This paper presents an improved shell theory for the analysis of shallow shells of composite materials such as pyrolytic graphite, that exhibit certain unusual and complex thermal properties. In the formulation of this theory, the effects of transverse isotropy, transverse shear deformation and thermal expansion through the thickness are taken into account. In the specific case of shallow spherical shell, the governing equations are reduced to two coupled second order ordinary differential equations. The Meissner constant is defined to include a term representative of transverse shear deformation. These two equations are then fused into a single second-order complex differential equation. By means of Langer’s method of asymptotic integration a solution of the homogeneous differential equation is obtained. Edge load solutions are developed for two edge loads (bending moment and shear resultant). Particular solutions are also obtained for various mechanical and thermal loads. Several numerical examples are presented to prove the validity of the assumptions in the present theory and the accuracy and the adequacy of this theory in the prediction of the behavior of shallow shells of composite materials.
On the growth of solutions of second order complex differential equation with meromorphic coefficients
