Shape optimization of elastoplastic bodies obeying Hencky's law

Ivan Hlaváček

Aplikace matematiky (1986)

  • Volume: 31, Issue: 6, page 486-499
  • ISSN: 0862-7940

Abstract

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A minimization of a cost functional with respect to a part of the boundary, where the body is fixed, is considered. The criterion is defined by an integral of a yield function. The principle of Haar-Kármán and piecewise constant stress approximations are used to solve the state problem. A convergence result and the existence of an optimal boundary is proved.

How to cite

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Hlaváček, Ivan. "Shape optimization of elastoplastic bodies obeying Hencky's law." Aplikace matematiky 31.6 (1986): 486-499. <http://eudml.org/doc/15472>.

@article{Hlaváček1986,
abstract = {A minimization of a cost functional with respect to a part of the boundary, where the body is fixed, is considered. The criterion is defined by an integral of a yield function. The principle of Haar-Kármán and piecewise constant stress approximations are used to solve the state problem. A convergence result and the existence of an optimal boundary is proved.},
author = {Hlaváček, Ivan},
journal = {Aplikace matematiky},
keywords = {optimal design; shape optimization; two dimensional elasto-plastic bodies; Hencky’s law; minimum of cost functional; convergence; existence of an optimal boundary; variational inequality; optimal design; shape optimization; two dimensional elasto-plastic bodies; Hencky's law; minimum of cost functional; convergence; existence of an optimal boundary},
language = {eng},
number = {6},
pages = {486-499},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Shape optimization of elastoplastic bodies obeying Hencky's law},
url = {http://eudml.org/doc/15472},
volume = {31},
year = {1986},
}

TY - JOUR
AU - Hlaváček, Ivan
TI - Shape optimization of elastoplastic bodies obeying Hencky's law
JO - Aplikace matematiky
PY - 1986
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 31
IS - 6
SP - 486
EP - 499
AB - A minimization of a cost functional with respect to a part of the boundary, where the body is fixed, is considered. The criterion is defined by an integral of a yield function. The principle of Haar-Kármán and piecewise constant stress approximations are used to solve the state problem. A convergence result and the existence of an optimal boundary is proved.
LA - eng
KW - optimal design; shape optimization; two dimensional elasto-plastic bodies; Hencky’s law; minimum of cost functional; convergence; existence of an optimal boundary; variational inequality; optimal design; shape optimization; two dimensional elasto-plastic bodies; Hencky's law; minimum of cost functional; convergence; existence of an optimal boundary
UR - http://eudml.org/doc/15472
ER -

References

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  1. D. Bégis R. Glowinski, 10.1007/BF01447854, Appl. Math. & Optimization, Vol. 2, 1975, 130-169. (1975) MR0443372DOI10.1007/BF01447854
  2. G. Duvaut J. L. Lions, Les inéquations en mécanique et en physique, Paris, Dunod 1972. (1972) MR0464857
  3. R. Falk B. Mercier, Estimation d'erreur en élasto-plasticité, C.R. Acad. Sc. Paris, 282, A, (1976), 645-648. (1976) MR0426575
  4. R. Falk B. Mercier, Error estimates for elasto-plastic problems, R.A.I.R.O. Anal. Numer., 11 (1977), 135-144. (1977) MR0449119
  5. I. Hlaváček, A finite element analysis for elasto-plastic bodies obeying Hencky's law, Appl. Mat. 26 (1981), 449-461. (1981) Zbl0467.73096MR0634282
  6. B. Mercier, Sur la théorie et l'analyse numérique de problèmes de plasticité, Thesis, Université Paris VI, 1977. (1977) MR0502686
  7. J. Nečas, Les méthodes directes en théorie des équations elliptiques, Academia, Praha 1967. (1967) MR0227584

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