 | | 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 42, Issue 2 / 2007 | Next article >> |
| G. V. Kostin and V. V. Saurin, "Method of integro-differential relations in linear elasticity," Mech. Solids. 42 (2), 197-208 (2007) |
| Year |
2007 |
Volume |
42 |
Number |
2 |
Pages |
197-208 |
| Title |
Method of integro-differential relations in linear elasticity |
| Author(s) |
G. V. Kostin (Institute for Problems in Mechanics, Russian Academy of Sciences, pr-t Vernadskogo 101, str. 1, Moscow, 119526, Russia, kostin@ipmnet.ru)
V. V. Saurin (Institute for Problems in Mechanics, Russian Academy of Sciences, pr-t Vernadskogo 101, str. 1, Moscow, 119526, Russia, saurin@ipmnet.ru) |
| Abstract |
Boundary-value problems in linear elasticity can be solved by a method based on introducing integral relations between the components of the stress and strain tensors. The original problem is reduced to the minimization problem for a nonnegative functional of the unknown displacement and stress functions under some differential constraints. We state and justify a variational principle that implies the minimum principles for the potential and additional energy under certain boundary conditions and obtain two-sided energy estimates for the exact solutions. We use the proposed approach to develop a numerical analytic algorithm for determining piecewise polynomial approximations to the functions under study. For the problems on the extension of a free plate made of two different materials and bending of a clamped rectangular plate on an elastic support, we carry out numerical simulation and analyze the results obtained by the method of integro-differential relations. |
| References |
| 1. | K. Washizu, Variational Methods in Elasticity and
Plasticity (Mir, Moscow, 1987) [Russian translation]. |
| 2. | P. Ciarlet, The Finite Element Method for Elliptic
Problems (Mir, Moscow, 1980) [Russian translation]. |
| 3. | O. Zienkiewicz, The Finite Element Method in
Engineering (Mir, Moscow, 1975) [Russian translation]. |
| 4. | K. Bathe and E. Wilson, Numerical Methods in Finite
Element Analysis (Stroiizdat, Moscow, 1982) [Russian
translation]. |
| 5. | K. C. Kwon, S. H. Park, B. N. Jiang, and S. K. Youn,
"The Least Squares Mesh-Free Method for Solving Linear Elastic Problems,"
Comput. Mech.
30 (3), 196-211 (2003). |
| 6. | S. N. Alturi and T. Zhu,
"A New Meshless Local Petrov-Galerkin (MLPG) Approach
in Computational Mechanics,"
Comput. Mech.
22 (2), 117-127 (1998). |
| 7. | T. Belytschko, Y. Y. Lu, and L. Gu,
"Element-Free Galerkin Method,"
Intern. J. Numer. Methods Engrg.
37 (2), 229-256 (1994). |
| 8. | G. V. Kostin and V. V. Saurin,
"Integrodifferential Approach to Solving the Linear Elasticity Problems,"
Dokl. Ross. Akad. Nauk
404 (5), 628-631 (2005). |
| 9. | G. V. Kostin and V. V. Saurin,
"Integrodifferential Statement and the Variational Method for Solving the
Linear Elasticity Problems,"
in Probl. Prochn. Plast.
(Mezhvuz. Sb., Nizhnii Novgorod, 2005)
No. 67, pp. 190-198. |
| 10. | G. V. Kostin and V. V. Saurin,
"The Method of Integrodifferential Relations
for Linear Elasticity Problems,"
Arch. Appl. Mech.
76 (7-8), 391-402 (2006). |
| 11. | N. V. Banichuk,
Introduction to Optimization of Structures
(Nauka, Moscow, 1986)
[in Russian]. |
| 12. | E. J. Haug and J. S. Arora, Applied Optimal Design:
Mechanical and Structural Systems (Mir, Moscow, 1983)
[Russian translation]. |
| 13. | G. V. Kostin and V. V. Saurin,
"Analytical Derivation of Basis Functions for Argyris Triangle,"
ZAMM
81 (4), 871-872 (2001). |
| 14. | G. V. Kostin and V. V. Saurin,
"Analysis of Triangle Membrane Vibration by FEM and Ritz Method
with Smooth Piecewise Polynomial Basis Functions,"
ZAMM
81 (4), 873-874 (2001). |
| 15. | H. Hahn, Theory of Elasticity: Foundations of Linear
Theory and Its Applications (Mir, Moscow, 1988) [Russian
translation]. |
|
| Received |
24 October 2005 |
| Link to Fulltext |
|
| << Previous article | Volume 42, Issue 2 / 2007 | Next article >> |
|
 If you find a misprint on a webpage, please help us correct it promptly - just highlight and press Ctrl+Enter
|
|
Russian 
English