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La methode de Kikuchi appliquee aux equations de von Kármán. (German) Zbl 0395.73054

MSC:
74K20 Plates
74G60 Bifurcation and buckling
74S05 Finite element methods applied to problems in solid mechanics
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
35B32 Bifurcations in context of PDEs
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References:
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[2] Bauer, L., Reiss, E.: Non-linear buckling of rectangular plates. SIAM13, 603-626 (1965)
[3] Berger, M.S.: On Von Karman’s equations and the buckling of a thin elastic plate. I. The clamped plate. Communications on Pure and Appl. Mathematics20, 687-719 (1967) · Zbl 0162.56405 · doi:10.1002/cpa.3160200405
[4] Brezzi, F.: Finite element approximations of the Von Karman equations. RAIRO, (à paraître) 1978 · Zbl 0398.73070
[5] Ciarlet, P.G.: The Finite Element Method for Elliptic Problems. Amsterdam: North-Holland 1978 · Zbl 0383.65058
[6] Ciarlet, P.G.: Derivation of the Von Karman equations from three-dimensional elasticity. To appear in Proceedings Fourth Coference on Basic Problems in Numerical Analysis (Plze?, Sept. 1978)
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[9] Kesavan, S., Vanninathan, M.: Sur une méthode d’éléments finis mixte pour l’équation biharmoique. RAIRO Analyse Numérique11, 255-270 (1977) · Zbl 0372.65039
[10] Kikuchi, F.: An iterative finite element scheme for bifurcation analysis of semi-linear elliptic equations, Report No542. Institute of Space and Aeronautical Science, University of Tokyo, Japan 1976
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[13] Mignot, F., Puel, J.P., Suquet, P.: à paraître
[14] Miyoshi, T.: A mixed finite element method for the solution of the Von Karman equations. Numer. Math.26, 255-269 (1976) · Zbl 0315.65064 · doi:10.1007/BF01395945
[15] Miyoshi, T.: Some aspects of a mixed finite element method applied to fourth order partial differential equations. Colloque IRIA, Versailles 1975
[16] Miyoshi, T.: Application of a mixed finite element method to a non-linear problem of elasticity. Mathematical Aspects of Finite Elements, Proceedings of the Symposium held at Rome, Dec. 1975, Springer-Verlag Lecture Notes in Mathematics, No 606, pp. 210-223, 0000 · doi:10.1007/BFb0064465
[17] Strang, G., Fix, G.: Analysis of the Finite Element Method. Prentice-Hall, Inc. 1972 · Zbl 0272.65099
[18] Von Karman, T.: Festigkeitsprobleme im Maschinenball. Encyl. du Math. Wissenschaften,IV-4, 348-352 (1907-1914)
[19] Yamaguti, M., Fujii, H.: On numerical deformation of singularities in non-linear elasticity, Colloque IRIA, Versailles 1977 (à paraître) · Zbl 0402.73044
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