Higher order bending and membrane responses of thin linearly elastic plates

Abstract The limit behaviors of three-dimensional displacements in thin linearly elastic plates, as the half-thickness e tends to zero, is now known for various lateral boundary conditions (see [1], [5]). In the generic case one obtains that the leading term of the asymptotic series u 0 + ge 1 +e 2 u 2 +… 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 u k and an error estimate for its deviation from the scaled solution u(e) multiplied by e −k . 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.