Advertisement

Archive for Rational Mechanics and Analysis

, Volume 27, Issue 1, pp 33–94 | Cite as

On the geometric structures of simple bodies, a mathematical foundation for the theory of continuous distributions of dislocations

  • C. -C. Wang
Article

Keywords

Neural Network Complex System Nonlinear Dynamics Electromagnetism Geometric Structure 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    Truesdell, C., & W. Noll, The Non-linear Field Theories of Mechanics. Handbuch der Physik, Vol. III/3. Berlin-Heidelberg-New York: Springer 1965.Google Scholar
  2. [2]
    Noll, W., Arch. Rational Mech. Anal. 2, 197–226 (1958/59).Google Scholar
  3. [3]
    Kondo, K., Memoirs of the Unifying Study of the Basic Problems in Engineering by Means of Geometry, Vol. I (1955), II (1958). Tokyo: Gakujutsu Bunken Fukyu-Kai.Google Scholar
  4. [4]
    Nye, J. F., Acta Met. 1, 153–162 (1953).Google Scholar
  5. [5]
    Bilby, B. A., R. Bullough, & E. Smith, Proc. Roy. Soc. Lond. A231, 263–273 (1955).Google Scholar
  6. [6]
    Bilby, B. A., Progress in Solid Mechanics 1, 329–398 (1960). Ed. I. N. Sneddon & R. Hill.Google Scholar
  7. [7]
    Kröner, E., & A. Seeger, Arch. Rational Mech. Anal. 3, 97–119 (1959).Google Scholar
  8. [8]
    Chern, S. S., Differentiable Manifolds. Lecture Notes, Dept. Math., Univ. Chicago (1959).Google Scholar
  9. [9]
    Sternberg, S., Lectures on Differential Geometry. Prentice-Hall 1964.Google Scholar
  10. [10]
    Nomizu, K., Lie Groups and Differential Geometry. Math. Soc. Japan (1956).Google Scholar
  11. [11]
    Kobayashi, S., & K. Nomizu, Foundations of Differential Geometry. John Wiley & Sons Interscience Publishers 1963.Google Scholar
  12. [12]
    Lang, S., Introduction to Differentiable Manifolds. John Wiley & Sons Interscience Publishers 1962.Google Scholar
  13. [13]
    Auslander, L., & R. Mackenzie, Introduction to Differentiable Manifolds. McGraw-Hill 1963.Google Scholar
  14. [14]
    Nôno, T., Paper to appear in J. Math. Anal. Appl.Google Scholar
  15. [15]
    Lie, S., & F. Engel, Theorie der Transformationsgruppen. Vol. 3. Leipzig: Teubner 1893.Google Scholar
  16. [16]
    Noll, W., Proc. Sym. Applied Math. Vol. XVII, 93–101 (1965).Google Scholar
  17. [17]
    Gurtin, M. E., & W. C. Williams, Arch. Rational Mech. Anal. 23, 163–172 (1966).Google Scholar
  18. [18]
    Halmos, P. R., Measure Theory. Van Nostrand 1950.Google Scholar
  19. [19]
    Coleman, B. D., Arch. Rational Mech. Anal. 20, 41–58 (1965).Google Scholar
  20. [20]
    Wang, C.-C., Arch. Rational Mech. Anal. 20, 1–40 (1965).Google Scholar
  21. [21]
    Chevalley, C., Theory of Lie Groups. Princeton University Press 1946.Google Scholar
  22. [22]
    Cohn, P. M., Lie Groups. Cambridge University Press 1957.Google Scholar
  23. [23]
    Coleman, B. D., & W. Noll, Arch. Rational Mech. Anal. 6, 355–370 (1960).Google Scholar
  24. [24]
    Wang, C.-C., Arch. Rational Mech. Anal. 18, 343–366 (1965).Google Scholar
  25. [25]
    Wang, C.-C., Arch. Rational Mech. Anal. 18, 117–126 (1965).Google Scholar
  26. [26]
    Coleman, B. D., & V. J. Mizel, Arch. Rational Mech. Anal. 23, 87–123 (1966).Google Scholar
  27. [27]
    Mizel, V. J., & C.-C. Wang, Arch. Rational Mech. Anal. 23, 124–134 (1966).Google Scholar
  28. [28]
    Steenrod, N., The Topology of Fibre Bundles. Princeton University Press 1951.Google Scholar
  29. [29]
    Frank, F. C., Phil. Mag. 42, 809–819 (1951).Google Scholar
  30. [30]
    Schouten, J. A., Ricci-Calculus. Berlin-Göttingen-Heidelberg: Springer 1954.Google Scholar
  31. [31]
    Ambrose, W., & I. M. Singer, Trans. Amer. Math. Soc. 75, 428–443 (1953).Google Scholar
  32. [32]
    Coleman, B. D., & W. Noll, Arch. Rational Mech. Anal. 15, 87–111 (1964).Google Scholar
  33. [33]
    Green, A. E., & J. E. Adkins, Large Elastic Deformations and Non-linear Continuum Mechanics. Oxford: Clarendon Press 1960.Google Scholar
  34. [34]
    Kröner, E., Arch. Rational Mech. Anal. 3, 273–334 (1959/60).Google Scholar

Copyright information

© Springer-Verlag 1967

Authors and Affiliations

  • C. -C. Wang
    • 1
  1. 1.The Johns Hopkins UniversityBaltimore

Personalised recommendations