U.S. Department of Energy Office of Scientific and Technical Information
A simple, stable, and accurate linear tetrahedral finite element for transient, nearly, and fully incompressible solid dynamics: A dynamic variational multiscale approach [A simple, stable, and accurate tetrahedral finite element for transient, nearly incompressible, linear and nonlinear elasticity: A dynamic variational multiscale approach]
Journal Article·· International Journal for Numerical Methods in Engineering
Here, we propose a new approach for the stabilization of linear tetrahedral finite elements in the case of nearly incompressible transient solid dynamics computations. Our method is based on a mixed formulation, in which the momentum equation is complemented by a rate equation for the evolution of the pressure field, approximated with piece-wise linear, continuous finite element functions. The pressure equation is stabilized to prevent spurious pressure oscillations in computations. Incidentally, it is also shown that many stabilized methods previously developed for the static case do not generalize easily to transient dynamics. Extensive tests in the context of linear and nonlinear elasticity are used to corroborate the claim that the proposed method is robust, stable, and accurate.
Scovazzi, Guglielmo, et al. "A simple, stable, and accurate linear tetrahedral finite element for transient, nearly, and fully incompressible solid dynamics: A dynamic variational multiscale approach [A simple, stable, and accurate tetrahedral finite element for transient, nearly incompressible, linear and nonlinear elasticity: A dynamic variational multiscale approach]." International Journal for Numerical Methods in Engineering, vol. 106, no. 10, Nov. 2015. https://doi.org/10.1002/nme.5138
Scovazzi, Guglielmo, Carnes, Brian, Zeng, Xianyi, & Rossi, Simone (2015). A simple, stable, and accurate linear tetrahedral finite element for transient, nearly, and fully incompressible solid dynamics: A dynamic variational multiscale approach [A simple, stable, and accurate tetrahedral finite element for transient, nearly incompressible, linear and nonlinear elasticity: A dynamic variational multiscale approach]. International Journal for Numerical Methods in Engineering, 106(10). https://doi.org/10.1002/nme.5138
Scovazzi, Guglielmo, Carnes, Brian, Zeng, Xianyi, et al., "A simple, stable, and accurate linear tetrahedral finite element for transient, nearly, and fully incompressible solid dynamics: A dynamic variational multiscale approach [A simple, stable, and accurate tetrahedral finite element for transient, nearly incompressible, linear and nonlinear elasticity: A dynamic variational multiscale approach]," International Journal for Numerical Methods in Engineering 106, no. 10 (2015), https://doi.org/10.1002/nme.5138
@article{osti_1341405,
author = {Scovazzi, Guglielmo and Carnes, Brian and Zeng, Xianyi and Rossi, Simone},
title = {A simple, stable, and accurate linear tetrahedral finite element for transient, nearly, and fully incompressible solid dynamics: A dynamic variational multiscale approach [A simple, stable, and accurate tetrahedral finite element for transient, nearly incompressible, linear and nonlinear elasticity: A dynamic variational multiscale approach]},
annote = {Here, we propose a new approach for the stabilization of linear tetrahedral finite elements in the case of nearly incompressible transient solid dynamics computations. Our method is based on a mixed formulation, in which the momentum equation is complemented by a rate equation for the evolution of the pressure field, approximated with piece-wise linear, continuous finite element functions. The pressure equation is stabilized to prevent spurious pressure oscillations in computations. Incidentally, it is also shown that many stabilized methods previously developed for the static case do not generalize easily to transient dynamics. Extensive tests in the context of linear and nonlinear elasticity are used to corroborate the claim that the proposed method is robust, stable, and accurate.},
doi = {10.1002/nme.5138},
url = {https://www.osti.gov/biblio/1341405},
journal = {International Journal for Numerical Methods in Engineering},
issn = {ISSN 0029-5981},
number = {10},
volume = {106},
place = {United States},
publisher = {Wiley},
year = {2015},
month = {11}}
Sandia National Laboratories (SNL-NM), Albuquerque, NM (United States)
Sponsoring Organization:
USDOE National Nuclear Security Administration (NNSA)
Grant/Contract Number:
AC04-94AL85000
OSTI ID:
1341405
Report Number(s):
SAND--2016-12567J; 649881
Journal Information:
International Journal for Numerical Methods in Engineering, Journal Name: International Journal for Numerical Methods in Engineering Journal Issue: 10 Vol. 106; ISSN 0029-5981