Guidelines and Recommendations to Construct Theories for Metallic and Composite Plates

Abstract

This work has evaluated the refinement of some classical theories, such as the Kirchhoff and Reissner-Mindlin theories, adding generalized displacement variables (up to fourth-order) to the Taylor-type expansion in the thickness plate direction. Isotropic, orthotropic, and laminated plates have been analyzed, varying the thickness ratio, orthotropic ratio, and stacking sequence of the layout. Higher-order theories have been implemented according to the compact scheme known as the Carrera unified formulation. The results have been restricted to simply-supported orthotropic plates subjected to harmonic distributions of transverse pressure for which closed-form solutions are available. For a given plate problem (isotropic, orthotropic, or laminated), the effectiveness of each employed generalized displacement variable has been established comparing the error obtained accounting for and removing the variable in the plate governing equations. A number of theories have therefore been constructed imposing a given error with respect to the available best results. Guidelines and recommendations that are focused on the proper selection of the displacement variables that have to be retained in refined plate theories are then furnished. It has been found that the terms that have to be used according to a given error vary from problem to problem, but they also vary when the variable that has to be evaluated (displacement, stress components) is changed. Diagrams (errors in terms of geometrical and orthotopic ratios) and graphical schemes have been built to establish the appropriate theories with respect to the data of the problem under consideration.