Spectral analysis of a high-order Hermitian algorithm for structural dynamics

Applied Mathematical Modelling

Volumn 35, Issue 2, 2011, Pages 965-971

  Laier, José Elias ^a  

^a UNIVERSITY OF SÃO PAULO   (Brazil)

Author keywords

High order Hermitian finite difference operators; Spectral analysis; Step by step algorithm; Structural dynamic

Indexed keywords

COMPUTATIONAL EFFORT; DIRECT INTEGRATION; FINITE DIFFERENCE OPERATORS; FOURTH-ORDER; GLOBAL ERRORS; HERMITIANS; HIGH-ORDER; HIGHER ORDER; LOCAL TRUNCATION ERRORS; NONLINEAR STRUCTURAL DYNAMICS; NUMERICAL APPLICATIONS; NUMERICAL DAMPING; SECOND ORDERS; SPECTRAL ANALYSIS; STEP-BY-STEP; STEP-BY-STEP ALGORITHM; TRUNCATION ERRORS; UNCONDITIONALLY STABLE;

ALGORITHMS; SPECTRUM ANALYSIS; SPECTRUM ANALYZERS; STRUCTURAL ANALYSIS; STRUCTURAL DYNAMICS;

MATHEMATICAL OPERATORS;

EID: 77956185427     PISSN: 0307904X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.apm.2010.07.056     Document Type: Article

References (16)

1. Laier J.E. Hermitian one-step numerical integration algorithm for structural dynamic equations. Adv. Eng. Software 2000, 31:203-206.
2. Collatz L. The Numerical Treatment of Differential Equations 1966, Springer-Verlag. second ed.
3. Laier J.E. Asymptotic annihilation hermitian algorithm for integration in time. Comput. Struct. 2000, 76:683-689.
4. Trujillo D.M. The direct numerical integration of linear matrix differential equations using Padè approximations. Int. J. Numer. Methods Eng. 1975, 9:259-270.
5. Fung T.C. Third-order time-step integration methods with controllable numerical dissipation. Commun. Numer. Methods Eng. 1997, 13:307-315.
6. Hulbert G.M. Time finite element methods for structural dynamics. Int. J. Numer. Methods Eng. 1992, 33:307-331.
7. Wiberg N.E., Li X. Adaptative finite element procedure for linear and non-linear dynamics. Int J. Numer. Methods Eng. 1999, 46:1781-1802.
8. Kujawski J., Gallagher R.H. A generalised least-squares family of algorithms for transient dynamic analysis. Earthquake Eng. Struct. Dynam. 1989, 18:539-550.
9. Carey G.F. Computational Grids: Generation, Adaptation, and Solution Strategies 1997, Taylor & Francis.
10. Spotz W., Carey G.F. A high-order compact formulation for 3D Poisson equation. Numer. Methods PDE's 1966, 12:235-243.
11. Ruge P. Restricted Padè scheme in computational structural dynamics. Comput. Struct. 2001, 79:1913-1921.
12. Laier J.E. Hermitian lumped mass matrix formulation for flexural wave propagation. Commun. Appl. Numer. Methods 1998, 14:43-49.
13. Hilbert H.M., Hughes T.J.R. Collocation, dissipation and overshoot for time integration schemes in structural dynamics. Earthquake Eng. Struct. Dynam. 1978, 6:99-117.
14. Bathe K.J., Wilson E.L. Stability and accuracy analysis of direct integration methods. Earthquake Eng. Struct. Dynam. 1973, 1:283-291.
15. Brusa L., Nigro L. A one-step method for direct integration of structural dynamic equations. Int. J. Numer. Methods Eng. 1980, 15:685-699.
16. Argyris J., Mlejek H.P. Dynamics of Structures in Texts on Computational Mechanics 1991, North-Holland, Amsterdam.