Modeling and justification of eigenvalue problems for junctions between elastic structures

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review

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Original languageEnglish
Pages (from-to)392-427
Journal / PublicationJournal of Functional Analysis
Issue number2
Publication statusPublished - Dec 1989
Externally publishedYes


We consider a problem in three-dimensional linearized elasticity, posed over a domain consisting of a plate with thickness 2ε inserted into a solid whose Lamé constants and density are independent of ε. If the Lamé constants of the material constituting the plate vary as ε-3 and its density as ε-1, we show that the solutions of the three-dimensional eigenvalue problem converge, as ε approaches zero, to the solutions of a "coupled," "pluri-dimensional" eigenvalue problem of a new type, posed simultaneously over a three-dimensional open set with a slit and a two-dimensional open set. © 1989.