Spectral Homogenization Problems in Linear Elasticity: The Averaged Robin Reaction Matrix

D. Gómez () and M. -E. Pérez-Martínez ()
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D. Gómez: Universidad de Cantabria
M. -E. Pérez-Martínez: Universidad de Cantabria

Chapter Chapter 12 in Integral Methods in Science and Engineering, 2023, pp 145-154 from Springer

Abstract: Abstract We consider a spectral 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 free out of “small regions”, where we impose Winkler-Robin boundary conditions. These regions are periodically placed along the plane; its size can be smaller than the period or of the same order of magnitude. The Winkler-Robin condition links stresses and displacements in these 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. We address the convergence of the spectrum in the case where the reaction parameter multiplied by the total area of the regions is of order 1, while the size of the regions is large enough.

Date: 2023
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DOI: 10.1007/978-3-031-34099-4_12

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