Extended High Order Theory For Sandwich Panels And Comparison With Elasticity

The linear and the non-linear behavior of a curved sandwich panel with a stiff or compliant core when subjected to a pressure load is presented. First, the Extended High Order Sandwich Panel Theory (EHSPAT), which had been formulated up to now for the beam or plate configuration, is extended to the case of a curved panel. Based on the derivation of the displacement field from the equations of elasticity for a zero in-plane rigidity core assumption, the displacement is suggested to have a logarithmic dependence on the radial coordinate (this was also the assumption in the HSAPT theory). Thus, two cases are considered: a logarithmic functional dependence of the assumed displacement field and a polynomial dependence (just as in the plate formulation). In order to assess the merits of each approach, an Elasticity solution is derived for the special case of a simply-supported panel and sinusoidal distributed external pressure. The Elasticity solution is formulated based on the displacement approach and it is in closed form. It is proven that the logarithmic approach is more accurate. Subsequently, based on the logarithmic displacement field, the variational approach yields the governing differential equations and boundary conditions of the EHSAPT. Finally, a numerical study is conducted for the non-linear response of a curved panel loaded by a distributed pressure at the upper face sheet. The non-linear study reveals that the post-buckling response of a curved sandwich panels is associated with deep or small wrinkling deformations of the upper face sheet in the case of a simply-supported panel or a general non-linear in the case of pinned supports.