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Full asymptotic expansions for thin elastic free plates. (English. Abridged French version) Zbl 0916.73021
Summary: We investigate a linearly elastic plate with free boundary conditions on the lateral sides as the half-thickness \(\varepsilon\) tends to zero. As for hardly clamped plates, the 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 three-dimensional solution to the two-dimensional limit is of improved accuracy. Conditions under which the asymptotic expansion ‘starts later’ are given, and the structure of the first non-vanishing term is studied.

MSC:
74K20 Plates
35Q72 Other PDE from mechanics (MSC2000)
35C20 Asymptotic expansions of solutions to PDEs
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