A method for static analysis of multistage cyclic structure based on group theory and two-stage Guyan reduction

Considering the non-negligible multistage coupling effect of stages in multi-stage cyclic structure, such as bladed disk systems in aircraft turbo engines, a method is established for the static analysis of multistage cyclic structures. A special coordinate system is established based on the structural characteristics of the multistage cyclic structure. In this coordinate system, the sectors of a given disk have the same position; therefore, the stiffness matrices of any sector of the same disk are identical. Then, based on a two-stage Guyan reduction, the internal degrees of freedom (DOFs) of the disks are condensed and the number of DOFs corresponding to the full structure is reduced to that corresponding to the interdisk structures. Furthermore, group theory and the properties of the block circulant matrix are used to significantly reduce the computational cost of the two-stage Guyan reduction. Compared to the analysis of the full finite element model, the proposed method introduces no approximation. The main advantages of the proposed method are its high accuracy, high efficiency, and less demand on computational resources. Numerical examples demonstrate the accuracy and efficiency of the proposed method.