Geodesic
Asymptotic modelling of bonded plates by a soft thin adhesive layer
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 17 (2020), pp. 615-625

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In the present paper, a composite structure is considered. The structure is made of three homogeneous plates: two linear elastic adherents and a thin adhesive. It is assumed that elastic properties of the adhesive layer depend on its thickness $\varepsilon$ as $\varepsilon$ to the power of $3$. Passage to the limit as $\varepsilon$ goes to zero is justified and a limit model is found in which the influence of the thin adhesive layer is replaced by an interface condition between adherents. As a result, we have analog of the spring type condition in the plate theory. Moreover, a representation formula of the solution in the adhesive layer has been obtained.
Keywords: bonded structure, Kirchhoff-Love's plate, composite material, spring type interface condition, biharmonic equation. 
@article{SEMR_2020_17_a91,
     author = {E. M. Rudoy},
     title = {Asymptotic modelling of bonded plates by a soft thin adhesive layer},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {615--625},
     publisher = {mathdoc},
     volume = {17},
     year = {2020},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2020_17_a91/}
}
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E. M. Rudoy. Asymptotic modelling of bonded plates by a soft thin adhesive layer. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 17 (2020), pp. 615-625. http://geodesic.mathdoc.fr/item/SEMR_2020_17_a91/