Asymptotic analysis of thin linear elastic layers constrained by two rigid plates

Abstract

Two asymptotic solutions are presented for linear elastic thin, not necessarily circular, cylindrical layers fully constrained by two rigid plates. Other than being small, the plate displacements and rotations are not restricted, and therefore, in general, a constrained layer is subjected to combined stretching, bending, shearing, and twisting. The first solution is restricted to layers formed by compressible solids, whose Poisson’s ratio is not too close to one half. This solution is a superposition of a polynomial displacement field, valid in the bulk of the layer, and a corrective displacement field, which decays exponentially fast away from the cylindrical surface and becomes negligible at distances comparable to the layer thickness. The second solution is not restricted in terms Poisson’s ratio but it is correct only to a leading order. This solution unifies leading-order solutions for layers formed by compressible, nearly incompressible, and incompressible solids. The unification involves a parameter characterizing the competition between compressibility and thinness.