Algorithms by design: A new normalized time-weighted residual methodology and design of a family of energy-momentum conserving algorithms for non-linear structural dynamics

International Journal for Numerical Methods in Engineering

Volumn 79, Issue 9, 2009, Pages 1094-1146

  Masuri, S U ^a   Hoitink, A ^a   Zhou, X ^a   Tamma, K K ^a  

^a University of Minnesota   (United States)

Author keywords

Computational structural dynamics; Energy momentum conservation; Finite elements; Non linear structural dynamics; Time integration

Indexed keywords

COMPUTATIONAL STRUCTURAL DYNAMICS; ENERGY-MOMENTUM CONSERVATION; FINITE ELEMENTS; NON-LINEAR STRUCTURAL DYNAMICS; TIME INTEGRATION;

ALGORITHMS; DESIGN; DYNAMICAL SYSTEMS; DYNAMICS; MATHEMATICAL OPERATORS; MOMENTUM; STRUCTURAL DYNAMICS; SYSTEM STABILITY;

ENERGY CONSERVATION;

EID: 69249131639     PISSN: 00295981     EISSN: 10970207     Source Type: Journal    
DOI: 10.1002/nme.2592     Document Type: Article

References (23)

1. Zhou X, Tamma KK. Design, analysis, and synthesis of generalized single step single solve and optimal algorithms for structural dynamics. International Journal for Numerical Methods in Engineering 2004; 59:597-668.
2. Zhou X, Tamma KK. Algorithms by design with illustrations to solid and structural mechanics/dynamics. International Journal for Numerical Methods in Engineering 2006; 66:1738-1790.
3. Hoitink A, Masuri S, Zhou X, Tamma KK. Algorithms by design: part I-on the hidden point collocation within LMS methods and implications for nonlinear dynamics applications. International Journal for Computational Methods in Engineering Science and Mechanics 2008; 8:383-407.
4. Masuri S, Hoitink A, Zhou X, Tamma KK. Algorithms by design: part II-a novel normalized time weighted residual methodology and design leading to a family of symplectic-momentum conserving algorithms for nonlinear structural dynamics. International Journal for Computational Methods in Engineering Science and Mechanics 2009; 10:27-56.
5. Masuri S, Hoitink A, Zhou X, Tamma KK. Algorithms by design: part III-a novel normalized time weighted residual methodology and design of optimal symplectic-momentum based controllable numerical dissipative algorithms for nonlinear structural dynamics. International Journal for Computational Methods in Engineering Science and Mechanics 2009; 10:57-90.
6. Simo JC, Tarnow N. Exact energy-momentum conserving algorithms and symplectic schemes for nonlinear dynamics. Computer Methods in Applied Mechanics and Engineering 1992; 100:63-116.
7. Zhou X, Tamma KK. A new unified theory underlying time dependent linear first-order systems: a prelude to algorithms by design. International Journal for Numerical Methods in Engineering 2004; 60:1699-1740.
8. Tamma KK, Namburu RR. Applicability and evaluation of an implicit self-starting unconditionally stable methodology for the dynamics of structures. Computers and Structures 1990; 34:835-842.
9. LaBudde RA, Greenspan D. Energy and momentum conserving methods of arbitrary order for the numerical integration of equations of motion. Numerische Mathematike 1976; 25:323-346.
10. Wood WL, Odour ME. Stability properties of some algorithms for the solution of nonlinear dynamic vibration equations. Communications in Applied Numerical Methods 1988; 4:205-212.
11. Crisfield MA, Galvanetto U. Some unreliable finite element solutions for nonlinear dynamics. Proceedings of the Fifth International Conference on Reliability of Finite Element Methods for Engineering Applications, Amsterdam, The Netherlands, 10-12 May 1995; 346-355.
12. Hughes TJR. Stability, convergence and growth and decay of energy of the average acceleration method in nonlinear structual dynamics. Computers and Structures 1976; 6:313-324.
13. Belytschko T, Schoeberle DF. On the unconditional stability of an implicit algorithm for nonlinear structural dynamics. Journal of Applied Mechanics 1975; 42:865-869.
14. Hughes TJR. A note on the stability of Newmark's algorithm in nonlinear structural dynamics. International Journal for Numerical Methods in Engineering 1977; 11(2):383-386.
15. Simo JC, Tarnow N. The discrete energy-momentum method. Conserving algorithms for nonlinear elastodynamics. Journal of Applied Mathematics and Physics 1992; 43:757-792.
16. Gonzalez O. Exact energy and momentum conserving algorithms for general models in nonlinear elasticity. Computer Methods in Applied Mechanics and Engineering 2000; 190:1763-1783.
17. Hughes TJR, Caughy TK, Liu WK. Finite-element methods for nonlinear elastodynamics which conserve energy. Journal of Applied Mechanics 1978; 45:366-370.
18. Newmark NM. A method of computation for structural dynamics. Journal of American Society of Civil Engineers 1959; 1:67-94.
19. Kuhl D, Ramm E. Constraint energy momentum algorithm and its application to nonlinear dynamics of shell. Computer Methods in Applied Mechanics and Engineering 1996; 136:293-315.
20. Kuhl D, Crisfield MA. Energy-conserving and decaying algorithms in non-linear structural dynamics. International Journal for Numerical Methods in Engineering 1999; 45:569-599.
21. Zhou X, Tamma KK, Sha D. The time dimension: a theory of development/evolution, classification, characterization and design of computational algorithms for transient/dynamic applications. Archives in Computational Mechanics 2000; 7:67-290.
22. Zhou X, Tamma KK, Sha D. A theory of development and design of generalized integration operators for computational structural dynamics. International Journal for Numerical Methods in Engineering 2000; 50: 1619-1664.
23. Finlayson BA. The Method of Weighted Residuals and Variational Principles. Academic Press: New York, 1971.