Mechanics of Solids (about journal) Mechanics of Solids
A Journal of Russian Academy of Sciences
 Founded
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
 


IssuesArchive of Issues2006-3pp.55-68

Archive of Issues

Total articles in the database: 11223
In Russian (Èçâ. ÐÀÍ. ÌÒÒ): 8011
In English (Mech. Solids): 3212

<< Previous article | Volume 41, Issue 3 / 2006 | Next article >>
K. F. Chernykh, "An aternative method in elasticity: boundary condition splitting," Mech. Solids. 41 (3), 55-68 (2006)
Year 2006 Volume 41 Number 3 Pages 55-68
Title An aternative method in elasticity: boundary condition splitting
Author(s) K. F. Chernykh (St. Petersburg)
Abstract Of wide use in plane linear elasticity is the traditional method based on Cauchy-type integrals. Being a student (1951), the author noticed that all problems that can be solved on the basis of the traditional approach can also be solved by a simpler method, which does not require a special mathematical background, - the so-called boundary condition splitting method. Later that method was extended to cover conjugation conditions and two-dimensional problems of nonlinear elasticity (plane problem, anti-plane strain, axisymmetric strain of bodies of revolution). This new method was used in a new version of the nonlinear elasticity theory proposed by the author. This version is extremely simple and entails no loss of generality. In this way (with the development of the method of complex variable, the introduction of new types of boundary conditions, conjugation conditions, and constitutive relations of elasticity), it turned out possible to obtain exact solutions of two-dimensional boundary value problems.

The next step was the introduction of conjugate static and distortional resolving functions, which are obtained from a compact system of resolving functions. The resolving functions determined in this way were used to determine "secondary" quantities, such as the coordinates of material points of a strained domain, rotations and stresses. Statically determinate problems for arbitrary (not only elastic) materials, as well as distortionally determinate problems, were identified.

This paper contains mostly new results, in particular, the splitting method demonstrated on a nonlinear plane problem.
References
1.  V. V. Novozhilov, Theory of Elasticity [in Russian], Sudpromgiz, Leningrad, 1958.
2.  K. F. Chernykh, Nonlinear Elasticity in Engineering [in Russian], Mashinostroenie, Leningrad, 1986.
3.  K. F. Chernykh, An Introduction to Anisotropic Elasticity [in Russian], Mauka, Moscow, 1988.
4.  K. F. Chernykh, An Introduction to the Geometrically and Physically Nonlinear Theory of Cracks [in Russian], Nauka, Moscow, 1996.
5.  K. F. Chernykh, Nonlinear Theory of Anisotropic Elasticity, Begell Publishing House, New York, 1998.
6.  K. F. Chernykh, Nonlinear Singular Elasticity. Part I. Theory [in Russian]. Izd-vo St. Peterburg. Univ., St. Petersburg, 1999.
7.  K. F. Chernykh, Nonlinear Singular Elasticity. Part II. Applications [in Russian]. Izd-vo St. Peterburg. Univ., St. Petersburg, 1999.
8.  K. F. Chernykh, "Complex nonlinear theory of elasticity," Uspekhi Mekhaniki, Vol. 1, No. 4, pp. 212-161, 2002.
9.  K. F. Chernykh, "On the approach to nonlinear physical mesomechanics," Fiz. Mezomekh., Vol. 5, No. 2, pp. 5-15, 2002.
10.  K. F. Chernykh, Nonlinear Elasticity (Theory and Applications) [in Russian], Izd-vo St. Peterb. Univ., St. Petersburg, 2004.
Received 26 March 2004
<< Previous article | Volume 41, Issue 3 / 2006 | 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 mechsol@ipmnet.ru https://mtt.ipmnet.ru
Founders: Russian Academy of Sciences, Ishlinsky Institute for Problems in Mechanics RAS
© Mechanics of Solids
webmaster
Rambler's Top100