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Convergence of an equilibrium finite element model for plane elastostatics. (English) Zbl 0441.73101

MSC:
74S05 Finite element methods applied to problems in solid mechanics
35J20 Variational methods for second-order elliptic equations
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
74S30 Other numerical methods in solid mechanics (MSC2010)
49S05 Variational principles of physics
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References:
[1] J. Haslinger I. Hlaváček: Convergence of a finite element method based on the dual variational formulation. Apl. mat. 21 (1976), 43 - 65.
[2] B. Fraeijs de Veubeke M. Hogge: Dual analysis for heat conduction problems by finite elements. Inter. J. Numer. Meth. Eng. 5 (1972), 65 - 82. · Zbl 0251.65061
[3] V. B. Watwood, Jr. B. J. Hartz: An equilibrium stress field model for finite element solutions of two-dimensional elastostatic problems. Inter. J. Solids and Struct. 4 (1968), 857-873. · Zbl 0164.26201
[4] I. Hlaváček: Variational principles in the linear theory of elasticity for general boundary conditions. Apl. mat. 12 (1967), 425-448. · Zbl 0153.55401
[5] G. Sander: Application of the dual analysis principle. Proc. of IUTAM Symp. on High Speed Computing of Elastic Structures, 167-207, Univ. de Liege, 1971
[6] B. Fraeijs de Veubeke: Finite elements method in aerospace engineering problems. Proc. of Inter. Symp. Computing Methods in Appl. Sci. and Eng., Versailles, 1973, Part 1, 224-258. · Zbl 0283.73029
[7] J. Nečas: Les méthodes directes en théorie des équations elliptiques. Academia, Prague, 1967. · Zbl 1225.35003
[8] C. Johnson B. Mercier: Some equilibrium finite element methods for two-dimensional elasticity problems. Numer. Math. 30, (1978), 103-116. · Zbl 0427.73072
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