| Abstract: | By considering the characteristics of deformation of rotationally periodic structures subjected to rotationally periodic loads, the periodic structure is divided into several identical substructures in this paper. If the structure is really periodic but not axisymmetric, the number of the substructures can be defined accordingly. If the structure is axisymmetric (special in the case of the periodic), the structure can be divided into any number of substructures. It means, in this case, the number of substructures is independent of the number of buckling waves. The degrees of freedom (DOFs) of joint nodes between the neighbouring substructures are classified as master and slave ones. The stress and strain conditions of the whole structure are obtained by solving the elastic static equations for only one substructure by introducing the displacement constraints between master and slave DOFs. The complex constraint method is used to get the bifurcation buckling load and mode for the whole rotationally periodic structure by solving the eigenvalue problem for only one substructure without introducing any additional approximation. Finite element (FE) formulation of shell element of relative degrees of freedom (SERDF) in the buckling analysis is then derived. Different measures of tackling internal degrees of freedom for different kinds of buckling problems and different stages of numerical analysis are presented. Some numerical examples are given to illustrate the high efficiency and validity of this method. Copyright © 2001 John Wiley & Sons, Ltd. |
