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IssuesArchive of Issues2011-4pp.635-644

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Total articles in the database: 10864
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N.K. Akhmedov and S.B. Akperova, "Asymptotic Analysis of a 3D Elasticity Problem for a Radially Inhomogeneous Transversally Isotropic Hollow Cylinder," Mech. Solids. 46 (4), 635-644 (2011)
Year 2011 Volume 46 Number 4 Pages 635-644
DOI 10.3103/S0025654411040133
Title Asymptotic Analysis of a 3D Elasticity Problem for a Radially Inhomogeneous Transversally Isotropic Hollow Cylinder
Author(s) N.K. Akhmedov (Baku State University, Zahida Halilova 23, Baku, AZ 1000 Azerbaijan, anatiq@mail.ru)
S.B. Akperova (Baku State University, Zahida Halilova 23, Baku, AZ 1000 Azerbaijan, ibragimovasariya@yandex.ru)
Abstract The method of asymptotic integration of equations of elasticity [1] is used to study the behavior of the solution of a 3D elasticity problem for a radially inhomogeneous transversally isotropic hollow cylinder of small thickness. Under the assumption that the load is sufficiently smooth, the asymptotic method [1] is used to construct inhomogeneous solutions. An algorithm for constructing exact particular solutions of the equilibrium equations is given for loads of specific types in the case where the cylinder lateral surface is loaded by forces polynomially depending on the axial coordinate. Then the homogeneous solutions are constructed. The asymptotic expansions of homogeneous solutions are obtained, and the above analysis is used to explain the character of the stress-strain state.
Keywords homogeneous solution, inhomogeneous solution, boundary layer, boundary effect
References
1.  A. L. Gol'denveizer, "Derivation of an Approximate Theory of Shells by Means of Asymptotic Integration of the Equations of the Theory of Elasticity," Prikl. Mat. Mekh. 27 (4), 593-608 (1963) [J. Appl. Math. Mech. (Engl. Transl.) 27 (4), 903-924 (1963)].
2.  S. G. Lekhnitskii, Theory of Elasticity of an Anisotropic Body (Nauka, Moscow, 1977) [in Russian].
3.  Yu. A. Ustinov, "Axisymmetric Stress-Strain State of an Inhomogeneous Thin Cylindrical Shell," Prikl. Mekh. 11 (7), 35-41 (1975) [Int. Appl. Mech. (Engl. Transl.) 11 (7), 714-719 (1975)].
4.  Yu. A. Ustinov, Mathematical Theory of Transversely Inhomogeneous Plates (Izd-vo OOO "TsVVR," Rostov-on-Don, 2006) [in Russian].
5.  I. I. Vorovich, I. G. Kadomtsev, and Yu. A. Ustinov, "To the Theory of Plates Inhomogeneous in Thickness," Izv. Akad. Nauk SSSR. Mekh. Tverd. Tela, No. 3, 119-129 (1975) [Mech. Solids (Engl. Transl.)].
6.  N. A. Bazarenko and I. I. Vorovich, "Asymptotic Solution of the Elasticity Problem for a Hollow, Finite Length, Thin Cylinder," Prikl. Mat. Mekh. 29 (6), 1035-1052 (1965) [J. Appl. Math. Mech. (Engl. Transl.) 29 (6), 1219-1238 (1965)].
7.  M. F. Mekhtiev and Yu. A. Ustinov, "Asymptotic Analysis of a Solution of the Problem of the Theory of Elasticity for a Shallow Cone," Prikl. Mat. Mekh. 35 (6), 1108-1115 (1971) [J. Appl. Math. Mech. (Engl. Transl.) 35 (6), 1058-1065 (1971)].
8.  N. K. Akhmedov and M. F. Mekhtiyev, "Analysis of a Three-Dimensional Problem of the Theory of Elasticity for an Inhomogeneous Truncated Hollow Cone," Prikl. Mat. Mekh. 57 (5), 113-119 (1993) [J. Appl. Math. Mech. (Engl. Transl.) 57 (5), 871-877 (1993)].
9.  N. K. Akhmedov and M. F. Mekhtiev, "The Axisymmetric Problem of the Theory of Elasticity for a Non-Uniform Plate of Variable Thickness," Prikl. Mat. Mekh. 59 (3), 516-523 (1995) [J. Appl. Math. Mech. (Engl. Transl.) 59 (3), 491-495 (1995)].
10.  A. I. Lurie, The Theory of Elasticity (Nauka, Moscow, 1970) [in Russian].
11.  Yu. A. Ustinov and V. I. Iudovich, "On the Completeness of a System of Elementary Solutions of the Biharmonic Equation in a Semi-Strip," Prikl. Mat. Mekh. 37 (4), 706-714 (1973) [J. Appl. Math. Mech. (Engl. Transl.) 37 (4), 665-674 (1973)].
Received 26 January 2009
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