Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



On Gunther's stress functions for couple stresses

Author: Donald E. Carlson
Journal: Quart. Appl. Math. 25 (1967), 139-146
DOI: https://doi.org/10.1090/qam/99904
MathSciNet review: QAM99904
Full-text PDF Free Access

References | Additional Information

References [Enhancements On Off] (What's this?)

  • [1] E. and F. Cosserat, Théorie des corps déformables, Hermann, Paris, 1909
  • [2] C. Truesdell and R. A. Toupin, The classical field theories, Handbuch der Physik, Vol. III/l, edited by S. Flügge, Springer, Berlin, 1960 MR 0118005
  • [3] W. Günther, Zur Statik und Kinematik des Cosseratschen Kontinuums, Abh. Braunschweig. Wiss. Ges. 10, 195-213 (1958)
  • [4] D. E. Carlson, Stress functions for couple and dipolar stresses, Quart. Appl. Math. 24, 29-35 (1966)
  • [5] D. E. Carlson, The general solution of the stress equations of equilibrium for a Cosserat continuum, Proc. Fifth U. S. Nat. Cong. Appl. Mech., 1966, p. 249
  • [6] M. Misicu, On a general solution of the theory of singular dislocations of media with couple-stresses, Rev. Roum. Sci. Techn. Méc. Appl. 10, 35-46 (1965)
  • [7] R. D. Mindlin, On the equations of elastic materials with micro-structure, Int. J. Solids Structures 1, 73-78 (1965)
  • [8] M. E. Gurtin, A generalization of the Beltrami stress functions in continuum mechanics, Arch. Rat. Mech. Anal. 13, 321-329 (1963) MR 0153154
  • [9] A. F. Stevenson, Note on the existence and determination of a vector potential, Quart. Appl. Math. 12, 194-198 (1954) MR 0062886
  • [10] D. E. Carlson, On the completeness of the Beltrami stress functions in continuum mechanics, J. Math. Anal. Appl. (in press) MR 0207264
  • [11] N. M. Günter, Die Potentialtheorie, Teubner, Leipzig, 1957
  • [12] L. Lichtenstein, Grundlagen der Hydromechanik, Springer, Berlin, 1929 MR 0228225
  • [13] M. Stippes, A note on stress functions, (to appear)

Additional Information

DOI: https://doi.org/10.1090/qam/99904
Article copyright: © Copyright 1967 American Mathematical Society

American Mathematical Society