THIN AND THICK SHELL THEORY CONSISTENT WITH CONTINUUM MECHANICS

In this paper, we develop a thin and thick shell theory consistent with continuum mechanics, taking an asymptotic expansion on the ratio of thickness to radius. A Lagrangian for displacement function is derived, and the first- or second-order expansion corresponds to thin or thick shell, respectively. The form of the Lagrangian is surprisingly simple because its integrand consists of four terms for the thin shell and two terms are added for the thick shell. Important features of the theory, such as the causes of the simple form Lagrangian and the sectional force equilibrium, are discussed.