A new numerical approach for computer simulation of acoustic and elastic waves is suggested. The new technique is very general, and would be of equal value in such diverse applications as: earthquakes; elastic and acoustic wave propagation; crashes; dynamics testing of aerospace vehicles, airplanes, bridges and buildings; and others. The new approach, which resolves the issues listed, includes two main components: a) a new dispersion reduction technique for linear finite elements based on the extension of the modified integration rule method to elastodynamics problems, and b) a new two-stage time-integration technique with the filtering stage.

The suggested dispersion-reduction technique is based on the analytical study of the numerical dispersion of linear finite elements for harmonic plane waves propagating in the 1-D, 2-D and 3-D isotropic elastic media. Based on this study, we have found the special coordinates of integration points for the mass and stiffness matrices that essentially reduce the dispersion error for elastodynamics problems (these coordinates depend on Poisson’s ratio).

The suggested two-stage time-integration technique includes a new two-stage solution strategy with the stage of basic computations and the filtering stage, new first-, second- and high-order accurate time-integration methods for elastodynamics, a new exact analytical a-priori error estimator in time for second- and high-order methods; and a new calibration procedure for the selection of the minimum necessary amount of numerical dissipation for time-integration methods, new criteria for the selection of time-integration methods for elastodynamics. In contrast to existing approaches, the new technique does not require guesswork for the selection of numerical dissipation and does not require interaction between users and computer codes for the suppression of spurious high-frequency oscillations. Different discretization methods in space such as the finite element method, the spectral element method, isogeometric finite elements, and others can be used with the suggested two-stage time-integration approach. The comparative study of these space-discretization methods for elastodynamics is presented.

1-D, 2-D and 3-D numerical examples show that the new approach yields an accurate non-oscillatory solution for impact and wave propagation problems and considerably reduces the number of degrees of freedom and the computation time in comparison with existing methods. The new technique can be easily incorporated into research and commercial finite element codes (including those implemented on parallel computers), significantly improving their computational capabilities. Using the new approach, wave propagation and structural dynamics problems are uniformly solved. The new numerical technique is also applied for the analysis of wave propagation in the Split Hopkinson Pressure Bar (SHPB). A good agreement between the numerical and experimental results for wave propagation in the SHPB is obtained at impact loading.

Host: Misha Shashkov