Article
MSC:
49A27,
49J40,
65K10,
65N30,
73E99,
73k40,
74P99,
74S05,
74S30 | MR 0870484 | Zbl 0616.73081 | DOI: 10.21136/AM.1986.104226
Full entry |
PDF
(1.6 MB)
Feedback
PDF
(1.6 MB)
Feedback
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; variational inequality
Summary:
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.
References:
[1] D. Bégis R. Glowinski: Application de la méthode des élements finis à l'approximation d'un problème de domaine optimal. Appl. Math. & Optimization, Vol. 2, 1975, 130-169. DOI 10.1007/BF01447854 | MR 0443372
[2] G. Duvaut J. L. Lions: Les inéquations en mécanique et en physique. Paris, Dunod 1972. MR 0464857
[3] R. Falk B. Mercier: Estimation d'erreur en élasto-plasticité. C.R. Acad. Sc. Paris, 282, A, (1976), 645-648. MR 0426575
[4] R. Falk B. Mercier: Error estimates for elasto-plastic problems. R.A.I.R.O. Anal. Numer., 11 (1977), 135-144. MR 0449119
[5] I. Hlaváček: A finite element analysis for elasto-plastic bodies obeying Hencky's law. Appl. Mat. 26 (1981), 449-461. MR 0634282 | Zbl 0467.73096
[6] B. Mercier: Sur la théorie et l'analyse numérique de problèmes de plasticité. Thesis, Université Paris VI, 1977. MR 0502686
[7] J. Nečas: Les méthodes directes en théorie des équations elliptiques. Academia, Praha 1967. MR 0227584
Search
Partner of
