Classical and high-order computational models in the analysis of modern sandwich panels

Abstract

The classical and the high-order computational models of unidirectional sandwich panels with incompressible and compressible cores are presented. The significant theoretical and practical differences are discussed and elaborated through some numerical examples of typical sandwich panels. The classical models considered for the incompressible panel consists of two variants of the well-known splitted rigidity approach. The first one, due to Allen and Plantema and many others, assumes that the plane section of the shear substructure takes a specific ‘zigzag’ pattern with no in-plane deformation in the face sheets and a vertical one when the flexural rigidity of the faces is ignored. The second model, due to Frostig, assumes that the plane section of the core in the shear substructure remains vertical and the face sheets are subjected to in-plane deformation as well as flexural ones. They are compared with the accurate incompressible model, denoted as ordinary sandwich panel theory (OSPT) and with the high-order sandwich panel theory (HSAPT) based on a variational approach. In case of a sandwich panel with a compressible core the elastic foundation models based are compared with the high-order one. The governing equations and the appropriate boundary conditions of the classical models have been rederived to clarify the ambiguity involved in the definition of the boundary conditions of the various computational models. The cases of simply supported panel, cantilevered and a two-span panel are used to demonstrate numerically the differences in the overall response of the panel as well as in the near vicinity of the localized loads and supports.