Finite element analysis of sandwich structures

Abstract

Sandwich construction may be defined as a three-layer type of construction where a relatively weak, low-density core material supports and stabilizes thin layers of high strength face material. Its typical features, namely high strenght-thin and low strength-thick materials, interfaces, bonding and load transfer suggest that each of the layers will perform accordingly to its material characteristics and laminate position. Most of the theories used for the analysis of such structures are based either in the Kirchhoff or Mindlin assumptions. The first model does not accounts for transverse shear deformations while the second assumes a first order shear-deformation behaviour. However, both models consider for all the layers a common and unique rotation of the middle-surface normal. In the model which will be described in this paper, it is assumed that each layer (skin or core) can rotate independently, due to their different material characteristics. With this assumption, each layer can deform locally, this being a more accurate model for high-stress gradient areas. In each layer, transverse shear deformation is considered by the imposition of Mindlin-type kinematic relations. In the displacement-based finite-element model, each node possesses 9 degrees of freedom, three displacements of the plate middle-surface and two rotations of the normal of each layer middle-surface. Displacement continuity at the interfaces is imposed. The transverse shear stresses at the middle-surface of the layers are accuratelly computed, although constant in each layer. However, in this model shear correction factors are not used, which simplifies the usual Mindlin-type models, in which these factors are calculated through cylindrical bending assumptions. In this paper, the three-layer sandwich element formulation for linear static analysis will be described. The four, eight and nine-noded isoparametric plate elements are considered. Numerical examples are discussed in order to access the model accuracy.