Theory of bending multi-layer sandwich plates.

Abstract

The governing equations for bending of multilayered sandwich, plates are developed by variational methods. The plate is considered to be composed of n membranes, having different thicknesses and possessing different isotropic elastic properties, and (n-1) orthotropic cores. The variation of stresses across the membranes is neglected as are the face-parallel stresses in the core. These assumptions are consistent with those usually employed when treating sandwich plates as thin plates. The energy functional is formulated with the stresses considered as independent variables and the stress resultants are introduced as constraint conditions utilizing Lagrange multipliers. It is possible to identify a neutral surface in such a manner that the equation defining deflection of the plate may be obtained in a similar form as that obtained by Reissner and Cheng. It is shown that existing solutions for either Reissner's equation for a single sandwich with an isotropic core or Cheng's equation for a single sandwich with an orthotropic core may be extended to include similar multilayer sandwich plates by redefining the physical constants of the plate.