Problèmes variationnels en plasticité parfaite des plaques. (French) Zbl 0554.73030

The behaviour of elastoplastic plates, subjected to orthogonal forces and boundary moments is studied. The proper material of the paper is presented in the following three parts: 1. Variational formulation of the plate problem in Sobolev spaces; 2. Functions spaces with bounded Hessian and 3. Existence of solutions.
Starting from the variational formulation of the problem given by G. Duvaut and J. L. Lions [Les inéquations en mécanique et en physique (1972; Zbl 0298.73001)], and from some results obtained by himself [in ”Thèse de 3e Cycle, Univ. Paris (1982)] for elastic plates, the author extends these results to plastic plates. Then he introduces a fit space for solutions in displacements with bounded Hessian, a natural space for deformations without breaking. Finally, he establishes existence and uniqueness theorems for the solution of the elastoplastic problem.
Reviewer: St.Zanfir


74R20 Anelastic fracture and damage
74K20 Plates
74S30 Other numerical methods in solid mechanics (MSC2010)
49J27 Existence theories for problems in abstract spaces
49J40 Variational inequalities


Zbl 0298.73001
Full Text: DOI


[1] Adams R.S., Sobolev Spaces (1975)
[2] Demengel F., These de 3e Cycle 6 (1982)
[3] Demengel F., Fonctions a hessien borne · Zbl 0525.46020
[4] Demengel F., Fonctions convexes d’une mesure
[5] Deny J, Ann. Inst. Fourier 5 pp 305– (1954) · Zbl 0065.09903
[6] Duvaut, G.Lions, J.L. 1972. ”Les inequations en mecanique et en Physique”. Paris: Dunod. · Zbl 0298.73001
[7] Do L.D., J. Math. Anal. Appl. 60 (2) pp 435– (1977) · Zbl 0364.73030
[8] Temam, R. 1976. ”Convex Analysis and variational problems”. Amsterdam, North-Holland · Zbl 0322.90046
[9] Gagliardo E., Rend. Sem. Mat. Univ. Padova 27 pp 284– (1957)
[10] Hadhri. 1982. ”These de Docteur Ingenieur”. Ecole Polytechnique.
[11] Kohn R., Appl. Math. Optim. (1982)
[12] Lions, J.L.Magenes, E. 1968. ”Problemes aux limites non homogenes et applications”. Vol. 1, Paris: Dunod. Traduction anglaise. Springer Verlag, Heidelberg, New-York, 1972
[13] Mignot, F.Puel, J.P. 1981. ”Flambage des plaques elastoplastiques.”. Vol. 6, Paris: Publication de I’Universite. · Zbl 0509.73048
[14] Miranda M., Rend Sem. Mat. Univ. Padova (1967)
[15] Taylor Rauch communication privée
[16] Strang C., Arch. Rational Mech. Anal. 75 pp 7– (1980)
[17] Suquet P., serie A 286 pp 1129– (1978)
[18] Suquet P., Mathematical problems in the theory of elastoplastic plates · Zbl 0445.73042
[19] Temam R., Applicable Anal. 11 pp 291– (1981) · Zbl 0504.46027
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.