| Title:
|
Shape optimization of an elasto-perfectly plastic body (English) |
| Author:
|
Hlaváček, Ivan |
| Language:
|
English |
| Journal:
|
Aplikace matematiky |
| ISSN:
|
0373-6725 |
| Volume:
|
32 |
| Issue:
|
5 |
| Year:
|
1987 |
| Pages:
|
381-400 |
| Summary lang:
|
English |
| Summary lang:
|
Russian |
| Summary lang:
|
Czech |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
optimal design |
| Keyword:
|
model of Prandtl-Reuss |
| Keyword:
|
variational inequality of evolution |
| Keyword:
|
piecewise linear approximation of the unknown boundary |
| Keyword:
|
piecewise constant triangular elements for stress |
| Keyword:
|
backward differences in time |
| Keyword:
|
convergence |
| Keyword:
|
elasto-plasticity |
| Keyword:
|
finite elements |
| MSC:
|
65K10 |
| MSC:
|
65N30 |
| MSC:
|
73E99 |
| MSC:
|
73k40 |
| MSC:
|
74P99 |
| MSC:
|
74S05 |
| MSC:
|
74S30 |
| idZBL:
|
Zbl 0632.73082 |
| idMR:
|
MR0909545 |
| DOI:
|
10.21136/AM.1987.104269 |
| . |
| Date available:
|
2008-05-20T18:33:07Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/104269 |
| . |
| Reference:
|
[1] I. Hlaváček: Shape optimization in two-dimensional elasticity by the dual finite element method.Math. Model. and Numerical Anal. 21 (1987), 63-92, MR 0882687, 10.1051/m2an/1987210100631 |
| Reference:
|
[2] I. Hlaváček: Shape optimization of elasto-plastic bodies obeying Hencky's law.Appl. Mat. 31 (1986), 486-499. Zbl 0616.73081, MR 0870484 |
| Reference:
|
[3] G. Duvaut J. L. Lions: Les inéquations en mécanique et en physique.Paris, Dunod 1972. MR 0464857 |
| Reference:
|
[4] J. Nečas I. Hlaváček: Mathematical theory of elastic and elasto-plastic bodies: An introduction.Elsevier, Amsterdam 1981. (Czech version - SNTL, Praha 1983.) MR 0600655 |
| Reference:
|
[5] C. Johnson: Existence theorems for plasticity problems.J. Math, pures et appl. 55 (1976), 431-444. Zbl 0351.73049, MR 0438867 |
| Reference:
|
[6] C. Johnson: On finite element methods for plasticity problems.Numer. Math. 26 (1976), 79-84. Zbl 0355.73035, MR 0436626, 10.1007/BF01396567 |
| Reference:
|
[7] J. Nečas: Les méthodes directes en théorie des équations elliptiques.Academia, Praha 1967. MR 0227584 |
| Reference:
|
[8] I. Hlaváček: A finite element solution for plasticity with strain-hardening.R.A.I.R.O. Analyse numér. 14 (1980), 347-368. MR 0596540 |
| Reference:
|
[9] D. Begis R. Glowinski: Application de la méthode des éléménts finis à l'approximation d'un problème de domaine optimal.Appl. Math. Optimiz., 2 (1975), 130-169. MR 0443372, 10.1007/BF01447854 |
| . |
