received 17 December 2015
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