Buckling Modes of Thin Circular Cylindrical Shells Under Fundamental Loads

Abstract

O VER the past 100 years, much research has been directed at circular cylindrical shell buckling. One area of particular interest is in clarifying the reasons for the discrepancy between theoretical and experimental buckling stress of thin isotropic circular cylindrical shells, especially under axial compression. Postbuckling behavior, initial imperfections, or boundary conditions have been used to explain the discrepancy, although the main causes are now considered to be the effects of initial imperfections and their relationship to postbuckling characteristics [1,2]. The effects of boundary conditions, on the other hand, were discussed by Hoff [3], who showed that axial buckling stress calculated for the special boundary conditions is one-half of the classical value. The employed boundary conditions, however, are considered to be unrealistic [4]. Yoshimura [5] attributed postbuckling characteristics under axial compression to the developability of the initial cylindrical surface; that is, the Gauss curvature equals zero. The postbuckling mode presented by Yoshimura is a developable polyhedral surface (Fig. 1a) that is different from the chessboard-type (rectangle-type) mode andwas named the “Yoshimura pattern” byHoff et al. [6]. Key references related to the present problem are found in texts by Yamaki [7] and Singer et al. [8]. In recent years, numerous studies have focused on buckling of composite or laminated cylindrical shells. For example, Riddick and Hyer [9] employed finite element analysis for segmented circular composite cylindrical models under axial compression, ultimately showing calculated postbuckling modes. Here, it is shown that the developability of cylindrical surfaces also leads to buckling mode patterns under torsional load (Fig. 2a) and external lateral pressure (Fig. 2b). Such developability leads to buckling and postbuckling characteristics that are quite different from flat-plate problems. In other words, the developability provides the mechanics of the cylindrical shell buckling process. It is concluded that 1) Buckling and postbuckling modes under axial compression should be the same. 2) The number of waves may change during the postbuckling process. Moreover, the axial buckling modes should be similar to the modes described by Yoshimura [5], being different from the socalled chessboard pattern that has been traditionally been used in previous studies.