Shape optimization of an elasto-perfectly plastic body

Ivan Hlaváček

Aplikace matematiky (1987)

  • Volume: 32, Issue: 5, page 381-400
  • ISSN: 0862-7940

Abstract

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Within the range of Prandtl-Reuss model of elasto-plasticity the following optimal design problem is solved. Given body forces and surface tractions, a part of the boundary, where the (two-dimensional) body is fixed, is to be found, so as to minimize an integral of the squared yield function. The state problem is formulated in terms of stresses by means of a time-dependent variational inequality. For approximate solutions piecewise linear approximations of the unknown boundary, piecewise constant triangular finite elements for stress and backward differences in time are used. Convergence of the approximations to a solution of the optimal design problem is proven. As a consequance, the existence of an optimal boudary is verified.

How to cite

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Hlaváček, Ivan. "Shape optimization of an elasto-perfectly plastic body." Aplikace matematiky 32.5 (1987): 381-400. <http://eudml.org/doc/15509>.

@article{Hlaváček1987,
abstract = {Within the range of Prandtl-Reuss model of elasto-plasticity the following optimal design problem is solved. Given body forces and surface tractions, a part of the boundary, where the (two-dimensional) body is fixed, is to be found, so as to minimize an integral of the squared yield function. The state problem is formulated in terms of stresses by means of a time-dependent variational inequality. For approximate solutions piecewise linear approximations of the unknown boundary, piecewise constant triangular finite elements for stress and backward differences in time are used. Convergence of the approximations to a solution of the optimal design problem is proven. As a consequance, the existence of an optimal boudary is verified.},
author = {Hlaváček, Ivan},
journal = {Aplikace matematiky},
keywords = {optimal design; model of Prandtl-Reuss; variational inequality of evolution; piecewise linear approximation of the unknown boundary; piecewise constant triangular elements for stress; backward differences in time; convergence; elasto-plasticity; finite elements; optimal design; model of Prandtl-Reuss; variational inequality of evolution; piecewise linear approximation of the unknown boundary; piecewise constant triangular elements for stress; backward differences in time; convergence},
language = {eng},
number = {5},
pages = {381-400},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Shape optimization of an elasto-perfectly plastic body},
url = {http://eudml.org/doc/15509},
volume = {32},
year = {1987},
}

TY - JOUR
AU - Hlaváček, Ivan
TI - Shape optimization of an elasto-perfectly plastic body
JO - Aplikace matematiky
PY - 1987
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 32
IS - 5
SP - 381
EP - 400
AB - Within the range of Prandtl-Reuss model of elasto-plasticity the following optimal design problem is solved. Given body forces and surface tractions, a part of the boundary, where the (two-dimensional) body is fixed, is to be found, so as to minimize an integral of the squared yield function. The state problem is formulated in terms of stresses by means of a time-dependent variational inequality. For approximate solutions piecewise linear approximations of the unknown boundary, piecewise constant triangular finite elements for stress and backward differences in time are used. Convergence of the approximations to a solution of the optimal design problem is proven. As a consequance, the existence of an optimal boudary is verified.
LA - eng
KW - optimal design; model of Prandtl-Reuss; variational inequality of evolution; piecewise linear approximation of the unknown boundary; piecewise constant triangular elements for stress; backward differences in time; convergence; elasto-plasticity; finite elements; optimal design; model of Prandtl-Reuss; variational inequality of evolution; piecewise linear approximation of the unknown boundary; piecewise constant triangular elements for stress; backward differences in time; convergence
UR - http://eudml.org/doc/15509
ER -

References

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  1. I. Hlaváček, 10.1051/m2an/1987210100631, Math. Model. and Numerical Anal. 21 (1987), 63-92, (1987) MR0882687DOI10.1051/m2an/1987210100631
  2. I. Hlaváček, Shape optimization of elasto-plastic bodies obeying Hencky's law, Appl. Mat. 31 (1986), 486-499. (1986) Zbl0616.73081MR0870484
  3. G. Duvaut J. L. Lions, Les inéquations en mécanique et en physique, Paris, Dunod 1972. (1972) MR0464857
  4. J. Nečas I. Hlaváček, Mathematical theory of elastic and elasto-plastic bodies: An introduction, Elsevier, Amsterdam 1981. (Czech version - SNTL, Praha 1983.) (1981) MR0600655
  5. C. Johnson, Existence theorems for plasticity problems, J. Math, pures et appl. 55 (1976), 431-444. (1976) Zbl0351.73049MR0438867
  6. C. Johnson, 10.1007/BF01396567, Numer. Math. 26 (1976), 79-84. (1976) Zbl0355.73035MR0436626DOI10.1007/BF01396567
  7. J. Nečas, Les méthodes directes en théorie des équations elliptiques, Academia, Praha 1967. (1967) MR0227584
  8. I. Hlaváček, A finite element solution for plasticity with strain-hardening, R.A.I.R.O. Analyse numér. 14 (1980), 347-368. (1980) MR0596540
  9. D. Begis R. Glowinski, 10.1007/BF01447854, Appl. Math. Optimiz., 2 (1975), 130-169. (1975) MR0443372DOI10.1007/BF01447854

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