Exact, Hierarchical Solutions for Localized Loadings in Isotropic, Laminated, and Sandwich Shells

Abstract

This paper presents closed form solutions for simply supported cylindrical and spherical shells subjected to uniform localized distributions of transverse pressure and bending moment. These distributions have been expanded in terms of Fourier’s series for which Navier type “exact” solutions have been found for the governing differential equations of the employed shell theories. Shells made of isotropic materials, composites laminates, and sandwich have been analyzed. Carrera’s unified formulation has been adopted in order to implement a large variety of two-dimensional theories. Classical, refined, zigzag, layerwise, and mixed theories are compared in order to evaluate the stress and deformation variables. Conclusions are drawn with respect to the accuracy of the various theories for the considered loadings and layouts. The importance of the refined shell models in order to describe accurately the three-dimensional stress state in the neighborhood of the localized loading application area is outlined.