A hybrid finite element method to compute the free vibration frequencies of a clamped plate

Claudio Canuto

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (1981)

  • Volume: 15, Issue: 2, page 101-118
  • ISSN: 0764-583X

How to cite

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Canuto, Claudio. "A hybrid finite element method to compute the free vibration frequencies of a clamped plate." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 15.2 (1981): 101-118. <http://eudml.org/doc/193371>.

@article{Canuto1981,
author = {Canuto, Claudio},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {spectral problem; compact self-adjoint operator; complementary energy principle; saddle-point problem; duality theory; Lagrange multipliers; stress hybrid finite element; convergence; error estimates},
language = {eng},
number = {2},
pages = {101-118},
publisher = {Dunod},
title = {A hybrid finite element method to compute the free vibration frequencies of a clamped plate},
url = {http://eudml.org/doc/193371},
volume = {15},
year = {1981},
}

TY - JOUR
AU - Canuto, Claudio
TI - A hybrid finite element method to compute the free vibration frequencies of a clamped plate
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 1981
PB - Dunod
VL - 15
IS - 2
SP - 101
EP - 118
LA - eng
KW - spectral problem; compact self-adjoint operator; complementary energy principle; saddle-point problem; duality theory; Lagrange multipliers; stress hybrid finite element; convergence; error estimates
UR - http://eudml.org/doc/193371
ER -

References

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  2. 2 K. BRANDT, Calculation of vibration frequencies by a hybrid element method based on a generalized complementary energy principle, Int. J num. Meth. Engng., v. 12, 1977, pp. 231-246. Zbl0346.73054
  3. 3. F. BREZZI, On the existence, uniqueness and approximation of saddle-point problems arising from Lagrangian multipliers, R.A.I.R.O , R-2, 1974, pp 129-151. Zbl0338.90047MR365287
  4. 4 F. BREZZI, Sur la méthode des éléments finis hybrides pour le problème biharmonique, Num. Math. v 24, 1975, pp. 103-131. Zbl0316.65029MR391538
  5. 5. F BREZZI and L. D. MARINI, On the numerical solution of plate bending problems by hybrid methods, R.A.I.R.O., R-3, 1975, pp. 5-50. Zbl0322.73048
  6. 6 C CANUTO, Eigenvalue approximations by mixed methods, R.A.I.R.O. Anal Num., v. 12, 1978, pp. 27-50 Zbl0434.65032MR488712
  7. 7. C. CANUTO, A finite element to interpolate symmetric tensors with divergence in L 2 (To appear on Calcolo). Zbl0508.65051
  8. 8. P G CIARLET, The finite element method for elliptic problems, North-Holland, Amsterdam-New York-Oxford, 1978. Zbl0383.65058MR520174
  9. 9. G. FICHERA, Numerical and Quantitative Analysis, Pitman, London-San Francisco-Melbourne, 1978. Zbl0384.65043MR519677
  10. 10. P. GRISVARD, Singularité des solutions du problème de Stokes dans un polygone (To appear) 
  11. 11 W. G. KOLATA, Eigenvalue approximation by the finite element method : the method of Lagrange multipliers (To appear) Zbl0448.65067MR514810
  12. 12 V. A. KONDRAT'EV, Boundary problems for elliptic equations in domains with conical or angular points, Trans Moscow Math Soc., v 16, 1976, pp 227-313. Zbl0194.13405
  13. 13. B. MERCIER and J. RAPPAZ, Eigenvalue approximation via nonconforming and hybrid finite elements methods, Rapport Interne du Centre de Mathématiques Appliquées de l'École Polytechnique, n° 33, 1978 
  14. 14. B. MERCIER, J. OSBORN, J. RAPPAZ and P.-A. RAVIART, Eigenvalue approximation by mixed and hybrid methods (To appear). Zbl0472.65080MR606505
  15. 15. T. H. H. PIANG and P. TONG, The basis of finite element methods for solid continua, Int. J. num. Meth. Engng., v. 1, 1969, pp. 3-28. Zbl0252.73052
  16. 16. J. RAPPAZ, Approximation of the spectrum of a non-compact operator given by the magnetohydrodynamic stability of a plasma, Num. Math., v. 28, 1977, pp. 15-24. Zbl0341.65044MR474800
  17. 17. J. RAPPAZ, Spectral approximation by finite elements of a problem of MHD-stability of a plasma, The Mathematics of Finite Elements and Applications III, MAFELAP 1978 (Ed. J. R. Whiteman), Academic Press, London-New York-San Francisco, 1979, pp. 311-318. Zbl0442.76087MR559307
  18. 18. G. STRANG and G. FIX, An Analysis of the Finite Element Method, Prentice Hall, Englewood Cliffs, N.J., 1973. Zbl0356.65096MR443377
  19. 19. B. TABARROK, A variational principle for the dynamic analysis of continua by hybrid finite element method, Int. J. Solids Struct., v. 7, 1971, pp. 251-268. Zbl0228.73053
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  21. 21. P. G. GILARDI (To appear). 

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