Higher Order Shear Deformation Plate Theory

Abstract

Several plate theories have been developed to describe the static and dynamic behaviour of plates. This thesis is predominantly a study of plate theories including shear effects, with emphasis on higher order shear deformation theories. The plate theories of Reddy and Shi are specifically analysed. An effort towards the development of a unified higher order shear deformation plate theory is presented in this thesis.

The buckling behaviour of some generic higher order shear plate models is investigated in a unified framework. The governing equations of the buckling problem are obtained from a variational approach, leading to generic partial differential equations and associated boundary conditions. Buckling problems are analytically solved using the Navier method on isotropic simply supported plates under uniform in-plane loads. Buckling load relationships between classical plate theory and the plate theories including shear effects are also investigated. The accuracy of the unified shear deformation theory is demonstrated through these buckling results.

The numerical results of the buckling problems, indicate that the theories of Reddy and Shi yield exactly the same buckling loads for the problems in question, whereas the buckling loads estimated from some other higher order theories vary slightly. Due to the simple nature of the solved buckling problems, in terms of geometrical and material properties, all the higher order theories yield almost the same buckling loads as the first order shear deformation theory. This coincides with the fact that higher order plate theories have their advantages when being used for laminated composite plates.

It is the author's belief that the unified higher order shear deformation plate theory presented in this thesis, can contribute to gathering many of the higher order theories presented in the literature in a common framework.