 | | 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: | | 11262 |
| In Russian (Èçâ. ĐÀÍ. ̀̉̉): | | 8011
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| In English (Mech. Solids): | | 3251 |
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| << Previous article | Volume 55, Issue 7 / 2020 | Next article >> |
| Zveryaev E.M., "Saint-Venant–Picard–Banach Method for Integrating Thin-Walled System Equations of the Theory of Elasticity," Mech. Solids. 55 (7), 1042-1050 (2020) |
| Year |
2020 |
Volume |
55 |
Number |
7 |
Pages |
1042-1050 |
| DOI |
10.3103/S0025654420070225 |
| Title |
Saint-Venant–Picard–Banach Method for Integrating Thin-Walled System Equations of the Theory of Elasticity |
| Author(s) |
Zveryaev E.M. (Keldysh Institute of Applied Mathematics, Russian Academy of Sciences, Moscow, 125047 Russia, zveriaev@mail.ru) |
| Abstract |
A systematic presentation of the modified Saint-Venant semi-inverse method is given in the
example of constructing solutions of differential equations of the theory of elasticity with a small
parameter for a long strip. The method is interpreted as iterative. The solution convergence is provided
by a small thin wall parameter in accordance with the Banach contraction mapping principle. The
sequential computation of the unknowns takes place with the help of the Picard operators known in
the literature, so that the unknowns computed by one equation are the input magnitudes for the next
equation, and so on. The fulfillment of the boundary conditions on the long edges leads to the equa-
tions for slowly and quickly varying singular components of the solution. The solutions of singularly
perturbed equations satisfy the conditions lost in the classical theory and describe the stress concentration at the corners of the strip. |
| Keywords |
Saint-Venant semi-inverse method, contraction mapping principle, stress concentration at the corners |
| Received |
12 June 2019 | Revised |
09 August 2019 | Accepted |
16 September 2019 |
| Link to Fulltext |
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