Semi-Membrane and Effective Length Theory of Hybrid Anisotropic Materials

Among different shell theories, semi-membrane shell theory of isotropic materials is known to be developed nearly a century by Vlasov and it has been efficiently utilized to design and analysis. The aerospace vehicle structures and rocket fuel storage tanks designed efficiently however not much for composite materials, while most of recent structural materials are of the combination of anisotropic materials. This paper developed the theory for multiple combination of composite materials by means of asymptotic integration method starting from a three dimensional elastic element. The semi-membrane cylindrical shell theories are classified as that of very long effective length scale and we adopted here the longest possible longitudinal and short circumferential length scales, respectively, for the formulation. The edge effects due to the prescribed boundary condition penetrate differently depending on material orientation of each layer but all within the limit of length scale (ah) 1/2 where Donnell-Vlasov bending theory is valid. Demonstrated that beyond the limit of edge effective zone, membrane or pseudo-membrane state dominates, it is traditionally named semi-membrane state. Governing equations of semi-membrane theory of cylindrical shell are formulated and the physical interpretation of the theory is described. The theory is very useful to analyze and design long cylindrical shells such as rocket fuel storage tanks, open top oil stage tanks and chimney structures.