Pseudo element method (PEM) for solving matrix with elementary operation and its application

A pseudo element method (PEM) is presented in this paper for solving the matrix with elementary operation arising from the static analysis of cyclic symmetric structures. Three kinds of pseudo elements are devised to consider the transformed terms in the stiffness matrix during the elementary operation. Thus, the overall stiffness matrix may not be assembled by using the frontal solution technique. This can need relatively small computer memory and relatively short CPU time. The centrifugal displacements and stresses of a ring structure are calculated by introducing the cyclic symmetric conditions. The calculated results show, in comparison with theoretical ones, that the present method and its program are effective and can be conveniently used on a personal computer. At the end of this paper, the centrifugal fillet stresses of left-handed helical gear structures with different rim and web sizes are evaluated.