| Title:
|
Shape optimization of an elasto-plastic body for the model with strain- hardening (English) |
| Author:
|
Pištora, Vladislav |
| Language:
|
English |
| Journal:
|
Aplikace matematiky |
| ISSN:
|
0373-6725 |
| Volume:
|
35 |
| Issue:
|
5 |
| Year:
|
1990 |
| Pages:
|
373-404 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
domain optimization |
| Keyword:
|
time-dependent variational inequality |
| Keyword:
|
elasto-plasiicily |
| Keyword:
|
finite elements |
| Keyword:
|
uniqueness |
| Keyword:
|
state problem |
| Keyword:
|
optimal design |
| Keyword:
|
piecewise linear approximations of the unknown boundary |
| Keyword:
|
hardening parameter |
| Keyword:
|
backward differences in time |
| Keyword:
|
convergence |
| MSC:
|
49J40 |
| MSC:
|
65K10 |
| MSC:
|
65N30 |
| MSC:
|
73E05 |
| MSC:
|
73E99 |
| MSC:
|
73V25 |
| MSC:
|
73k40 |
| MSC:
|
74P10 |
| MSC:
|
74P99 |
| MSC:
|
74S05 |
| MSC:
|
74S30 |
| idZBL:
|
Zbl 0717.73054 |
| idMR:
|
MR1072608 |
| DOI:
|
10.21136/AM.1990.104419 |
| . |
| Date available:
|
2008-05-20T18:39:53Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/104419 |
| . |
| Reference:
|
[1] D. Begis R. Glowinski: Application de la méthode des éléments finis à l'approximation d'un problème de domaine optimal.Appl. Math. Optim. 2 (1975), 130-169. MR 0443372, 10.1007/BF01447854 |
| Reference:
|
[2] J. Céa: Optimization: Théorie et algorithmes.Dunod, Paris, 1971; (in Russian, Mir, Moskva, 1973). MR 0298892 |
| Reference:
|
[3] P. G. Ciarlet: The finite element method for elliptic problems.North Holland Publ. Соmр., Amsterdam, 1978; (in Russian, Mir, Moskva, 1980). Zbl 0383.65058, MR 0608971 |
| Reference:
|
[4] I. Hlaváček: A finite element solution for plasticity with strain-hardening.RAIRO Annal. Numér. 14 (1980), 347-368. MR 0596540 |
| Reference:
|
[5] I. Hlaváček: Optimization of the domain in elliptic problems by the dual finite element method.Apl. Mat. 30 (1985), 50-72. MR 0779332 |
| Reference:
|
[6] I. Hlaváček: Shape optimization of an elastic-perfectly plastic body.Apl. Mat. 32 (1987), 381-400. MR 0909545 |
| Reference:
|
[7] C. Johnson: Existence theorems for plasticity problems.J. Math. Pures Appl. 55 (1976), 431-444. Zbl 0351.73049, MR 0438867 |
| Reference:
|
[8] C. Johnson: A mixed finite element method for plasticity with hardening.SIAM J. Numer. Anal. 14 (1977), 575-583. MR 0489265, 10.1137/0714037 |
| Reference:
|
[9] C. Johnson: On plasticity with hardening.J. Math. Anal. Appl. 62 (1978), 325-336. Zbl 0373.73049, MR 0489198, 10.1016/0022-247X(78)90129-4 |
| Reference:
|
[10] A. Kufner O. John S. Fučík: Function spaces.Academia, Praha, 1977. MR 0482102 |
| Reference:
|
[11] J. Nečas: Les méthodes directes en théorie des équations elliptiques.Academia, Praha, 1967. MR 0227584 |
| Reference:
|
[12] I. Hlaváček: Shape optimization of elasto-plastic bodies obeying Hencky's law.Apl. Mat. 31 (1986), 486-499. Zbl 0616.73081, MR 0870484 |
| Reference:
|
[13] I. Hlaváček J. Haslinger J. Nečas J. Lovíšek: Solution of Variational Inequalities in Mechanics.Springer-Verlag, New York, 1988. MR 0952855 |
| . |
