Finite Element Formulation Based on the Extended High-Order Sandwich Panel Theory

The extended high-order sandwich panel theory was formulated in its one-dimensional version for orthotropic elastic sandwich beams. This theory includes the in-plane rigidity of the core, and the compressibility of the soft core in the transverse direction is also considered. The novelty of this theory is that it allows for three generalized coordinates in the core (the axial and transverse displacements at the centroid of the core, and the rotation at the centroid of the core) instead of just one (midpoint transverse displacement) commonly adopted in other available theories. The theory was derived so that all core/face displacement continuity conditions are fulfilled. It is proven, by comparison to the elasticity solution, that this approach results in superior accuracy, especially for the cases of stiffer cores, for which cases of the other available sandwich computational models cannot correctly predict the stress fields involved. In this paper, a linear finite element is formulated based on the extended high-order sandwich panel theory. The element equations are outlined, and numerical results for the simply supported case of transverse distributed loading are produced for several typical sandwich configurations. These results are compared with the corresponding ones from the elasticity solution. The comparison among these numerical results shows that, with a relatively small number of elements, the results are very close to the elasticity ones in terms of both the displacements and stress or strains. Thus, the finite element version of the extended high-order sandwich panel theory constitutes a very powerful analytical tool for sandwich panels.