A scaled boundary finite element partitioning based reduced order algorithm for the elastic analysis of cyclically symmetric structures

Abstract

An efficient reduced order algorithm is proposed for the elastic SBFE analysis for 2‐D cyclic symmetric structures with or without a common node. The general stiffness matrices of scaled boundary finite element (SBFE) is proved to be block‐circulant, and can be constructed via the basic region, instead of the whole computing domain. Thus, the expense on eigenvalue analysis required in generating stiffness matrix can be significantly reduced, and the solution scale can be reduced by partitioning the system equation into a series of small independent subproblems. Furthermore, the presented algorithm is combined with the Woodbury formula to reduce the computational cost on the analysis of incomplete cyclically symmetric structures, the original system equation is transformed into the equations with block‐circulant coefficient matrices, which is efficiently solved by partitioning algorithm. Four numerical examples are provided to demonstrate the effectiveness and advantages of the proposed approach.