 | | 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 |
Archive of Issues
| Total articles in the database: | | 12804 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8044
|
| In English (Mech. Solids): | | 4760 |
|
| << Previous article | Volume 37, Issue 1 / 2002 | Next article >> |
| I. G. Teregulov and S. N. Timergaliev, "Ritz method for approximate solution of boundary value problems in the nonlinear theory of thin shells," Mech. Solids. 37 (1), 129-137 (2002) |
| Year |
2002 |
Volume |
37 |
Number |
1 |
Pages |
129-137 |
| Title |
Ritz method for approximate solution of boundary value problems in the nonlinear theory of thin shells |
| Author(s) |
I. G. Teregulov (Kazan)
S. N. Timergaliev (Naberezhnye Chelny) |
| Abstract |
The application of the Ritz method is justified in relation to the
boundary value problems of the theory of geometrically and physically
nonlinear thin elastic non-shallow shells. A distinctive feature of the
paper is that we use some special function space, other than
the usual spaces of displacements and stresses, and
express the displacements and strains through some auxiliary functions.
Boundary value problems for non-shallow shells whose middle surface is
a surface of revolution or a convex surface having an involute,
were considered in [1-4]. In this paper, we propose a method for the
investigation of arbitrary non-closed non-shallow shells of a nonzero
Gaussian curvature. The shells are supposed to be rigidly fixed along the
entire boundary. We obtain equations for which the following
conditions hold: there exists at least one
point of absolute minimum for the total energy functional for the
"shell-external forces" system; approximate solutions converge to
a minimizer of this problem; the minimizer is a generalized solution of
the equation obtained from the variational Lagrange principle. |
| References |
| 1. | I. I. Vorovich, L. P. Lebedev, and Sh. M. Shlafman,
"Some direct methods and the existence of solutions in the nonlinear theory
of non-shallow shells of revolution,"
PMM [Applied Mathematics and Mechanics],
Vol. 38, No. 2, pp. 339-348, 1974. |
| 2. | I. I. Vorovich and Sh. M. Shlafman,
"On the solvability of nonlinear equations for a loaded non-shallow
symmetric spherical dome," PMM [Applied Mathematics and Mechanics],
Vol. 38, No. 5, pp. 944-946, 1974. |
| 3. | Sh. M. Shlafman, "On the existence of solutions in the nonlinear
theory of non-shallow shells," Izv. Sev. Kavk. Nauchn. Tsentr. Vyssh.
Shkol., Ser. Estestv. Nauk, No. 4, pp. 49-53, 1974. |
| 4. | I. I. Vorovich and Sh. M. Shlafman,
"On the convergence of the finite-element method in the
nonlinear theory of shells," in X All-Union Conf. on Shells and Plates,
Tbilisi [in Russian], Vol. 1, pp. 552-561, 1975. |
| 5. | K. Washitzu,
Variational Methods in Elasticity and Plasticity [Russian translation], Mir, Moscow, 1987. |
| 6. | I. N. Vekua, Generalized Analytic Functions [in Russian], Nauka, Moscow, 1988. |
| 7. | I. G. Teregulov and S. N. Timergaliev,
"An investigation of solvability of boundary value problems
in the theory of geometrically and physically nonlinear thin shells,"
Izv. AN. MTT [Mechanics of Solids], No. 6, pp. 116-128, 2000. |
| 8. | M. M. Vainberg, Variational Method and Monotone Operators
in the Theory of Nonlinear Equations [in Russian], Nauka, Moscow, 1972. |
| 9. | M. A. Krasnosel'skii, Topological Methods in the Theory of
Nonlinear Integral Equations [in Russian], Gostekhizdat, Moscow, 1956. |
| 10. | I. I. Vorovich, Mathematical Problems in the Nonlinear Theory
of Shallow Shells [in Russian], Nauka, Moscow, 1989. |
|
| Received |
11 November 1999 |
| << Previous article | Volume 37, Issue 1 / 2002 | Next article >> |
|
 If you find a misprint on a webpage, please help us correct it promptly - just highlight and press Ctrl+Enter
|
|
Russian 
English