A finite element analysis for elastoplastic bodies obeying Hencky's law

Ivan Hlaváček

Aplikace matematiky (1981)

  • Volume: 26, Issue: 6, page 449-461
  • ISSN: 0862-7940

Abstract

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Using the Haar-Kármán principle, approximate solutions of the basic boundary value problems are proposed and studied, which consist of piecewise linear stress fields on composite triangles. The torsion problem is solved in an analogous manner. Some convergence results are proven.

How to cite

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Hlaváček, Ivan. "A finite element analysis for elastoplastic bodies obeying Hencky's law." Aplikace matematiky 26.6 (1981): 449-461. <http://eudml.org/doc/15216>.

@article{Hlaváček1981,
abstract = {Using the Haar-Kármán principle, approximate solutions of the basic boundary value problems are proposed and studied, which consist of piecewise linear stress fields on composite triangles. The torsion problem is solved in an analogous manner. Some convergence results are proven.},
author = {Hlaváček, Ivan},
journal = {Aplikace matematiky},
keywords = {Haar-Kármán principle; basic boundary value problems; piecewise linear stress fields; composite triangles; torsion problem; Haar-Kármán principle; basic boundary value problems; piecewise linear stress fields; composite triangles; torsion problem},
language = {eng},
number = {6},
pages = {449-461},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {A finite element analysis for elastoplastic bodies obeying Hencky's law},
url = {http://eudml.org/doc/15216},
volume = {26},
year = {1981},
}

TY - JOUR
AU - Hlaváček, Ivan
TI - A finite element analysis for elastoplastic bodies obeying Hencky's law
JO - Aplikace matematiky
PY - 1981
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 26
IS - 6
SP - 449
EP - 461
AB - Using the Haar-Kármán principle, approximate solutions of the basic boundary value problems are proposed and studied, which consist of piecewise linear stress fields on composite triangles. The torsion problem is solved in an analogous manner. Some convergence results are proven.
LA - eng
KW - Haar-Kármán principle; basic boundary value problems; piecewise linear stress fields; composite triangles; torsion problem; Haar-Kármán principle; basic boundary value problems; piecewise linear stress fields; composite triangles; torsion problem
UR - http://eudml.org/doc/15216
ER -

References

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  2. B. Mercier, Sur la théorie et l'analyse numérique de problèmes de plasticité, Thesis, Université Paris VI, 1977. (1977) MR0502686
  3. P. Suquet, Existence and regularity of solutions for plasticity problems, (Preprint). Proc. IUTAM Congress in Evanston - 1978. (1978) 
  4. R. Falk B. Mercier, Estimation d'erreur en élastoplasticité, C. R. Acad. Sc. Paris, 282, A, (1976), 645-648. (1976) MR0426575
  5. R. Falk B. Mercier, Error estimates for elasto-plastic problems, R.A.I.R.O. Anal. Numer., 11 (1977), 135-144. (1977) MR0449119
  6. V. B. Watwood B. J. Hartz, An equilibrium stress field model for finite element solution of two-dimensionalelastostatic problems, Inter. J. Solids Structures 4, (1968), 857-873. (1968) 
  7. C. Johnson B. Mercier, 10.1007/BF01403910, Numer. Math. 30 (1978), 103-116. (1978) MR0483904DOI10.1007/BF01403910
  8. J. Céa, Optimisation, théorie et algorithmes, Dunod, Paris 1971. (1971) MR0298892
  9. F. Brezzi W. W. Hager P. A. Raviart, 10.1007/BF01404345, Numer. Math. 28, (1977), 431 - 443. (1977) MR0448949DOI10.1007/BF01404345
  10. M. Křížek, An equilibrium finite element method in three-dimensional elasticity, Apl. Mat. 27 (1982). (1982) MR0640139
  11. P. A. Raviart J. M. Thomas, A mixed finite element method for 2-nd order elliptic problems, Math. Aspects of Fin. El. Meth. Rome 1975, Springer-Verlag 1977, 292-315. (1975) MR0483555
  12. H. Brezis K. Stampacchia, Sur la regularité de la solution d'inéquations elliptiques, Bull. Soc. Math. France 96, (1968), 153-180. (1968) MR0239302

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