A review of temporal and spatial dispersions of linear and quadratic finite elements in linear elastic wave propagation problems (Q6630960)

The paper deals with the investigation of dispersion effects when using the finite element method (FEM) to model wave propagation in solid mechanics. The effects of spatial and temporal dispersions of the finite element method are treated. 1D and 2D linear and quadratic finite elements and their suitability are analysed for use with implicit and explicit integration methods. The findings are listed below:\N\N\begin{itemize}\N\item With respect to the speed of wave propagation of an ideal continuum, the speed of wave propagation in a finite element model is overestimated when the consistent mass matrix formulation is used. It is underestimated with the diagonal mass matrix formulation.\N\item In 2D and 3D spaces, discretization-induced anisotropy is observed.\N\item The high-frequency components of propagating waves are filtered out.\N\item The temporal discretization errors of the central difference method and the spatial discretization errors of the diagonal mass matrix formulation produce errors of opposite signs, which have a tendency to cancel each other out.\N\item Dispersion analysis of higher-order elements for optical modes tends to reveal unrealistic wave behaviour.\N\item For the temporal-spatial dispersion analysis of plane bilinear and biquadratic elements in explicit time integration, uniform finite element meshes are suggested and time steps are recommended.\N\end{itemize}