Theory of Composite Shells

This learning track covers a comprehensive understanding of composite shells, their theory, and applications. It starts with the basic understanding of shell geometry and classification, including the derivation of fundamental forms of surfaces, the theorem of Rodrigues, and Weingarten formulas. The track then delves into the governing equations for shells, explaining the concept of strain energy, Hamilton principle, kinetic energy, and special cases of shells. The learners then explore shell theories and formulations, including membrane and moment shell theories, and their applications in structural engineering. The track further covers the analysis of cylindrical shell structures, including the development of governing equations and the bending analysis of a composite cylindrical shell. The learners also explore the techniques for finite shell solutions, including the Ritz and Galerkin methods, and the extended Kantorovich method. The track then covers the study of shell buckling, including the causes of buckling and the governing equations for buckling in cylindrical shells. Lastly, the track covers the advanced composite shell theory and its applications, including the development of bending solutions and a three-dimensional buckling solution for a cylindrical shell.