Static analysis of sandwich beams using variable stiffness materials

The bending behavior of sandwich beams using an axially graded honeycomb core is investigated using a layer-wise sandwich beam model. Assumptions are made that both face sheets behave as Euler beams and the core is modelled with a first order shear deformation theory. With geometrical compatibility enforced at both upper and lower skin/core interfaces applied, the beam's field functions are reduced to only three, namely the extensional, transverse and rotational displacements at the mid-plane of the core. Governing formulations are developed via the minimum potential energy principle and the Ritz method is used to obtain an approximate solution. Geometrically nonlinear effects are considered in the present formulation by introducing von Karman strains into the face sheets and core. A variety of geometries and boundary conditions including clamped-clamped fixed and clamped-free cantilever type beams have been investigated using the present formulation. Results show that the proposed model provides accurate prediction of displacements and stresses, compared to three dimensional finite element analysis. The “Zig-Zag” effect shown in axial stresses through the beam thickness is also efficiently captured. Furthermore, with the proposed formulation, the effect of axial stiffness variation in the honeycomb core on the static response of sandwich beams is investigated. It is found that due to the axial stiffness variation in the core, displacements of beams and stresses of face sheets and core are significantly affected. As such, the potential design space has been expanded by utilizing variable stiffness materials in sandwich beams.