Elastic-plastic torsion problem over multiply connected domains

Ting, Tsuan Wu

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 4, Tome 4 (1977) no. 2, pp. 291-312.

[1] H. Brezis, Problèmes unitateraux, J. Math. Pures & Appl., 51 (1972), pp. 1-68; Multiplicateur de Lagrange en torsion « elasto-plastique », Arch. Rat. Mech. Anal., 49 (1972), pp. 32-40. | MR | Zbl

[2] H.R. Brezis - M. Sibony, Equivalence de deux inéquations variationnelles et applications, Arch. Rat. Mech. Anal., 41 (1971), pp. 254-265. | MR | Zbl

[3] H.R. Brezis - G. Stampacchia, Sur la régularité de la solution d'inéquations elliptiques, Bull. Soc. Math. France, 96 (1968), pp. 153-180. | Numdam | MR | Zbl

[4] L.A. Caffarelli - N.M. Riviere, On the smoothness and analyticity of free boundaries in variational inequalities, Ann. Scuola Norm. Sup. Pisa, Serie IV, 3 (1976), pp. 289-310. | Numdam | MR | Zbl

[5] G. Duvaut - J.L. Lions, Les inéquations en Mécanique et en physique, Dund, Paris, 1972, Chapt. 5. | MR | Zbl

[6] G. Fichera, Existence theorems in elasticity, Handbuch der physik, VI a/2, pp. 347-389, Springer - Verlag, New York, 1972.

[7] G. Gerhardt, Regularity of the solutions of non-linear variational inequalities with a gradient bound as constraint, Arch. Rat. Mach. Anal., 58(1975), pp. 308-315. | Zbl

[8] P.R. Garabedian, Proof of uniqueness by symmetrization, Studies in Math. Anal. and selected topics, Stanford University, Stanford Calif., 1962, pp. 126-127; Partial differential equations, John Wiley and Sons, New York, 1964. | MR | Zbl

[9] D. Kinderlehrer, The free boundary determined by the solution to a differential equation, I. U. Math. J., 25 (1976), pp. 195-208. | MR | Zbl

[10] H. Lanchon, Sur la solution du problème de torsion élastoplastique d'une barre cylindrique de section multiconnexe, Compte rendus, Serie A (1971), pp. 1137-1140; Torsion élastoplastique d'un arbre cylindrique de section simplement on multiplement connexe, J. Mech., 13 (1974), pp. 267-320.

[11] H. Lauchon - R. Glowinski, Torsion élasto-plastique d'une barre cylindrique de section multi-connexe, J. mécanique, 12 (1973), pp. 151-171. | MR | Zbl

[12] H. Lewy, On the nature of the boundary separating two domains with different regimes, Accad. Naz. Lincei, CCCLXXII (1975), pp. 181-188.

[13] H. Lewy - G. Stampacchia, On the regularity of the solution of a variational inequality, Comm. Pure Appl. Math., 22 (1969), pp. 153-188; On existence and smoothness of solutions of some non-coercive variational inequalities, Arch. Rat. Mech. Anal., 41 (1971), pp. 241-253. | MR

[14] J.L. Lions - G. Stampacchia, Variational inequalities, Comm. Pure Appl. Math., 20 (1967), pp. 493-519. | MR | Zbl

[15] W. Prager - P.G. Hodge, Jr., Theory of perfectly plastic solids, John Wiley and Sons, New York, 1951, Chapter 4. | MR | Zbl

[16] G. Stampacchia, Regularity of solutions of some variational inequalities, Nonlinear Functional Analysis (Proc. Symp. Pure Math.,Vol.18), Part. I, pp. 271-281. | MR | Zbl

[17] T.Y. Thomas, Plastic flow and fracture of solids, Academic Press, New York, 1961. | MR | Zbl

[18] T.W. Ting, (a) The ridge of a Jordan domain and complete plastic torsion, J. Math. Mech., 15 (1960), pp. 15-48. (b) Elastic-plastic torsion of convex cylindrical bars, J. Math. Mech., 19 (1969), pp. 531-551; (c) Elastic-plastic torsion of simply connected cylindrical bars, I. U. Math. J., 20 (1971), pp. 1047-1076; (d) The unloading problem of a severly twisted bar, Pacific J. Math. (to appear). | MR

[19] C. Truesdell - W. Noll, Handbuch der physik, Vol. III/3, Springer - Verlag, New York, 1965. | MR

[20] B. De St. VENANT, Memoire sur la torsion des prisms, Mem. div. Sav. Acad. Sci., 14 (1856), pp. 233-560.