The limit behaviors of three-dimensional displacements in thin linearly elastic plates, as the half-thickness tends to zero, is now known for various lateral boundary conditions, see our papers `The Influence of Lateral Boundary Conditions...' Part I and Part II. In the generic case one obtains that the leading term of the asymptotic series of the scaled displacement is a Kirchhoff-Love field. In this note we investigate the case where this leading term vanishes, giving the structure of the first non-vanishing term. There are essentially only three new cases (uncoupling in membrane and bending). Finally, in these situations a boundary layer term of the same order as the actual leading term appears in a generic way.
C. R. Acad. Sc. Paris Série I, 326, 519-524, 1998.
|Fichier pdf (140 k)|