Quelques methodes d'elements finis pour le probleme d'une plaque encastree

  • P. G. Ciarlet
Elements Finis
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10)

Keywords

Finite Element Method Patch Test Hermite Interpolation Nous Allons Finite Element Method Technical 
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References

  1. [1]
    Adini, A.; Clough, R.W.: Analysis of plate bending by the finite element method, NSF Report G. 7337, 1961.Google Scholar
  2. [2]
    Aubin, J.P.: Behavior of the error of the approximate solutions of boundary value problems for linear elliptic operators by Galerkin's and finite difference methods, Ann. Scuola Norm. Sup. Pisa 21 (1967), 599–637.Google Scholar
  3. [3]
    Babuška, I.; Aziz, A.K.: Survey Lectures on the Mathematical Foundations of the Finite Element Method, The Mathematical Foundations of the Finite Element Method with Applications to Partial Differential Equations (A.K. Aziz, Editor), pp. 3–359, Academic Press, New York, 1972.Google Scholar
  4. [4]
    Babuška, I.; Zlámal, M.: Nonconforming elements in the finite element method Technical Note BN-729, University of Maryland, College Park, 1972.Google Scholar
  5. [5]
    Bazeley, G.P.; Cheung, Y.K.; Irons, B.M.; Zienkiewicz, O.C.: Triangular elements in bending-conforming and nonconforming solutions, Conference on Matrix Methods in Structural Mechanics, Wright Patterson A.F.B., Ohio, 1965.Google Scholar
  6. [6]
    Birkhoff, G.; Mansfield, L.: Compatible triangular finite elements, J. Math. Anal. Appl., à paraître.Google Scholar
  7. [7]
    Bogner, F.K.; Fox, R.L.; Schmit, L.A.: The generation of interelement compatible stiffness and mass matrices by the use of interpolation formulas, Conference on Matrix Methods in Structural Mechanics, Wright Patterson A.F.B., Ohio 1965.Google Scholar
  8. [8]
    Bramble, J.H.; Hilbert, S.H.: Bounds for a class of linear functionals with applications to Hermite interpolation, Numer. Math. 16 (1971), 362–369.CrossRefGoogle Scholar
  9. [9]
    Bramble, J.H.; Zlámal, M.: Triangular Elements in the finite element method, Math. Comp. 24 (1970), 809–820.Google Scholar
  10. [10]
    Brezzi, F.: Sur la méthode des éléments finis hybrides pour le problème biharmonique, à paraître.Google Scholar
  11. [11]
    Ciarlet, P.G.; Orders of convergence in finite element methods, The Mathematics of Finite Elements and Applications (J.R. Whiteman, Editor), pp. 113–129, Academic Press, London, 1973.Google Scholar
  12. [12]
    Ciarlet, P.G.: Conforming and nonconforming finite element methods for solving the plate problem, Conference on the Numerical Solution of Differential Equations, University of Dundee, July 03–06, 1973.Google Scholar
  13. [13]
    Ciarlet, P.G.; Sur l'élément de Clough et Tocher, à paraître.Google Scholar
  14. [14]
    Ciarlet, P.G.; Raviart, P.-A.: General Lagrange and Hermite interpolation in Rn with applications to finite element methods, Arch. Rational Mech. Anal. 46 (1972), 177–199.CrossRefGoogle Scholar
  15. [15]
    Ciarlet, P.G.; Raviart, P.-A.: Interpolation theory over curved elements, with applications to finite element methods, Computer Meth. in Appl. Mech. and Engnrg 1 (1972), 217–249.CrossRefGoogle Scholar
  16. [16]
    Ciarlet, P.G.; Raviart, P.-A.: A nonconforming method for the plate problem, à paraître.Google Scholar
  17. [17]
    Ciavaldini, J.F.; Nédélec, J.C.: à paraître.Google Scholar
  18. [18]
    Clough, R.W.; Tocher, J.L.: Finite element stiffness matrices for analysis of plate in bending, Conference on Matrix Methods in Structural Mechanics, Wright Patterson A.F.B., Ohio, 1965.Google Scholar
  19. [19]
    Crouzeix, M.; Raviart, P.-A.: Conforming and nonconforming finite element methods for solving the stationary Stokes equations, I, à paraître.Google Scholar
  20. [20]
