Elastic buckling of multilayered anisotropic conical shells

On the basis of 3D elasticity, asymptotic solutions for buckling analysis of multilayered anisotropic conical shells under axial compression are presented. By means of proper nondimensionalization, asymptotic expansion, and successive integration, the classical shell theory is derived as a first-order approximation to the 3D theory. Because the governing equations for various orders consist of partial differential equations with variable coefficients, the use of analytical techniques is restricted. The method of differential quadrature is adopted in the present study. The modifications of the buckling loads and associated buckling modes can be determined in a consistent and hierarchic manner by considering the solvability and normalization conditions for various orders. The critical loads of cross-ply conical shells with simply supported-simply supported boundary conditions are studied to demonstrate the performance of the present asymptotic theory.