Accurate 3-D finite element simulation of elastic wave propagation with the combination of explicit and implicit time-integration methods

• Published in: Wave motion Vol. 48; no. 7; pp. 625 - 633
• Main Authors: Idesman, A.V., Schmidt, M., Foley, J.R.
• Format: Journal Article
• Language: English
• Published: Kidlington Elsevier B.V 01.11.2011; Elsevier
• Subjects: Dissipation; Elastic waves; Exact sciences and technology; Filtering; Filtration; Finite element method; Finite elements; Fundamental areas of phenomenology (including applications); Mathematical models; Oscillations; Physics; Solid mechanics; Spurious oscillations; Structural and continuum mechanics; Three dimensional; Vibration, mechanical wave, dynamic stability (aeroelasticity, vibration control...); Wave propagation; Finite elements; Elastic waves; Spurious oscillations; Viscosity; Refinement method; Continuous time; Wave interaction; Calibration; Elastic wave; Automatic mesh generation; Modeling; Adaptive method; Finite element method; Filter; Galerkin method; Elastodynamics; High frequency; Time integration; Mesh generation; Mechanical shock; Finite difference method
• ISSN: 0165-2125; 1878-433X
• DOI: 10.1016/j.wavemoti.2011.04.017

One of the big issues in finite element solutions of wave propagation problems is the presence of spurious high-frequency oscillations that may lead to divergent results at mesh refinement. The paper deals with the extension of the new two-stage time-integration technique developed in our previous papers to the solution of wave propagation problems with explicit time-integration methods.The explicit central difference method is used for accurate time-integration of the semi-discrete system of elastodynamics at the stage of basic computations and allows spurious high-frequency oscillations. To filter these oscillations, pre- or/and post-processing (the filtering stage) is applied using a few time increments of the implicit time-continuous Galerkin method with large numerical dissipation.A special calibration procedure is used for the selection of the minimum necessary amount of numerical dissipation (in terms of a time increment) at the filtering stage. In contrast to existing approaches that use a time-integration method with the same dissipation (or artificial viscosity) for all time increments, the new technique yields accurate and non-oscillatory results for wave propagation problems without interaction between user and computer code. The solutions of 3-D wave propagation and impact problems show the effectiveness of the new approach. ► The extension of the two-stage time-integration approach for elastodynamics to the use of explicit time-integration methods. ► The calibration of the amount of numerical dissipation for filtering spurious oscillations for the lumped mass matrix. ► In contrast to existing finite element techniques, the suggested technique accurately solves wave propagation problems. ► Accurate finite element solutions of several 3-D wave propagation and impact problems.