A novel computational cost-effective approach in elastodynamic analysis with rotationally periodic symmetry

A novel computational cost-effective approach is presented for 2D elastic dynamic analysis by utilizing rotationally periodic symmetry. The proposed algorithm is developed on the platform of TPAA-SBFEM, integrating all its advantages. By recourse of TPAA, an elastic dynamic problem is converted into a series of recursive spatial problems which are solved by SBFEM. The block-circulant SBFEM global stiffness and mass matrices are derived for the structures with or without a common node under a symmetry-adapted reference coordinate system. Notably, these matrices are constructed based on a basic symmetric part, rather than the entire computational domain. Subsequently, a partitioning algorithm is presented to solve the system equation with block-circulant coefficient matrices via a series of small independent subproblems. This leads to significant reductions in both the computational cost associated with matrix construction and the solving of the system equation. In addition, the Woodbury formula is employed to reduce the computational cost in dealing with incomplete rotationally periodic symmetric structures. Three numerical examples are provided to elucidate the features of the proposed approach.