Space-Time Discontinuous Galerkin Method for Linear Elastodynamics
Publication: Journal of Aerospace Engineering
Volume 20, Issue 2
Abstract
Among the time-integration methods used in solid mechanics, Newmark family of algorithms (along with Galerkin finite element) has been most popular and has gathered much attention over the years. Recently, the time discontinuous Galerkin method (TDG) and discontinuous Galerkin method (DGM) are being investigated by the researchers due to their advantages in wave propagation problems. In this study, TDG and DGM are combined to have space-time discontinuous Galerkin formulation for the first time for solid mechanics problems. The basic formulations are presented and some examples are studied.
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Acknowledgments
The financial support of the Scientific and Technical Research Council of Turkey to the first writer is gratefully acknowledged.
References
Aksoy, H. G., and Senocak, E. (2005). “Modelling of functionally graded and layered materials with space-time discontinuous Galerkin method.” Proc., 46th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conf., Austin, Tex.
Bauchau, O. A., and Joo, T. (1999). “Computational schemes for nonlinear elastodynamics.” Int. J. Numer. Methods Eng., 45, 693–719.
Baumann, C. E. (1997). “An hp-adaptive discontinuous finite element method for computational fluid dynamics.” Ph.D. thesis, Univ. of Texas at Austin, Tex.
Betsch, P., and Steinmann, P. (2001). “Conservation properties of a time FE method. II: Time-stepping schemes for nonlinear elastodynamics.” Int. J. Numer. Methods Eng., 50, 1931–1955.
Chien, C. C., Yang, C. S., and Tang, J. H. (2003). “Three-dimensional transient elastodynamics analysis by a space and time-disontinuous Galerkin finite element method.” Finite Elem. Anal. Design, 39, 561–580.
Cockburn, B., and Shu, C.-W. (1998). “The local discontinuous-Galerkin method for the time-dependent convection-diffusion systems.” SIAM (Soc. Ind. Appl. Math.) J. Numer. Anal., 35(6), 2440–2463.
Hughes, T. J. R., and Hulbert, G. M. (1988). “Space-time finite element methods for elastodynamics: Formulations and error estimates.” Comput. Methods Appl. Mech. Eng., 66, 339–363.
Kane, C., Marsden, J. E., Ortiz, M., and West, M. (2000). “Variational integrators and the Newmark algorithm for conservative and dissipative mechanical systems.” Int. J. Numer. Methods Eng., 49, 1295–1325.
Lesaint, P., and Raviart, P.-A. (1974). “On a finite element method for solving the neutron transport equation.” Mathematical aspects of finite elements in partial differential equations, C. de Boor, ed., Academic, New York, 89–145.
Lowrie, R. B. (1996). “Compact higher-order numerical methods for hyperbolic conservation laws.” Ph.D. thesis, Univ. of Michigan, Ann Arbor, Mich.
Newmark, N. M. (1959). “A method of computation for structural dynamics.” J. Engrg. Mech. Div., 8, 67–94.
Simo, J. C., Tarnow, N., and Wong, K. K. (1992). “Exact energy-momentum conserving algorithms and symplectic schemes for nonlinear dynamics.” Comput. Methods Appl. Mech. Eng., 100, 63–116.
Zhang, M., and Shu, C.-W. (2003). “An analysis of three different formulations of the discontinuous Galerkin method for diffusion equations.” Math. Models Meth. Appl. Sci., 13(3), 395–413.
Zienkiewicz, O. C., Taylor, R. L., Sherwin, S. J., and Peiro, J. (2003). “On discontinuous Galerkin methods.” Int. J. Numer. Methods Eng., 58, 1119–1148.
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Published In
Journal of Aerospace Engineering
Volume 20 • Issue 2 • April 2007
Pages: 128 - 131
Copyright
© 2007 ASCE.
History
Received: May 21, 2004
Accepted: Apr 28, 2006
Published online: Apr 1, 2007
Published in print: Apr 2007
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