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Title: Convergence of an equilibrium finite element model for plane elastostatics (English)
Author: Hlaváček, Ivan
Language: English
Journal: Aplikace matematiky
ISSN: 0373-6725
Volume: 24
Issue: 6
Year: 1979
Pages: 427-457
Summary lang: English
Summary lang: Czech
Summary lang: Russian
Category: math
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. (English)
Keyword: convergence
Keyword: equilibrium
Keyword: plane elastostatics
Keyword: principle of minimum complementary energy
Keyword: weak version of Castigliano principle
MSC: 35J20
MSC: 49S05
MSC: 65N30
MSC: 73K25
MSC: 74S05
MSC: 74S30
idZBL: Zbl 0441.73101
idMR: MR0547046
DOI: 10.21136/AM.1979.103826
Date available: 2008-05-20T18:13:09Z
Last updated: 2020-07-28
Stable URL:
Reference: [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
Reference: [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.
Reference: [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.
Reference: [4] I. Hlaváček: Variational principles in the linear theory of elasticity for general boundary conditions.Apl. mat. 12 (1967), 425-448. MR 0231575
Reference: [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).
Reference: [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.
Reference: [7] J. Nečas: Les méthodes directes en théorie des équations elliptiques.Academia, Prague, 1967. MR 0227584
Reference: [8] C. Johnson B. Mercier: Some equilibrium finite element methods for two-dimensional elasticity problems.Numer. Math. 30, (1978), 103-116. MR 0483904, 10.1007/BF01403910


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