    Fraeijs de Veubeke, B.: Bending and stretching of plates, Conference on Matrix Methods in Structural Mechanics, Wright Patterson A.F.B., Ohio, 1965.Google Scholar
  21. [21]
    Glowinski, R.: Approximations externes, par éléments finis de Lagrange d'ordre un et deux, du problème de Dirichlet pour l'opérateur biharmonique. Méthode itérative de résolution des problèmes approchés, Conference on Numerical Analysis, Royal Irish Academy, 1972.Google Scholar
  22. [22]
    Irons, B.M.; Razzaque, A.: Experience with the patch test for convergence of finite elements, The Mathematical Foundations of the Finite Element Method with Applications to Partial Differential Equations (A.K. Aziz, Editor), pp. 557–587, Academic Press, New York, 1972.Google Scholar
  23. [23]
    Johnson, C.: On the convergence of some mixed finite element methods in plate bending problems, à paraître.Google Scholar
  24. [24]
    Johnson, C.: Convergence of another mixed finite-element method for plate bending problems, Report No. 27, Department of Mathematics, Chalmers Institute of Technology and the University of Göteborg, 1972.Google Scholar
  25. [25]
    Kondrat'ev, V.A.: Boundary value problems for elliptic equations in domains with conical or angular points, Trudy Mosk. Mat. Obšč. 16 (1967), 209–292.Google Scholar
  26. [26]
    Landau, L.; Lifchitz, E.: Théorie de l'Elasticité, Mir, Moscou, 1967.Google Scholar
  27. [27]
    Lascaux, P.; Lesaint, P.: Convergence de certains éléments finis non conformes pour le problème de la flexion des plaques minces, à paraître.Google Scholar
  28. [28]
    Morley, L.S.D.: The triangular equilibrium element in the solution of plate bending problems, Aero. Quart. 19 (1968), 149–169.Google Scholar
  29. [29]
    Nečas, J.: Les Méthodes Directes en Théorie des Equations Elliptiques, Masson, Paris, 1967.Google Scholar
  30. [30]
    Nitsche, J.: Ein Kriterium für die quasi-optimalität des Ritzchen Verfahrens, Numer. Math. 11 (1968), 346–348.CrossRefGoogle Scholar
  31. [31]
    Oden, J.T., Some contributions to the mathematical theory of mixed finite element approximations, Tokyo Seminar on Finite Elements, 1973.Google Scholar
  32. [32]
    Pian, T.H.H.: Finite element formulation by variational principles with relaxed continuity requirements, The Mathematical Foundations of the Finite Element Method with Applications to Partial Differential Equations (A.K. Aziz, Editor), pp. 671–687, Academic Press, New York, 1972.Google Scholar
  33. [33]
    Raviart, P.-A.: Méthode des Eléments Finis, Université de Paris VI, Paris, 1972.Google Scholar
  34. [34]
    Sander, C.: Bornes supérieures et inférieures dans l'analyse matricielle des plaques en flexion-torsion, Bull. Soc. Roy. Sci. Liège 33 (1964), 456–494.Google Scholar
  35. [35]
    Strang, G.: Approximation in the finite element method, Numer. Math. 19 (1972), 81–98.CrossRefGoogle Scholar
  36. [36]
    Strang, G.: Variational Crimes in the finite element method, The Mathematical Foundations of the Finite Element Method with Applications to Partial Differential Equations (A.K. Aziz, Editor), pp. 689–710, Academic Press, New York, 1972.Google Scholar
  37. [37]
    Strang, G.; Fix, G.: An Analysis of the Finite Element Method, Prentice-Hall, Englewood Cliffs, 1973.Google Scholar
  38. [38]
    Zienkiewicz, O.C.: The Finite Element Method in Engineering Science, McGraw-Hill, London, 1971.Google Scholar
  39. [39]
    Zienkiewicz, O.C.: Constrained variational principles and penalty function methods in finite element analysis, Conference on the Numerical Solution of Differential Equations, University of Dundee, July 03–06, 1973.Google Scholar
  40. [40]
    Zlámal, M.: On the finite element method, Numer. Math. 12 (1968), 394–409.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1974

Authors and Affiliations

  • P. G. Ciarlet
    • 1
  1. 1.Analyse Numérique, Tour 55Université de Paris VIParis Cedex 05

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