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.
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REFERENCES
S. G. Lekhnitskii, Anisotropic Plates, Gordon and Breach, New York (1968).
D. V. Grilitskii (1956) ArticleTitleThe effect of the point of application of a force or moment on the stress distribution in an infinite anisotropic plate with an elliptical hole Prikl. Mekh 2 IssueID2 159–166
L. T. Berezhnitskii M. V. Delyavskii V. V. Panasyuk (1979) Bending of Thin Plates with Crack-Like Defects Kiev Naukova Dumka
V. N. Maksimenko E. G. Podruzhin (2003) ArticleTitleFundamental solutions in problems of bending of anisotropic plates J. Appl. Mech. Tech. Phys 44 IssueID4 564–573
L. T. Berezhnitskii V. M. Sadivskii L. I. Onyshko (1978) ArticleTitleBending of an anisotropic plate with a crack Prikl. Mekh 14 IssueID11 42–49
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Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 46, No. 1, pp. 144–152, January–February, 2005
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Maksimenko, V.N., Podruzhin, E.G. Singular solutions for an anisotropic plate with an elliptical hole. J Appl Mech Tech Phys 46, 117–123 (2005). https://doi.org/10.1007/s10808-005-0016-6
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DOI: https://doi.org/10.1007/s10808-005-0016-6