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Asymptotics for Spectral Problems with Rapidly Alternating Boundary Conditions on a Strainer Winkler Foundation

Abstract: We consider a spectral homogenization problem for the linear elasticity system posed in a domain of the upper half-space R3+, a part of its boundary being in contact with the plane {x3=0}. We assume that the surface is traction-free out of small regions T, where we impose Winkler-Robin boundary conditions. This condition links stresses and displacements by means of a symmetric and positive definite matrix-function M(x) and a reaction parameter () that can be very large when 0. The size of the regions T is O(r), where r, and they are placed at a distance between them. We provide all the possible spectral homogenized problems depending on the relations between , r and (), while we address the convergence, as 0, of the eigenpairs in the critical cases where some strange terms arise on the homogenized Robin boundary conditions on . New capacity matrices are introduced to define these strange terms.

 Fuente: Journal of Elasticity, 2020, 142, 89-120

Editorial: Springer Nature

 Año de publicación: 2020

Nº de páginas: 32

Tipo de publicación: Artículo de Revista

ISSN: 0374-3535,1573-2681

Proyecto español: PGC2018-098178-B-I00

Url de la publicación: https://doi.org/10.1007/s10659-020-09791-8