Finite element formulation for cylindrical bending of a transversely compressible sandwich plate, based on assumed transverse strains

In order to construct a plate theory for cylindrical bending of a sandwich plate with isotropic homogeneous thick face sheets and an isotropic core, t he authors make simplifying assumptions regarding distribution of transvers e strain components in the thickness direction. It is assumed that the tran sverse strains (i.e. epsilon (xz) and epsilon (zz)) do not vary in the thic kness direction within the face sheets and the core, but can be different f unctions of the in-plane coordinate in different sublaminates (the face she ets and the core). The purpose of this work is to investigate the accuracy of the theory, based on such assumptions and upon the continuity of displac ements and transverse stresses at the interfaces between the layers. The fi nite element formulation, based on this plate theory, is made using degrees of freedom related to transverse strains and datum surface displacements. The in-plane direct stress, sigma (xx), is computed from the constitutive e quations, and the improved values of transverse stress components are compu ted by integration of equilibrium equations sigma (ijj) = 0 in a post proce ss stage. The values of the transverse strains can also be computed in the post process stage by substituting the improved transverse stresses into th e constitutive relations. The improved transverse strains, unlike the assum ed ones, vary in the thickness direction within a sublaminate. A problem of cylindrical bending of a simply supported plate under a uniform load on th e upper surface is considered, and comparison is made between the in-plane stress, improved transverse stresses (obtained by integration of equilibriu m equations) and displacements, computed from the plate theory with the cor responding values from an exact elasticity solution. This comparison showed that good agreement of both solutions is achieved. The model of a sandwich plate in cylindrical bending, presented in the present paper, has a wider range of applicability than the models presented in literature so far: it c an be applied to plates with both thin and thick faces, with the cores both transversely rigid and transversely flexible, and to the plates with a wid e range of thickness-to-length ratios. Published by Elsevier Science Ltd.