Mechanics of Solids (about journal) Mechanics of Solids
A Journal of Russian Academy of Sciences
in January 1966
Issued 6 times a year
Print ISSN 0025-6544
Online ISSN 1934-7936

Russian Russian English English About Journal | Issues | Guidelines | Editorial Board | Contact Us

IPMech RASWeb hosting is provided
by the Ishlinsky Institute for
Problems in Mechanics
of the Russian
Academy of Sciences
IssuesArchive of Issues2011-4pp.635-644

Archive of Issues

Total articles in the database: 10864
In Russian (. . ): 8009
In English (Mech. Solids): 2855

<< Previous article | Volume 46, Issue 4 / 2011 | Next article >>
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,
S.B. Akperova (Baku State University, Zahida Halilova 23, Baku, AZ 1000 Azerbaijan,
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
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
Link to Fulltext
<< Previous article | Volume 46, Issue 4 / 2011 | Next article >>
Orphus SystemIf you find a misprint on a webpage, please help us correct it promptly - just highlight and press Ctrl+Enter

101 Vernadsky Avenue, Bldg 1, Room 246, 119526 Moscow, Russia (+7 495) 434-3538
Founders: Russian Academy of Sciences, Branch of Power Industry, Machine Building, Mechanics and Control Processes of RAS, Ishlinsky Institute for Problems in Mechanics RAS
© Mechanics of Solids
Rambler's Top100