Spectral Homogenization Problems in Linear Elasticity with Large Reaction Terms Concentrated in Small Regions of the Boundary

Delfina Gómez (), Sergey A. Nazarov () and Maria-Eugenia Pérez-Martínez ()
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Delfina Gómez: Universidad de Cantabria
Sergey A. Nazarov: Saint-Petersburg State University
Maria-Eugenia Pérez-Martínez: Universidad de Cantabria

Chapter Chapter 7 in Computational and Analytic Methods in Science and Engineering, 2020, pp 127-150 from Springer

Abstract: Abstract We consider a homogenization problem for the elasticity operator posed in a bounded domain of the upper half-space, a part of its boundary being in contact with the plane. We assume that this surface is traction-free out of “small regions,” where we impose Winkler–Robin boundary conditions. These “reaction regions” are periodically placed along the plane while its size is much smaller than the period. The Winkler–Robin condition links stresses and displacements in the small reaction regions by means of a symmetric and definite positive matrix and a “reaction parameter” that can be large as the period tends to zero. Using the technique of matched asymptotic expansions, we provide all the possible homogenized problems, depending on the relations between the three parameters: period, size of the small regions, and reaction parameter.

Date: 2020
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-030-48186-5_7

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DOI: 10.1007/978-3-030-48186-5_7

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