Dispersive properties of the Natural Element Method

The Natural Element Method (NEM) is a meshfree numerical method for the sol ution of partial differential equations. In the natural element method, nat ural neighbor coordinates, which are based on the Voronoi tesselation of a set of nodes, are used to construct the interpolant. The performance of NEM in two-dimensional linear elastodynamics is investigated. A standard Galer kin formulation is used to obtain the weak form and a central-difference ti me integration scheme is chosen for time history analyses. Two different ap plications are considered: vibration of a cantilever beam and dispersion an alysis of the wave equations. The NEM results are compared to finite elemen t and analytical solutions. Excellent dispersive properties of NEM are obse rved and good agreement with analytical solutions is obtained.