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This article is cited in 18 scientific papers (total in 18 papers)
Asymptotics of solutions and modelling the problems of elasticity theory in domains with rapidly oscillating boundaries
S. A. Nazarov Institute of Problems of Mechanical Engineering, Russian Academy of Sciences
Abstract:
We obtain explicit formulae for two terms of asymptotics of solutions of the
Neumann and Dirichlet problems for the system of two-dimensional equations
of elasticity theory in a domain with rapidly oscillating boundary and suggest
an algorithm for constructing complete asymptotic expansions. We justify the
asymptotic representations of solutions using Korn's inequality in singularly
perturbed domains. We discuss two methods of modelling these problems of
elasticity theory by constructing new, simpler, boundary-value problems whose
solutions provide two-term asymptotics of solutions of the original problems.
The first method is based on the introduction of the so-called wall laws
containing a small parameter in the higher derivatives. The second method is
based on the use of the concept of a smooth image
of the singularly perturbed boundary.
Received: 19.12.2006
Citation:
S. A. Nazarov, “Asymptotics of solutions and modelling the problems of elasticity theory in domains with rapidly oscillating boundaries”, Izv. RAN. Ser. Mat., 72:3 (2008), 103–158; Izv. Math., 72:3 (2008), 509–564
Linking options:
https://www.mathnet.ru/eng/im2600https://doi.org/10.1070/IM2008v072n03ABEH002410 https://www.mathnet.ru/eng/im/v72/i3/p103
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Abstract page: | 715 | Russian version PDF: | 181 | English version PDF: | 43 | References: | 108 | First page: | 11 |
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