Shape optimization of an elasto-perfectly plastic body
Hlaváček, Ivan
Applications of Mathematics, Tome 32 (1987), p. 381-400 / Harvested from Czech Digital Mathematics Library
Access to full text
Full (PDF)

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.

Publié le : 1987-01-01
Classification:  65K10,  65N30,  73E99,  73k40,  74P99,  74S05,  74S30 
@article{104269,
     author = {Ivan Hlav\'a\v cek},
     title = {Shape optimization of an elasto-perfectly plastic body},
     journal = {Applications of Mathematics},
     volume = {32},
     year = {1987},
     pages = {381-400},
     zbl = {0632.73082},
     mrnumber = {0909545},
     language = {en},
     url = {http://dml.mathdoc.fr/item/104269}
}

Hlaváček, Ivan. Shape optimization of an elasto-perfectly plastic body. Applications of Mathematics, Tome 32 (1987) pp. 381-400. http://gdmltest.u-ga.fr/item/104269/

I. Hlaváček Shape optimization in two-dimensional elasticity by the dual finite element method, Math. Model. and Numerical Anal. 21 (1987), 63-92, (1987) | MR 0882687

I. Hlaváček Shape optimization of elasto-plastic bodies obeying Hencky's law, Appl. Mat. 31 (1986), 486-499. (1986) | MR 0870484 | Zbl 0616.73081

G. Duvaut J. L. Lions Les inéquations en mécanique et en physique, Paris, Dunod 1972. (1972) | MR 0464857

J. Nečas I. Hlaváček Mathematical theory of elastic and elasto-plastic bodies: An introduction, Elsevier, Amsterdam 1981. (Czech version - SNTL, Praha 1983.) (1981) | MR 0600655

C. Johnson Existence theorems for plasticity problems, J. Math, pures et appl. 55 (1976), 431-444. (1976) | MR 0438867 | Zbl 0351.73049

C. Johnson On finite element methods for plasticity problems, Numer. Math. 26 (1976), 79-84. (1976) | Article | MR 0436626 | Zbl 0355.73035

J. Nečas Les méthodes directes en théorie des équations elliptiques, Academia, Praha 1967. (1967) | MR 0227584

I. Hlaváček A finite element solution for plasticity with strain-hardening, R.A.I.R.O. Analyse numér. 14 (1980), 347-368. (1980) | MR 0596540

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. (1975) | Article | MR 0443372