A <scp>TPAA</scp>‐<scp>SBFE</scp> Based Partitioning Algorithm for Structural Viscoelastic Dynamic Analysis With Cyclic Symmetry

ABSTRACT An innovative and efficient reduced order algorithm is proposed for the dynamic analysis of 2‐D and 3‐D viscoelastic structures featuring cyclic symmetry, which is applicable to complete cyclically symmetric structures with or without common nodes, as well as incomplete cyclically symmetric structures. The proposed algorithm is developed on a recursive platform based on TPAA‐SBFEM and inherits all the advantages of TPAA‐SBFEM. For complete cyclically symmetric structures with or without common nodes, the global stiffness and mass matrices are proved to be block‐circulant and can be generated via a cyclically symmetric part instead of the whole domain. And then a recursive partitioning algorithm is rendered, such that the solution scale and computational cost can be efficiently reduced via solving a series of independent problems with small scales. For incomplete cyclically symmetric structures, the complete cyclic symmetry and Woodbury formula are utilized to reduce computational expense. Four numerical examples are provided to elucidate the effectiveness and efficiency of the proposed approach with satisfactory results.