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Publication Information : Volume 24 - Number 1 - Successive Number 1
Type : Article
Topics of Paper : Transaction on Mechanical Engineering
English Title : On the solution of a contact problem for a rhombus weakened with a full-strength hole
English Abstract : This paper addresses a problem of plane elasticity theory for a doubly connected body whose external boundary is a rhombus with its diagonals lying at the coordinate axes OX and OY . The internal boundary is the required full-strength hole and the symmetric axes are the rhombus diagonals. Absolutely smooth stamps with rectilinear bases are applied to the linear parts of the boundary, and the middle points of these stamps are under the action of concentrated forces, so there are no friction forces between the stamps and the elastic body. The hole boundary is free from external load and the tangential stresses are zero along the entire boundary of the rhombus. Using the methods of complex analysis, the analytical image of Kolosov-Muskhelishvili's complex potentials (characterising an elastic equilibrium of the body), and the equation of an unknown part of the boundary are determined under the condition that the tangential normal stress arising at it takes the constant value. Such holes are called full-strength holes. Numerical analysis are performed and the corresponding graphs are constructed.
English Keywords : plate elasticity theory, complex variable theory, stress state.
Refrences : [1] N. V. Banichuk, Optimality conditions in the problem of seeking the hole shapes in elastic bodiesJournal of Applied Mathematics and Mechanics 41 (1977), no. 5, 946-951.[2] R. Bantsuri, On one mixed problem of the plane theory of elasticity with a partially unknown boundary, Proc. A. Razmadze Math. Inst. 140 (2006), 9-16 (English, with English and Georgian summaries).[3] ------------ Solution of the mixed problem of plate bending for a multi-connected domain with partially unknown boundary in the presence of cyclic symmetry, Proc. A. Razmadze Math. Inst. 145 (2007), 9-22 (English, with English and Georgian summaries).[4] R. Bantsuri and Sh. Mzhavanadze, The mixed problem of the theory of elasticity for a rectangle weakened by unknown equiv-string holes, Proc. A. Razmadze Math. Inst. 145 (2007), 23-33 (English, with English and Georgian summaries).[5] R. D. Bantsuri, Some inverse problems of plane elasticity and of bending of thin plates, Continuum mechanics and related problems of analysis, Metsniereba", Tbilisi, 1991, pp. 100-107.[6] G. P. Cherepanov, Inverse problems of the plane theory of elasticity, J. Appl. Math. Mech. 38 (1974), n. 6, 915-931 (1975). [7] F. D. Gakhov, Boundary value problems, Dover Publications, Inc., New York, 1990, Translated from the Russian; Reprint of the 1966 translation.[8] M.V. Keldysh and L.D. Sedov, The effective solution of some boundary problems for harmonicfunctions, Dokl. Akad. Nauk SSSR 16 (1937), no. 1, 7-10, Russian.[9] N. I. Muskhelishvili, Some basic problems of the mathematical theory of elasticity, reprint of the second english edition ed., Noordhod International Publishing, Leiden, 1977.[10] ---------------- , Singular integral equations, Dover Publications, Inc., New York, 1992.[11] N. Odishelidze, Solution of the mixed problem of the plane theory of elasticity for a multiply connected domain with partially unknown boundary in the presence of axial symmetry, Proceedings of A. Razmadze Mathematical Institute 146 (2008), 97-112.[12] N. Odishelidze and F. Criado-Aldeanueva, A mixed problem of plane elasticity for a domain with partially unknown boundary, Acta Mech. 199 (2008), 227-240.[13] ---------------------, A mixed problem of plate bending for a doubly connected domains with partially unknown boundary in the presence of cycle symmetry, Science China Physics, Mechanics and Astronomy 53 (2010), no. 10, 1884-1894.[14] N. T. Odishelidze, Solution of the mixed problem of the plane theory of elasticity for a multiply connected domain with partially unknown boundary in the presence of axial symmetry, Proc. A. Razmadze Math. Inst. 146 (2008), 97-112 (English, with English and Georgian summaries).[15] S. B. Vigdergauz, On a case of the inverse problem of the two-dimensional theory of elasticity, J.Appl. Math. Mech. 41 (1977), no. 5, 927-933 (1979).
Number Of Pages :
From 183 to 190


Authors :
The AuthorAuthor SequenceOrganizationOrganization ( english )AffiliationEmailEducation
Dr Francisco Criado-Aldeanueva
(Author)
1University of Malaga  fcriado@uma.es 
Dr Nana Odishelidze 1 Tbilisi State University   
Dr J.M. Sanchez 3 University of Malaga   
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2017
Transactions on Civil Engineering
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Transactions on Chemistry and Chemical Engineering
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2015
Transactions on Civil Engineering
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Transactions on Civil Engineering
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