The analysis of sandwich beams and plates
This thesis is concerned with the linear and non-linear bending analysis of sandwich beams and plates with flexible cores and thick or profiled metal faces. the project commences with a review of previous work in structural aspects of sandwich construction. It reveals that analytical solutions have been obtained for a small number of simply supported and continuous sandwich beams with equal spans subjected to simple cases of loading. Due to the increasing popularity of such panels in the building industry, there have been demands for more general solutions. Therefore, the purpose of the first part of the present investigation is to find explicit solutions for both single and multispan sandwich beams subject to various cases of loading. The analysis of sandwich beams subject to combined uniform transverse load and compressive or tensile axial load is also presented. Furthermore, simple expressions are presented for the analysis of sandwich beams continuous over supports subject to settlement. This is followed by the derivation of more general solutions for sandwich beams with arbitrary loading and boundary conditions using the finite element technique. The method is exact because the solutions of the governing differential equations are used to derive the element stiffness matrices for sandwich beams subject to combined bending and axial loads. Attention is first confined to the general case of panels with profiled faces, followed by the analysis of panels with plane faces as a special case. Some tests for sandwich panels subject to axial compressive load are presented and the results compared with the theoretical values. In the second part of the investigation, the analysis of sandwich plates is considered. The general equations presented by Alien were first redeveloped in a different way. Then, the buckling and bending analysis of orthotropic rectangular sandwich panels with all edges simply supported and subject to uniform lateral and edge loads is presented. This analysis was based on a series solution of the governing differential equations. Expressions for determining the deflection, stress resultants and critical buckling load of such panels are also presented. This is followed by the linear and geometrically non-linear finite element analysis of multi-layer plates. The formulations were incorporated in existing, modified and new elements for the analysis of three and five layer plates. Finally, the thermal and flexural analysis of sandwich panels is carried out using a three dimensional composite element. Several illustrative examples are also presented to demonstrate the accuracy and versatility of the various formulations.