Asymptotic modelling of bonded plates by a soft thin adhesive layer

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.