Theory Review for Cylindrical Shells and Parametric Study of Chimneys and Tanks

Since the considerable effort in the development of rigorous shell theories - dating back to the early twentieth century - many approximate shell theories have been developed, mainly on the assumption that the shell is thin. With the development of the numerical formulations and the continuously increasing computing power, a gradual cessation of attempts to find closed-form solutions to rigorous formulations has taken place. This has led to an increasing lack of understanding of the basic and generic knowledge of the shell behaviour, the prevailing parameters and the underlying theories, which is obviously required for the use of numerical programs and to understand and validate the results. This intends to combine the classic shell theories with the contemporary numerical approach. The goal is to derive and employ a consistent and reliable theory of shells of revolution and to present that theory in the context of modern computational mechanics. The author derived an expeditious PC-oriented computer program for that by reshaping the closed-form solutions to the rigorous shell formulations into the well-known direct stiffness approach of the displacement method. The objective was to conduct a generic study of the physically and geometrically linear behaviour of the typical thin shells of revolution, i.e. circular cylindrical, conical and spherical shells, under static loading by evaluating both the closed-form solution to the thin shell equations and the output of the computer program.