Elastic Wave Propagation Analysis Using the Space-Time Discontinuous Galerkin Quadrature Element Method
Publication: Journal of Engineering Mechanics
Volume 150, Issue 10
Abstract
Wave propagation in elastic solids is analyzed by a space-time discontinuous Galerkin quadrature element method. First, the space-time quadrature element is conveniently formulated based on the space-time discontinuous Galerkin formulation. This method treats both the spatial and temporal domains in a unified manner, enabling it to handle not only structured space-time meshes but also unstructured ones. It effectively captures discontinuities or sharp gradients in the solution. To transform the formulation into a system of algebraic equations, the Gauss-Lobatto quadrature rule and the differential quadrature analog are utilized. High-order elements are constructed simply by increasing the order of integration and differentiation without the laborious construction of shape functions. Then, dispersion analysis is conducted for one- and two-dimensional elements. The analysis reveals that as the Courant number decreases, the total dispersion error monotonically converges to the spatial dispersion error, which can be reduced by increasing the element order. Additionally, high-order elements nearly eliminate numerical anisotropy in different directions. Finally, several numerical examples of elastic wave propagation validate the method’s effectiveness and high accuracy.
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Data Availability Statement
All data, models, or code that support the finding of this study are available from the corresponding author upon reasonable request.
Acknowledgments
The last numerical example was performed on TianHe-1A at the National Supercomputer Center in Tianjin, China.
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Published In
Journal of Engineering Mechanics
Volume 150 • Issue 10 • October 2024
Copyright
© 2024 American Society of Civil Engineers.
History
Received: Dec 29, 2023
Accepted: May 10, 2024
Published online: Jul 23, 2024
Published in print: Oct 1, 2024
Discussion open until: Dec 23, 2024
ASCE Technical Topics:
- Aerospace engineering
- Analysis (by type)
- Continuum mechanics
- Discontinuities
- Dynamics (solid mechanics)
- Elastic analysis
- Engineering fundamentals
- Engineering mechanics
- Errors (statistics)
- Mathematical functions
- Mathematics
- Methodology (by type)
- Numerical methods
- Solid mechanics
- Space colonies
- Space structures
- Statistics
- Structural analysis
- Structural engineering
- Two-dimensional analysis
- Wave propagation
- Waves (mechanics)
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