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Russian Academy of Sciences
in January 1936
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IssuesArchive of Issues2011-4pp.472-475

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V.M. Aleksandrov and V.Yu. Salamatova, "The bending of a circular membrane on a linearly deformed foundation," J. Appl. Math. Mech. 75 (4), 472-475 (2011)
Year 2011 Volume 75 Issue 4 Pages 472-475
Title The bending of a circular membrane on a linearly deformed foundation
Author(s) V.M. Aleksandrov (Moscow, Russia)
V.Yu. Salamatova (Moscow, Russia,
Abstract The axisymmetric problem of the bending of a circular transversely-loaded membrane (i.e., a thin plate having no flexural stiffness), which lies without friction on a linearly deformed foundation, where there is contact over the whole area of the membrane, is considered. The problem is reduced to the combined investigation of a differential equation for the bending of the membrane and an integral equation of the first kind with an irregular kernel in the unknown contact pressure. The method of special orthonormalized polynomials and the regular asymptotic "large λ" method are used to solve the problem.
Received 3 September 2009
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