Averaged reaction for nonlinear boundary conditions on a grill-type Winkler foundation

We consider a homogenization problem for the elasticity operator posed in a bounded domain of the half-space, a part of its boundary being in contact with the plane. This surface is traction-free out of “small regions”, where we impose nonlinear Winkler-Robin boundary conditions containing “large re...

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Bibliographic Details
Published inMathematical modelling and analysis Vol. 29; no. 4; pp. 694 - 713
Main Authors Gómez, Delfina, Pérez-Martínez, María-Eugenia
Format Journal Article
LanguageEnglish
Published Vilnius Vilnius Gediminas Technical University 22.11.2024
Subjects
Boundary conditions
boundary homogenization
elasticity operator
Foundations
Half spaces
Homogenization
nonlinear Winkler foundations
Parameters
elasticity operator
nonlinear Winkler foundations
boundary homogenization
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ISSN1392-6292
1648-3510
DOI10.3846/mma.2024.20137

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Summary:We consider a homogenization problem for the elasticity operator posed in a bounded domain of the half-space, a part of its boundary being in contact with the plane. This surface is traction-free out of “small regions”, where we impose nonlinear Winkler-Robin boundary conditions containing “large reaction parameters”. Non-periodical distribution of these regions is allowed provided that they have the same area. We show the convergence of solutions towards those of the homogenized problems depending on the relations between the parameters distance, sizes, and reaction.
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ISSN:1392-6292
1648-3510
DOI:10.3846/mma.2024.20137