engleski

3D structure–2D plate interaction model

In this paper, we derive models for the interaction of a linearized three-dimensional elastic structure with a thin elastic layer of possibly different material attached to it. Rigorous derivation is performed by considering a thin three-dimensional layer and the asymptotics of the solution of the full remaining three-dimensional problem when the thickness ε of the thin layer tends to zero. Furthermore, the attached thin material is assumed to have the elasticity coefficients which are of order 1∕εp, for p≥0 with respect to the coefficients of the three-dimensional body. In the limit, five different models are obtained with respect to different choices of p, namely p∈[0, 1⟩, p=1, p∈⟨1, 3⟩, p=3, and p∈⟨3, ∞⟩. Furthermore a three-dimensional–two- dimensional model is proposed that has the same asymptotics as the original three-dimensional problem. This is convenient for applications because one does not have to decide in advance which limit model to use.

linearized elasticity, 3D structure, 2D plate model, interaction model, justification

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