Analysis of Composite Shell Structures Using Chebyshev Series

In this work, solutions for various boundary-value problems of isotropic and laminated composite shells are proposed in the form of Chebyshev series. To simplify the technique, matrix formulation of the problem based on expanding the shell displacements and their derivatives and products in Chebyshev series is performed. The proposed technique is used to analyze arbitrarily laminated cylindrical, conical and spherical shells in the framework of the classical lamination theory, under different loading and boundary conditions. The technique is further developed to analyze general composite shells of revolution with arbitrary shape by dividing them into conical segments, and applying compatibility conditions between successive segments. The idea of dividing the shell into segments makes it also possible to solve problems of compound shells (composed of different shells connected together), and shells with variable thickness. Finally, the proposed technique is used to solve free vibration problems of isotropic and composite shell structures with different boundary conditions. In all cases, the problem is converted into a simple process of matrix multiplication and inversion.