Extension and reduction of Donnell-Vlasov shell theory to hybrid anisotropic materials

The laminated circular cylindrical shells are complicated to analyze and more complicated when anisotropic materials are used with different thickness and different material properties. Also computing the critical stresses under various boundary and loading conditions is exceptionally sensitive and therefore reasonable simplification of the governing equation is in demand for practical design purpose. This article first formulated a shell theory for hybrid anisotropic materials by use of asymptotic integration method, the results are same as classical Donnell-Vlasov theory of single layer isotropic material, then a simplified governing equation was developed by means of adopting a different length scale. The new simplified version can be very useful when multiple materials and thicknesses are designed for practical purpose. Comparison of two different shell bending theories is discussed. Also presented are proper choices of the governing equations for different loading conditions. The theories are extremely useful for the analysis and design of advanced space vehicles and pressure vessels featured cylindrical shells with laminated walls of various materials and thicknesses.