Shape optimization of an elasto-plastic body for the model with strain- hardening

Vladislav Pištora

Aplikace matematiky (1990)

  • Volume: 35, Issue: 5, page 373-404
  • ISSN: 0862-7940

Abstract

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The state problem of elasto-plasticity (for the model with strain-hardening) is formulated in terms of stresses and hardening parameters by means of a time-dependent variational inequality. The optimal design problem is to find the shape of a part of the boundary such that a given cost functional is minimized. For the approximate solutions piecewise linear approximations of the unknown boundary, piecewise constant triangular elements for the stress and the hardening parameter, and backward differences in time are used. Existence and uniqueness of a solution of the approximate state problem and existence of a solution of the approximate optimal design problem are proved. The main result is the proof of convergence of the approximations to a solution of the original optimal design problem.

How to cite

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Pištora, Vladislav. "Shape optimization of an elasto-plastic body for the model with strain- hardening." Aplikace matematiky 35.5 (1990): 373-404. <http://eudml.org/doc/15638>.

@article{Pištora1990,
abstract = {The state problem of elasto-plasticity (for the model with strain-hardening) is formulated in terms of stresses and hardening parameters by means of a time-dependent variational inequality. The optimal design problem is to find the shape of a part of the boundary such that a given cost functional is minimized. For the approximate solutions piecewise linear approximations of the unknown boundary, piecewise constant triangular elements for the stress and the hardening parameter, and backward differences in time are used. Existence and uniqueness of a solution of the approximate state problem and existence of a solution of the approximate optimal design problem are proved. The main result is the proof of convergence of the approximations to a solution of the original optimal design problem.},
author = {Pištora, Vladislav},
journal = {Aplikace matematiky},
keywords = {domain optimization; time-dependent variational inequality; elasto-plasiicily; finite elements; uniqueness; state problem; optimal design; piecewise linear approximations of the unknown boundary; hardening parameter; backward differences in time; convergence; domain optimization; existence; uniqueness; state problem; time-dependent variational inequality; optimal design; piecewise linear approximations of the unknown boundary; piecewise constant triangular elements for the stress; hardening parameter; backward differences in time; convergence},
language = {eng},
number = {5},
pages = {373-404},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Shape optimization of an elasto-plastic body for the model with strain- hardening},
url = {http://eudml.org/doc/15638},
volume = {35},
year = {1990},
}

TY - JOUR
AU - Pištora, Vladislav
TI - Shape optimization of an elasto-plastic body for the model with strain- hardening
JO - Aplikace matematiky
PY - 1990
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 35
IS - 5
SP - 373
EP - 404
AB - The state problem of elasto-plasticity (for the model with strain-hardening) is formulated in terms of stresses and hardening parameters by means of a time-dependent variational inequality. The optimal design problem is to find the shape of a part of the boundary such that a given cost functional is minimized. For the approximate solutions piecewise linear approximations of the unknown boundary, piecewise constant triangular elements for the stress and the hardening parameter, and backward differences in time are used. Existence and uniqueness of a solution of the approximate state problem and existence of a solution of the approximate optimal design problem are proved. The main result is the proof of convergence of the approximations to a solution of the original optimal design problem.
LA - eng
KW - domain optimization; time-dependent variational inequality; elasto-plasiicily; finite elements; uniqueness; state problem; optimal design; piecewise linear approximations of the unknown boundary; hardening parameter; backward differences in time; convergence; domain optimization; existence; uniqueness; state problem; time-dependent variational inequality; optimal design; piecewise linear approximations of the unknown boundary; piecewise constant triangular elements for the stress; hardening parameter; backward differences in time; convergence
UR - http://eudml.org/doc/15638
ER -

References

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  1. D. Begis R. Glowinski, 10.1007/BF01447854, Appl. Math. Optim. 2 (1975), 130-169. (1975) MR0443372DOI10.1007/BF01447854
  2. J. Céa: Optimization, Théorie et algorithmes, Dunod, Paris, 1971; (in Russian, Mir, Moskva, 1973). (1971) MR0298892
  3. P. G. Ciarlet, The finite element method for elliptic problems, North Holland Publ. Соmр., Amsterdam, 1978; (in Russian, Mir, Moskva, 1980). (1978) Zbl0383.65058MR0608971
  4. I. Hlaváček, A finite element solution for plasticity with strain-hardening, RAIRO Annal. Numér. 14 (1980), 347-368. (1980) MR0596540
  5. I. Hlaváček, Optimization of the domain in elliptic problems by the dual finite element method, Apl. Mat. 30 (1985), 50-72. (1985) MR0779332
  6. I. Hlaváček, Shape optimization of an elastic-perfectly plastic body, Apl. Mat. 32 (1987), 381-400. (1987) MR0909545
  7. C. Johnson, Existence theorems for plasticity problems, J. Math. Pures Appl. 55 (1976), 431-444. (1976) Zbl0351.73049MR0438867
  8. C. Johnson, 10.1137/0714037, SIAM J. Numer. Anal. 14 (1977), 575-583. (1977) MR0489265DOI10.1137/0714037
  9. C. Johnson, 10.1016/0022-247X(78)90129-4, J. Math. Anal. Appl. 62 (1978), 325-336. (1978) Zbl0373.73049MR0489198DOI10.1016/0022-247X(78)90129-4
  10. A. Kufner O. John S. Fučík, Function spaces, Academia, Praha, 1977. (1977) MR0482102
  11. J. Nečas, Les méthodes directes en théorie des équations elliptiques, Academia, Praha, 1967. (1967) MR0227584
  12. I. Hlaváček, Shape optimization of elasto-plastic bodies obeying Hencky's law, Apl. Mat. 31 (1986), 486-499. (1986) Zbl0616.73081MR0870484
  13. I. Hlaváček J. Haslinger J. Nečas J. Lovíšek, Solution of Variational Inequalities in Mechanics, Springer-Verlag, New York, 1988. (1988) MR0952855

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