Innovative Solution of a 2-D Elastic Transmission Problem
Date
2006-07-12T14:01:23Z
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Abstract
This 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.
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Keywords
Non-local boundary value problem, variational formulation, asymptotic expansions, boundary integral equations