A higher order finite element for sandwich plates

Abstract

A finite element model for the analysis of sandwich plates with laminated composites face-sheets is developed. In the model, the face-sheets are represented as ReissnerMindlin plates and therefore include shear deformation effects. The core is modelled as a three-dimensional continuum in which the through-thickness representation of the displacement fields is of a mixed form. That is the u, v deflections are cubic functions of z while w is a quadratic function of z. This representation allows accurate modelling of a wide range of core types (honeycomb and foam) and in particular core materials which have low in-plane stiffness compared to the transverse stiffness. Also, these through the thickness trial functions allow an accurate representation of transverse shear and normal stresses. The in-plane modelling of u, v, w use bi-cubic trial functions in both the face-sheets and the core. Such a representation avoids shear locking without special precautions. Evaluation of the stiffness matrices involves analytical through-thickness integration of the strain energy. Doing so reduces the three-dimensional problem to a quasi twodimensional problem and increases numerical efficiency. Standard finite element procedures are used to solve the resulting two-dimensional problem. The presented model provides a powerful general tool for the analysis of sandwich plates; transverse normal and shear stresses can be determined explicitly at the core/face-sheet interface. Also, because of the core model adopted, good accuracy is obtained when large differences in transverse versus in-plane core stiffness is present as well as for cases in which the core stiffness changes rapidly in the plane of the plate. The accuracy of the model is illustrated with several examples.