Energy dissipative time finite elements for classical mechanics

Computer Methods in Applied Mechanics and Engineering

Volumn 192, Issue 26-27, 2003, Pages 2925-2947

  Bui, Q V ^a  

^a UNIVERSITY OF LIÈGE   (Belgium)

Author keywords

Dissipative system; Hamilton's equations; Integration scheme; Time continuous Galerkin method; Time finite element

Indexed keywords

ENERGY DISSIPATION; FINITE ELEMENT METHOD; GALERKIN METHODS; HAMILTONIANS;

NUMERICAL DISSIPATION;

CONTINUUM MECHANICS;

FINITE ELEMENT ANALYSIS;

EID: 0037623749     PISSN: 00457825     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0045-7825(03)00310-4     Document Type: Article

References (12)

1. French D.A. Schaeffer J.W. Continuous finite element methods which preserve energy properties for nonlinear problems Appl. Math. Comput. 39 1990 271-295
2. Betsch P. Steinmann P. Inherently energy conserving time finite elements for classical mechanics J. Comput. Phys. 160 2000 88-116
3. Betsch P. Steinmann P. Conservation properties of a time FE method--part II: time-stepping schemes for nonlinear elastodynamics Int. J. Numer. Meth. Engrg. 50 2001 1931-1955
4. Armero F. Romero I. On the formulation of high-frequency dissipative time-stepping algorithms for nonlinear dynamics. Part I: low-order methods for two model problems and nonlinear elastodynamics Comput. Methods Appl. Mech. Engrg. 190 2001 2603-2649
5. Amero F. Romero I. On the formulation of high frequency dissipative time-stepping algorithms for nonlinear dynamics. Part II: second-order methods Comput. Methods Appl. Mech. Engrg. 190 2001 6783-6824
6. Bauchau O.A. Joo T. Computational schemes for non-linear elasto-dynamics Int. J. Numer. Meth. Engrg. 45 1999 693-719
7. Bottasso C.L. Bauchau O.A. Choi J.Y. An energy decaying scheme for nonlinear dynamics of shells Comput. Methods Appl. Mech. Engrg. 191 2002 3099-3121
8. Hansbo P. A note on energy conservation for Hamiltonian systems using continuous time finite elements Commun. Numer. Meth. Engrg. 17 2001 863-869
9. Kane C. Marsden J.E. Ortiz M. West M. Variational integrators and the Newmark algorithm for conservative and dissipative mechanical systems Int. J. Numer. Meth. Engrg. 49 2000 1295-1325
10. Zienkiewicz O.C. Wood W.L. Taylor R.L. An alternative single-step algorithm for dynamic problems Earthquake Engrg. Struct. Dynam. 8 1980 31-40
11. Géradin M. Rixen D. Mechanical Vibrations--Theory and Application to Structural Dynamics 1994 Wiley
12. Bottasso C. Borri M. Trainelli L. Integration of elastic multibody systems by invariant conserving/dissipating algorithms. Part II: numerical schemes and applications Comput. Methods Appl. Mech. Engrg. 190 2001 3701-3733