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Equilibrium finite elements for the linear elastic problem. (English) Zbl 0401.73079

MSC:
74S05 Finite element methods applied to problems in solid mechanics
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
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References:
[1] Amara, M.: Th?se de 3e cycle, (1978), Universit? P. et M. Curie, Paris
[2] Amara, M., Thomas, J.M.: Approximation par ?l?ments finis ?quilibre du syst?me de l’?lasticit? lin?aire. Comptes-rendus de l’Acad?mie des Sciences, Paris286, 1147-1150 (1978) · Zbl 0395.73011
[3] Babuska, I.: Error bounds for finite element method. Numer. Math.,16, 322-323 (1971) · Zbl 0214.42001 · doi:10.1007/BF02165003
[4] Brezzi, F.: On the existence, uniqueness and approximations of saddle-point problems arising from Langragian Multipliers. R.A.I.R.O,R 2, 129-151 (1974) · Zbl 0338.90047
[5] Ciarlet, P.G., Destuynder, P.: A justification of the two-dimensional linear plate model. Journal de M?canique (in press 1979) · Zbl 0415.73072
[6] Cowper, G.R., Lindberg, G.M., Olson, M.D.: A shallow shell finite element triangular shape, Inter. J. Solids and Structures,6, 1133-1156 (1970) · doi:10.1016/0020-7683(70)90052-1
[7] Crouzeix, M., Raviart, P.A.: Conforming and non conforming finite element methods for solving the stationary Stokes equations. R.A.I.R.O.,R 3, 33-75 (1973) · Zbl 0302.65087
[8] Duvaut, G., Lions, J.L.: Les in?quations en m?canique et en physique. Paris: Dunod 1972 · Zbl 0298.73001
[9] Fraeijs de Veubeke, B.X.: Stress function approach, World Congress in finite element method in structural mechanic, Bornemouth (1975) · Zbl 0359.76021
[10] Gallagher, R.H.: Finite Element Analysis, fundamentals, Englewood Cliffs, New Jersey: Prentice Hall 1975 · Zbl 0312.73088
[11] Germain, P.: M?canique des Milieux Continus. Paris: Masson 1962 · Zbl 0121.41303
[12] Johnson, C., Mercier, B.: Some equilibrium finite element methods for two-dimensional elasticity problems. Numer. Math.30, 103-116 (1977) · Zbl 0427.73072 · doi:10.1007/BF01403910
[13] Landau, L., Lifschitz, E.: Th?orie de l’?lasticit?. Moscou: Mir., 1967
[14] Oliveira, E.A.: Plane stress analysis by a general integral method. J. Eng. Mech. Div., Proc. Amer. Soc. Civil Eng., 79-101 (1968)
[15] Raviart, P.A., Girault, V.: Finite element approximation of the Navier-Stokes equations. Lecture Notes in Mathematics, Vol. 749. Berlin-Heidelberg-New York: Springer 1979 · Zbl 0413.65081
[16] Raviart, P.A., Thomas, J.M.: Mixed finite element methods for 2nd order elliptic problems. In: Mathematical Aspects of Finite Element Methods (I., Galligani, E. Magenes, eds.) Lecture Notes in Mathematics, Vol. 606, pp. 292-315. Berlin-Heidelberg-New York: Springer 1977 · Zbl 0362.65089
[17] Raviart, P.A., Thomas, J.M.: Dual finite element models for 2nd order elliptic problems. In: Energy Methods in Finite Element Analysis (Glowinski, Rodin, Zienkiewicz, Eds.), pp. 175-191. New York: Wiley 1979 · Zbl 0408.73070
[18] Temam, R.: Navier Stokes equations, Theory and Numerical Analysis. Amsterdam: North Holland 1977 · Zbl 0383.35057
[19] Thomas, J.M.: M?thode des ?l?ments finis hybrides et mixtes pour les probl?mes elliptiques du second ordre. Th?se, Univ. P. et M. Curie. Paris, 1977
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