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The Quarterly Journal of Mechanics and Applied Mathematics Advance Access originally published online on March 20, 2009
The Quarterly Journal of Mechanics and Applied Mathematics 2009 62(2):201-220; doi:10.1093/qjmam/hbp005
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© The author 2009. Published by Oxford University Press; all rights reserved. For Permissions, please email: journals.permissions@oxfordjournals.org

Interaction of elastic plate weakened by multiple holes with a set of patches

A. Y. Zemlyanova{dagger}

( Department of Mathematics, Louisiana State University, Baton Rouge, LA 70803, USA )

V. V. Silvestrov

( Department of Mathematics, Gubkin Russian State University of Oil and Gas, Moscow, Russia )

{dagger} <azem{at}math.lsu.edu>

Received 24 November 2008. Revise 8 February 2009.
  Abstract

The problem of interaction of a thin elastic infinite plate weakened by several holes with a system of superimposed patches is considered. Each patch covers completely one or several holes or is located in the exterior of all holes. Some holes may not be covered by patches. The patches are attached to the plate continuously along their boundaries. The patches and the holes can be of arbitrary shape and size. The plate is loaded with given in-plane stresses at infinity and along the boundaries of the holes. All parts of the construction are assumed to be in a generalised plane stressed state. Using special integral representations of complex potentials, the problem is reduced to a system of singular integral equations. Numerical examples on reinforcement of a plate with two or three holes covered by one or two patches are given.


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