Article
MSC:
35J20,
49S05,
65N30,
73K25,
74S05,
74S30 | MR 0547046 | Zbl 0441.73101 | DOI: 10.21136/AM.1979.103826
Full entry |
PDF
(3.5 MB)
Feedback
PDF
(3.5 MB)
Feedback
Keywords:
convergence; equilibrium; plane elastostatics; principle of minimum complementary energy; weak version of Castigliano principle
convergence; equilibrium; plane elastostatics; principle of minimum complementary energy; weak version of Castigliano principle
Summary:
An equilibrium triangular block-element, proposed by Watwood and Hartz, is subjected to an analysis and its approximability property is proved. If the solution is regular enough, a quasi-optimal error estimate follows for the dual approximation to the mixed boundary value problem of elasticity (based on Castigliano's principle). The convergence is proved even in a general case, when the solution is not regular.
References:
[1] J. Haslinger I. Hlaváček: Convergence of a finite element method based on the dual variational formulation. Apl. mat. 21 (1976), 43 - 65. MR 0398126
[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.
[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.
[4] I. Hlaváček: Variational principles in the linear theory of elasticity for general boundary conditions. Apl. mat. 12 (1967), 425-448. MR 0231575
[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 (ruský překlad - izdat. Sudostrojenije, Leningrad 1974).
[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.
[7] J. Nečas: Les méthodes directes en théorie des équations elliptiques. Academia, Prague, 1967. MR 0227584
[8] C. Johnson B. Mercier: Some equilibrium finite element methods for two-dimensional elasticity problems. Numer. Math. 30, (1978), 103-116. DOI 10.1007/BF01403910 | MR 0483904
Search
Partner of
