An extension of Karman-Donnell's theory for non-shallow, long cylindrical shells undergoing large deflection

Conventionally cylindrical shells are often treated as shallow shells whose governing equation, according to Karman-Donnell's theory, can be approximated by those of thin plates. In this paper Karman-Donnell's theory for shallow shells is extended for long cylindrical shells undergoing large, nonlinear flexural deflection. The kinematic relations between the changes of curvature and the displacement are derived and the governing equations are established by considering the influence of the initial curvature of the cylindrical shells. In particular, the extended Karman-Donnell's theory is applied for the failure analysis of infinitely cylindrical shell under lateral pressure. A regional collapse mode is identified to occur in the shell with a longitudinal span proportional to (radius³/thickness)^(1/2) and a transverse profile of dog bone shape. It is found that the buckling pressure of the shell is in proportion to (thickness/radius)³ and converges to the classic solution given by Timoshenko and Gere (1961). A comparison to the previous works indicates that ignoring the effect of the initial curvature will result in an overestimate of the buckling pressure for 33%. It shows that the initial curvature of long cylindrical shells has significant influence on the load carrying capacity and the extended Karman-Donnell's equations give very accurate predictions.