Convergence of an equilibrium finite element model for plane elastostatics

Ivan Hlaváček

Aplikace matematiky (1979)

  • Volume: 24, Issue: 6, page 427-457
  • ISSN: 0862-7940

Abstract

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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.

How to cite

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Hlaváček, Ivan. "Convergence of an equilibrium finite element model for plane elastostatics." Aplikace matematiky 24.6 (1979): 427-457. <http://eudml.org/doc/15121>.

@article{Hlaváček1979,
abstract = {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.},
author = {Hlaváček, Ivan},
journal = {Aplikace matematiky},
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},
language = {eng},
number = {6},
pages = {427-457},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Convergence of an equilibrium finite element model for plane elastostatics},
url = {http://eudml.org/doc/15121},
volume = {24},
year = {1979},
}

TY - JOUR
AU - Hlaváček, Ivan
TI - Convergence of an equilibrium finite element model for plane elastostatics
JO - Aplikace matematiky
PY - 1979
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 24
IS - 6
SP - 427
EP - 457
AB - 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.
LA - eng
KW - 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
UR - http://eudml.org/doc/15121
ER -

References

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  1. J. Haslinger I. Hlaváček, Convergence of a finite element method based on the dual variational formulation, Apl. mat. 21 (1976), 43 - 65. (1976) MR0398126
  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. (1972) 
  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. (1968) 
  4. I. Hlaváček, Variational principles in the linear theory of elasticity for general boundary conditions, Apl. mat. 12 (1967), 425-448. (1967) MR0231575
  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). (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. (1973) 
  7. J. Nečas, Les méthodes directes en théorie des équations elliptiques, Academia, Prague, 1967. (1967) MR0227584
  8. C. Johnson B. Mercier, 10.1007/BF01403910, Numer. Math. 30, (1978), 103-116. (1978) MR0483904DOI10.1007/BF01403910

Citations in EuDML Documents

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  1. I. Hlaváček, Shape optimization in two-dimensional elasticity by the dual finite element method
  2. Michal Křížek, An equilibrium finite element method in three-dimensional elasticity
  3. Ivan Hlaváček, A finite element solution for plasticity with strain-hardening
  4. Ivan Hlaváček, Michal Křížek, Internal finite element approximation in the dual variational method for the biharmonic problem
  5. Jaroslav Haslinger, Ivan Hlaváček, Contact between elastic bodies. III. Dual finite element analysis
  6. Michal Křížek, Conforming equilibrium finite element methods for some elliptic plane problems
  7. Miroslav Vondrák, Slab analogy in theory and practice of conforming equilibrium stress models for finite element analysis of plane elastostatics
  8. Ivan Hlaváček, Convergence of dual finite element approximations for unilateral boundary value problems

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