Naslov
3D structure–2D plate interaction model

Autori
Ljulj, Matko ; Tambača, Josip

Izvornik
Mathematics and mechanics of solids (1081-2865) 24 (2019), 10; 3354-3377

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

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

Sažetak
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.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

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