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Prikladnaya Mekhanika i Tekhnicheskaya Fizika, 2005, Volume 46, Issue 1, Pages 144–152
(Mi pmtf2234)
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This article is cited in 1 scientific paper (total in 1 paper)
Singular solutions for an anisotropic plate with an elliptical hole
V. N. Maksimenko, E. G. Podruzhin Novosibirsk State Technical University, 630092, Novosibirsk
Abstract:
A solution of the bending problem for a plate with an elliptical hole subjected to a point force (a singular solution) is obtained using the engineering theory of thin anisotropic plates and Lekhnitskii’s complex potentials. The solution is constructed by conformal mapping of the exterior of the elliptical hole onto the exterior of a unit circle with evaluation of the Cauchy-type integrals over closed contours. Different versions of the boundary conditions on the holw contour are considered. In the limiting case where the ellipse becomes a slot, the solution describes the bending of a plate with a rectilinear crack or a rigid inclusion.
Keywords:
bending, anisotropic and isotropic materials, conformal mapping, Cauchy-type integral, unit circle.
Received: 24.09.2003 Accepted: 19.02.2004
Citation:
V. N. Maksimenko, E. G. Podruzhin, “Singular solutions for an anisotropic plate with an elliptical hole”, Prikl. Mekh. Tekh. Fiz., 46:1 (2005), 144–152; J. Appl. Mech. Tech. Phys., 46:1 (2005), 117–123
Linking options:
https://www.mathnet.ru/eng/pmtf2234 https://www.mathnet.ru/eng/pmtf/v46/i1/p144
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