Innovative Solution of a 2-D Elastic Transmission Problem

Author(s)Hsiao, George C.
Author(s)Nigam, Nilima
Author(s)Sändig, Anna-Margarete
Date Accessioned2006-07-12T14:01:23Z
Date Available2006-07-12T14:01:23Z
Publication Date2006-07-12T14:01:23Z
AbstractThis paper is concerned with a boundary-field equation approach to a class of boundary value problems exterior to a thin domain. A prototype of this kind of problems is the interaction problem with a thin elastic structure. We are interested in the asymptotic behavior of the solution when the thickness of the elastic structure approaches to zero. In particular, formal asymptotic expansions will be developed, and their rigorous justification will be considered. As will be seen, the construction of these formal expansions hinges on the solutions of a sequence of exterior Dirichlet problems, which can be treated by employing boundary element methods. On the other hand, the justification of the corresponding formal procedure requires an independence on the thickness of the thin domain for the constant in the Korn inequality. It is shown that in spite of the reduction of the dimensionality of the domain under consideration, this class of problems are in general not singular perturbation problems, because of appropriate interface conditions.en
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Part of SeriesTechnical Report;2006-06
KeywordsNon-local boundary value problemen
Keywordsvariational formulationen
Keywordsasymptotic expansionsen
Keywordsboundary integral equationsen
TitleInnovative Solution of a 2-D Elastic Transmission Problemen
TypeTechnical Reporten
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