Asymptotics of the solution of the problem of deformation of an arbitrary locally periodic thin plate
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E. A. Akimova, S. A. Nazarov and G. A. Chechkin
Translated by: H. H. McFaden - Trans. Moscow Math. Soc. 2004, 1-29
- DOI: https://doi.org/10.1090/S0077-1554-04-00142-6
- Published electronically: November 2, 2004
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Abstract:
This paper is concerned with a problem in the theory of elasticity for a thin composite plate. The principal terms are constructed for the asymptotics of the solution, with only local periodicity of the elastic moduli of the material and the shape of the plate assumed. The asymptotic expression is justified with the help of a weighted anisotropic Korn’s inequality, which is proved by means of the “tetris” procedure for constructing a supporting set.References
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Bibliographic Information
- E. A. Akimova
- Affiliation: Moscow State University, Department of Mechanics and Mathematics, Moscow 119899, Russia
- Email: chechkin@mech.math.msu.su
- S. A. Nazarov
- Affiliation: St. Petersburg State University, St. Petersburg, Russia
- MR Author ID: 196508
- Email: serna@snark.ipme.ru
- G. A. Chechkin
- Affiliation: Moscow State University, Department of Mechanics and Mathematics, Moscow 119899, Russia
- Email: chechkin@mech.math.msu.su
- Published electronically: November 2, 2004
- Additional Notes: The work of S. A. Nazarov and G. A. Chechkin was supported in part by the Russian Foundation for Basic Research (grants no. 00–01–00455 and 02–01–00693, and 02–01–00868, respectively).
- © Copyright 2004 American Mathematical Society
- Journal: Trans. Moscow Math. Soc. 2004, 1-29
- MSC (2000): Primary 74K20, 35B40; Secondary 35J55, 74B15, 74E30, 74E10, 35Q72
- DOI: https://doi.org/10.1090/S0077-1554-04-00142-6
- MathSciNet review: 2193435