Advertisement

Applied Mathematics and Mechanics

, Volume 4, Issue 4, pp 465–480 | Cite as

Theorems on the limit analysis dealing with the yield condition expressed by the sum of the homogeneous linear form of stress tensor and the homogeneous quadratic form of stress tensor

  • Zhao Jia-yi
  • Hsueh Dah-wei
Article

Abstract

In this paper a generalized variational principle on the limit, analysis dealing with the yield condition expressed by the sum of the homogeneous linear form of stress tensor and the homogeneous quadratic form of stress tensor is suggested. This variational principle can be applied to the limit analysis in rock mechanics and it takes the situation, in which the yield condition is expressed by the homogeneous linear form of stress tensor or the homogeneous quadratic form of stress tensor, as its special case.

Keywords

Mathematical Modeling Stress Tensor Quadratic Form Industrial Mathematic Variational Principle 
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]
    Hu Hai-chang,On some variational principle in the theory of elasticity and the theory of plasticity, Acta Physica, Vol. 10, No. 3 (1954). (in Chinese)Google Scholar
  2. [2]
    Reissner, E.,On the variational theorem in elasticity, J. Math. Phys. 29, (1950).Google Scholar
  3. [3]
    Shi, P.M.,On the variational principles of elastoplastic body and their application, Acta Mechanics Sinica, Vol. 1, No. 3, (1957). (in Chinese)Google Scholar
  4. [4]
    Chien, W. Z.,Studies on generalized variational principle in elasticity and their applications in finite element calculations, Mechanics and Its Applications, Vol. 1, No. 1–2, (1979). (in Chinese)Google Scholar
  5. [5]
    Tsien Ling-hi et al.,A generalized variational principle for the limit analysis in solid mechanics, Scientia Sinica, Vol. 13, No. 11, (1964). (in Chinese)Google Scholar
  6. [6]
    Mura, T. and S.L. Lee,Application of variational principle of limit analysis, Quart. Appl. Math. Vol. 21, No. 3, (1963).Google Scholar
  7. [7]
    Wang, A. J., et al.,Discussion on “The limit analysis in solid mechanics and suggested a generalized variational principle”, Acta Mechanics Sinica, Vol. 8, No.1, (1965). (in Chinese)Google Scholar
  8. [8]
    Hsueh Dah-wei,Theorems on the limit analysis, Bulletin of Science, Vol. 20, No. 4, (1975). (in Chinese)Google Scholar
  9. [9]
    Hsueh Dah-wei,A theorem on the limit analysis of finite displacement, Bulletin of Science (A Special Issue of Mathematics, Physics and Chemistry), Vol. 25, (1980). (in Chinese)Google Scholar
  10. [10]
    Zhao Peng-nian,The united expression of three kinds of yield equilibrium conditions, Underground Engineering, (1981). (in Chinese)Google Scholar
  11. [11]
    Chien, W. Z.,Variational calculus and finite element methods, Science Publishers, Beijing, (1980). (in Chinese)Google Scholar
  12. [12]
    Wai-fah Chen,Limit Analysis and Soil Plasticity, (1975).Google Scholar

Copyright information

© Hust Press 1983

Authors and Affiliations

  • Zhao Jia-yi
    • 1
  • Hsueh Dah-wei
    • 1
  1. 1.Beijing Institute of TechnologyBeijingChina

Personalised recommendations