### Full Asymptotic Expansions for Thin Elastic Free Plates

Monique Dauge, Ivica Djurdjevic and Andreas Rössle

The case of a linearly elastic plate with free boundary conditions on the lateral side is investigated as the half-thickness $\varepsilon$ tends to zero. As in hard clamped plates, the generic leading term of the asymptotic expansion of the scaled displacement is a Kirchhoff-Love field with in-plane generating functions satisfying classical bending and membrane problems of Neumann type. The first boundary layer profile is of bending type, so that in the case of a membrane load the convergence of the 3D solution to the 2D limit one is of improved accuracy. See also the proof in our papers The Influence of Lateral Boundary Conditions...' Part I and Part II. Conditions under which the asymptotic expansion starts later' are also given and the structure of the first non-vanishing term is studied.

C. R. Acad. Sc. Paris Série I, 326, 1243-1248, 1998.

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