Asymptotic formulae for correcting finite element predicted natural frequencies of gravity and embankment dams

Soil Dynamics and Earthquake Engineering

Volumn 15, Issue 3, 1996, Pages 161-169

  Zhao, Chongbin ^a   Steven, G P ^a  

^a NONE

Author keywords

Asymptotic solution; Dams; Natural frequency

Indexed keywords

ASYMPTOTIC SOLUTION; CORRECTION FORMULA; DAM; FINITE ELEMENT METHOD; SEISMIC DESIGN;

ASYMPTOTIC FORMULA; DISCRETIZATION ERROR; SEISMIC DESIGN; SEISMIC RESPONSE;

APPROXIMATION THEORY; BOUNDARY ELEMENT METHOD; DYNAMIC RESPONSE; EMBANKMENT DAMS; FINITE ELEMENT METHOD; GEOMETRY; GRAVITY DAMS; MATHEMATICAL MODELS; SEISMOLOGY; STRUCTURAL DESIGN;

NATURAL FREQUENCIES;

EID: 0043039521     PISSN: 02677261     EISSN: None     Source Type: Journal    
DOI: 10.1016/0267-7261(95)00043-7     Document Type: Article

References (16)

1. Babuska, I. and Rheinboldt, W. C. Error estimates for adaptive finite element computation. SIAM J. Numer. Anal., 1978, 15, 736-754.
2. Kelly, D. W. The self-equilibration of residuals and complementary a-posteriori error estimates in the finite element method. Int. J. Num. Meth. Engng, 1984, 20, 1491-1506.
3. Kelly, D. W., Gago, J. P. De S. R. & Zienkiewicz, O. C. A-posteriori error analysis and adaptive processes in the finite element method: Part 1: Error analysis. Int. J. Num. Meth. Engng, 1983, 19, 1593-1619.
4. Oden, J. T., Demkowicz, L., Rachowicz, W. & Westermann, T. A. Toward a universal h-p adaptive finite element strategy, Part 2: A-posteriori error estimation. Computer Meth. Appl. Mech. Engng, 1989, 77, 113-180.
5. Rachowicz, W., Oden, J. T. & Demkowicz, L. Toward a universal h-p adaptive finite element strategy, Part 3: Design of h-p meshes. Computer Meth. Appl. Mech. Engng, 1989, 77, 181-212.
6. Zienkiewicz, O. C. & Zhu, J. Z. A simple error estimator and adaptive procedure for practical engineering analysis. Int. J. Num. Meth. Engng, 1987, 24, 337-357.
7. Zienkiewicz, O. C. & Zhu, J. Z. The superconvergent patch recovery and a-posteriori error estimates, Part 2: Error estimates and adaptivity. Int. J. Num. Meth. Engng, 1992, 33, 1365-1382.
8. Zhao, C. & Steven, G. P. Analytical solutions of mass transport problems for error estimation of finite/infinite element methods. Commun. Num. Meth. Engng, 1995, 11, 13-23.
9. Cook, R. D. & Avrashi, J. Error estimation and adaptive meshing for vibration problems. Computers and Structures, 1992, 44, 619-626.
10. Xie, Y. M. & Steven, G. P. Explicit formulas for correcting finite-element predictions of natural frequencies. Commun. Num. Meth. Engng, 1993, 9, 671-680.
11. Valliappan, S. & Zhao, C. Dynamic response of concrete gravity dams including dam-water-foundation interaction. Int. J. Num. Analy. Meth. Geomech., 1992, 16, 79-99.
12. Zhao, C. Effects of reservoir bottom sediments on hydrodynamic pressure of gravity dams. Computers and Structures, 1994, 52, 297-307.
13. Zhao, C., Valliappan, S. & Tabatabaie, J. Effect of impervious members and reservoir bottom sediment on dynamic response of embankment dams. Soil Dyn. Earthq. Engng, 1993, 12, 199-288.
14. Zhao, C. & Steven, G. P. A-posteriori error estimators/correctors for natural frequencies of membrane vibration problems. FEARC-9404, Finite Element Analysis Research Centre, University of Sydney, July, 1994.
15. Zhao, C. & Steven, G. P. A-posteriori error estimators/correctors for natural frequencies of thin plate vibration problems. FEARC-9405, Finite Element Analysis Research Centre, University of Sydney, August, 1994.
16. Hurty, W. L. & Rubinstein, M. F. Dynamics of Structures. Prentice-Hall, Englewood Cliffs, N. J., 1964.