Pacific Journal of Mathematics

The unloading problem for severely twisted bars.

Tsuan Wu Ting

Article information

Source
Pacific J. Math., Volume 64, Number 2 (1976), 559-582.

Dates
First available in Project Euclid: 8 December 2004

Permanent link to this document
https://projecteuclid.org/euclid.pjm/1102867107

Mathematical Reviews number (MathSciNet)
MR0452015

Zentralblatt MATH identifier
0352.73049

Subjects
Primary: 73.35

Citation

Ting, Tsuan Wu. The unloading problem for severely twisted bars. Pacific J. Math. 64 (1976), no. 2, 559--582. https://projecteuclid.org/euclid.pjm/1102867107


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References

  • [1] H. Brezis, Multiplicateur de Lagrange en torsion "elasto-plastique", Arch. Raj. Mech. Anal., 49 (1972), 32-40; Problemes unilateraux, J. Math. Pures and Appl., 51 (1972), 1-68.
  • [2] H. Brezis and M. Sibony, Equivalence de deux inequations ariationelles et applications, Arch. Rat. Mech. Anal., 41 (1971), 254-265.
  • [3] H. Brezis and G. Stampacchia, Sur la regularite de la solution d' inequations elliptiques, Bull. Soc. Math. France, 96 (1968), 153-180.
  • [4] G. Duvaut and J. L. Lions, Les inequations en mcanique et en physique, Dunod, Paris, 1972, Chapt. 5.
  • [5] G. Fichera, Existence theorems in elasticity, Handbuch der Physik, VI a/2, Springer-Verlag, New York, 1972, pp. 347-389.
  • [6] P. R. Garabedian, Partial differential equations, John Wiley and Sons, New York, 1964.
  • [7] P. R. Garabedian, H. Lewy and M. Schiffer, Axially symmetric cavitational flow, Ann. Math., 56 (1952), 560-602.
  • [8] H. Lewy and G. Stampacchia, On the regularity of the solution of a variational inequality, Comm. Pur. Appl. Math., 22 (1969), 153-188.
  • [9] H. Lanchon, Torsion elastoplastique d'un arbre cylindrique de section simplement ou multiplement connexe, J. Mech., 13 (1974), 267-320.
  • [10] H. Lanchon and G. Duvaut, Sur la solution du probleme de la torsion elasto-plastique d'une barre cylindrique de section quelconque, C. R. Acad. See. Paris, Ser A., 24 (1967), 502-503.
  • [11] W. Prager and P. G. Hodge Jr., Theory of perfectly plastic solids, John Wiley and Sons, New York, 1951.
  • [12] M. H. Protter and H. F. Weinberger, Maximum Principles in Differential Equations, Prentice- Hall, Englewood, NJ, 1967.
  • [13] G. Stampacchia, Regularity of solutions of some variational inequalities, Non-linear functional analysis, (Proc. Symp. Pure Math.) Vol. 18, Part I., (1970), 271-281.
  • [14] T. Y. Thomas, Plastic Flow and Fracture in Solids, Academic Press, New York, 1961.
  • [15] T. W. Ting, (a) The ridge of a Jordan domain and completely plastic torsion, J. Math. Mech.,15 (1966), 15-46; (b) Elastic-plastic torsion of a square bar, Trans. Amer. Math. Soc, 123 (1966), 369-401; (c) Elastic-plastic torsion of simply connected cylindrical bars, Indiana U. Math. J., 20 (1971), 1047-1076; (d) Torsional rigidities in the elastic-plastic torsion of simply connected cylindrical bars, Pacific J. Math., 46 (1973), 257-267;(e) Torsional rigidities of bars under fully plastic torsion, SIAMJ. Appl. Math., 25 (1973), 54-68. (f) Si. Venant's compatibility conditions, Tensor, N.S., 28 (1974), 5-12;
  • [16] C. Truesdell and W. Noll, The non-linear field theories of mechanics, Encyclopedia of physics, Vol. Ill--3. Springer-Verlag, New York, 1965.
  • [17] B. De St. Venant, Memoire sur la torsion des prisms, Mem. div. Sav. Acad. Sci., 14 (1856), 233-560.
  • [18] H. F. Weinberger, Upper and lower bounds for torsional rigidity, J. Math. Phys., 32(1953), 54-62.