Thermal Stresses in Spherical Shells

This paper presents an iterative finite-difference technique for the analysis of axisymmetric spherical shells with variable wall thickness. The formulation is based on thin elastic shell theory. One-dimensional finite-difference points are used to discretize the shell into strips along the meridian, and an iterative technique is employed to determine the normal and meridional displacements. The stress resultants and bending stresses are then evaluated. Unlike existing analytical and finite-difference techniques, the proposed method is applicable with ease to any variation in rigidity along the meridian, to general loading conditions, and to steep and shallow shells. Results are presented and compared with those of the finite-element method.