Wave finite element method based on isogeometric analysis for periodic structures

In this paper, an efficient numerical approach is proposed to calculate the band structure of periodic structures. It combines the advantages of isogeometric analysis (IGA) and the wave finite element method (WFEM). By utilizing NURBS basis functions, the new method achieves high-order cross-element continuity, resulting in a more accurate evaluation of the band structure. The high order element exhibits improved stability and faster convergence. It also has small dispersion errors, thereby partially overcoming the limitations imposed by the thumb rule. However, in scenarios involving material sudden change, IGA-WFEM necessitates the insertion of repeated knots to prevent over continuity in the analysis. The aforementioned characteristics of the method are demonstrated through numerical evaluations of one- and two-dimensional periodic structures.