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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