Two Dimensional Complex Wavenumber Dispersion Analysis using B-Spline Finite Elements Method

Grid dispersion is one of the criteria of validating the finite element method (FEM) in simulating acoustic or elastic wave propagation. The difficulty usually arisen when using this method for simulation of wave propagation problems, roots in the discontinuous field which causes the magnitude and the direction of the wave speed vector, to vary from one element to the adjacent one. To solve this problem and improve the response accuracy, two approaches are usually suggested: changing the integration method and changing shape functions. The Finite Element iso-geometric analysis (IGA) is used in this research. In the IGA, the B-spline or non-uniform rational B-spline (NURBS) functions are used which improve the response accuracy, especially in one-dimensional structural dynamics problems. At the boundary of two adjacent elements, the degree of continuity of the shape functions used in IGA can be higher than zero. In this research, for the first time, a two dimensional grid dispersion analysis has been used for wave propagation in plane strain problems using B-spline FEM is presented. Results indicate that, for the same degree of freedom, the grid dispersion of B-spline FEM is about half of the grid dispersion of the classic FEM.