Stresses in shallow spherical shells of composite materials subjected to localized loads.

TLDR: In this paper, an accurate shell theory is employed including effects of circular orthotropy and transverse shear deformation, and the governing equations are reduced to a single, second order complex differential equation.

Abstract: : Methods of analysis are developed to provide the stresses (both bending and membrane) and deformations in specially orthotropic shallow and nonshallow spherical shells of revolution subjected to localized loads at the apex. An accurate shell theory is employed including effects of circular orthotropy and transverse shear deformation. The governing equations are reduced to a single, second order complex differential equation. Solutions are obrained in terms of modified Bessel functions of non-integer order and complex argument. These functions are transformed into a set of infinite series, and upon proper non- dimensionalization, these series are shown to be uniformly and very rapidly convergent. Expressions are obtained for bending, membrane and shear stresses as well as lateral and inplane deflections everywhere in the shell. Comparisons and design curves are obtained for large variations in orthotropy and matrix shear properties which cover almost all known composite materials. Various boundary conditions, degrees of shallowness, and loading conditions are also systematically explored and reported. (Author, modified-PL)