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IssuesArchive of Issues2008-1pp.62-74

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A. Yu. Zemlyanova and V. V. Silívestrov, "Reinforcement of a plate with a circular hole by an eccentric circular patch," Mech. Solids. 43 (1), 62-74 (2008)
Year 2008 Volume 43 Number 1 Pages 62-74
DOI 10.3103/S0025654408010068
Title Reinforcement of a plate with a circular hole by an eccentric circular patch
Author(s) A. Yu. Zemlyanova (Ulíyanov Chuvash State University, Moskovskii pr-t 15, Cheboksary, 428015, Russia, a_zemlyanova@mail.ru)
V. V. Silívestrov (Ulíyanov Chuvash State University, Moskovskii pr-t 15, Cheboksary, 428015, Russia, v_silvestrov@mail.ru)
Abstract We study the reinforcement of an infinite elastic plate with a circular hole by a larger eccentric circular patch completely covering the hole and rigidly adjusted to the plate along the entire boundary of itself. We assume that the plate and the patch are in a generalized plane stress state generated by the action of some given loads applied to the plate at infinity and on the boundary of the hole. We use the power series method combined with the conformal mapping method to find the Muskhelishvili complex potentials and study the stress state on the hole boundary and on the adhesion line. We consider several examples, study how the stresses depend on the geometric and elastic parameters, and compare the problem under study with the case of a plate with a circular hole without a patch. In scientific literature, numerous methods for reinforcing plates with holes, in particular, with circular holes, have been studied. In the monographs [1, 2], the problem of reinforcing the hole edges by stiffening ribs is solved. Methods for reinforcing a circular hole by using two-dimensional patches pasted to the entire plate surface are studied in [3, 4]. The case of a plate with a circular cut reinforced by a concentric circular patch adjusted to the plate along the boundary of itself or along some other circle was studied in [5, 6]. The reinforcement of an elliptic hole by a confocal elliptic patch was considered in [7].
References
1.  G. N. Savin and N. P. Fleishman, Rib-Reinforced Plates and Shells (Naukova Dumka, Kiev, 1964; NASA, Washington, 1967).
2.  V. M. Alexandrov and S. M. Mkhitaryan, Contact Problems for Bodies with Thin Coverings and Interlayers (Nauka, Moscow, 1983) [in Russian].
3.  H. Engels, D. Zakharov, and W. Becker, "The Plane Problem of an Elliptically Reinforced Circular Hole in an Anisotropic Plate or Laminate," Arch. Appl. Mech. 71(9), 601-612 (2001).
4.  P. C. Tse, K. J. Lau, and W. H. Wong, "Stress and Failure Analysis of Woven Composite Plates with Adhesive Patch Reinforced Circular Hole," Composites. PB: Engineering 33(1), 57-65 (2002).
5.  V. V. Silívestrov and A. Yu. Zemlyanova, "Stress State of a System of Elastic Plates Connected along the Circumference," Izv. Nats. Akad. Nauk Iskus. Chuvash. Resp., No. 3, 57-71 (2003).
6.  V. V. Silívestrov and A. Yu. Zemlyanova, "Repair of a Plate with a Circular Hole by Applying a Patch," Zh. Prikl. Mekh. Tekh. Fiz. 45(4), 176-183 (2004) [J. Appl. Mech. Tech. Phys. (Engl. Transl.) 45 (4), 605-611 (2004)].
7.  V. V. Silívestrov and A. Yu. Zemlyanova, "Extension of a Plate with an Elliptic Hole Reinforced by a Cofocal Elliptic Patch," Mekh. Komp. Mater. Konstr. 10(4), 577-595 (2004).
8.  N. I. Muskhelishvili, Some Basic Problems of the Mathematical Theory of Elasticity (Nauka, Moscow, 1966; Noordhoff International Publishing, Leyden, 1977).
9.  L. V. Kantorovich and V. I. Krylov, Approximate Methods of Higher Analysis (Fizmatgiz, Moscow-Leningrad, 1962; Interscience, New York, 1964).
Received 12 May 2005
Link to Fulltext http://www.springerlink.com/content/p4603070790j6150
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