an:01222031
Zbl 0916.73021
Dauge, Monique; Djurdjevic, Ivica; R??ssle, Andreas
Full asymptotic expansions for thin elastic free plates
EN
C. R. Acad. Sci., Paris, S??r. I, Math. 326, No. 10, 1243-1248 (1998).
00050320
1998
j
74K20 35Q72 35C20
leading term of asymptotic expansion; convergence of three-dimensional solution to two-dimensional limit; free boundary conditions; Kirchhoff-Love field; in-plane generating functions; boundary layer; membrane load
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.