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Hybrid finite element methods for the von Kármán equations. (English) Zbl 0443.73035


MSC:

74K20 Plates
74S05 Finite element methods applied to problems in solid mechanics
65N15 Error bounds for boundary value problems involving PDEs
35Q99 Partial differential equations of mathematical physics and other areas of application
74B20 Nonlinear elasticity
74B10 Linear elasticity with initial stresses
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References:

[1] D. Allman,Some fundamental aspects of the Finite Element Analysis of Nonlinear Elastic plate Bending, International Conference on Finite Elements in Nonlinear Solid and Structural Mechanics. Geilo, Norway (1977), Vol. 1, C 06
[2] M. S. Berger, P. C. Fife,Von Karman’s Equations and the Buckling of a Thin Elastic Plate, II. Comm. Pure Appl. Math.21 (1968), 227–241. · Zbl 0162.56501
[3] F. Brezzi,Hybrid Methods for Fourth Order Elliptic Equations, Congress on Mathematical Aspects of Finite Element Methods, Lecture Notes in Mathematics606 (1977), 35–46.
[4] F. Brezzi,Finite Element Approximations of the Von Karman Equations, R.A.I.R.O., An. Num., vol. 12, n. 4 (1978), 303–312. · Zbl 0398.73070
[5] F. Brezzi, L. D. Marini,On the Numerical Solution of Plate Bending Problems by Hybrid Methods, R.A.I.R.O., R 3 (1975), 5–50. · Zbl 0322.73048
[6] P. G. Ciarlet,The Finite Element Method for Elliptic Problems (1978), North-Holland, Amsterdam. · Zbl 0383.65058
[7] J. L. Lions,Quelques Méthodes de Résolution des Problèmes aux Limites non Linéaires (1969), Dunod: Paris.
[8] J. L. Lions, E. Magenes,Non Homogeneus Boundary Value Problems and Applications, I, II, (1970) Grund. B. 181–182, Springer Berlin.
[9] T. Miyoshi,A Mixed Finite Element Method for the Solution of the Von Karman Equations, Numer. Math.26 (1976), 255–269. · Zbl 0315.65064
[10] A. Quarteroni,Error Estimates for the Assumed Stresses Hybrid Methods in the Approximation of 4th Order Elliptic Equations, to appear on R.A.I.R.O., An. Num., vol. 13, n. 4 (1979). · Zbl 0447.65066
[11] D. H. Sattinger,Topics in Stability and Bifurcation Theory. Lecture Notes in Mathematics309, (1973), Springer Verlag, Berlin. · Zbl 0248.35003
[12] T. Von Karman,Fastigkeitsproblem in Maschinbau, Encycl. der Math. Wissenschaften,4, (1910), 348–352.
[13] K. Washizu,Variational Methods in Elasticity and Plasticity (1975), Pergamon Press. · Zbl 0339.73035
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