Skip to main content
Log in

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

  • Published:
Applied Mathematics and Mechanics Aims and scope Submit manuscript

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  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)

  2. Reissner, E.,On the variational theorem in elasticity, J. Math. Phys. 29, (1950).

  3. Shi, P.M.,On the variational principles of elastoplastic body and their application, Acta Mechanics Sinica, Vol. 1, No. 3, (1957). (in Chinese)

  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)

  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)

  6. Mura, T. and S.L. Lee,Application of variational principle of limit analysis, Quart. Appl. Math. Vol. 21, No. 3, (1963).

  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)

  8. Hsueh Dah-wei,Theorems on the limit analysis, Bulletin of Science, Vol. 20, No. 4, (1975). (in Chinese)

  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)

  10. Zhao Peng-nian,The united expression of three kinds of yield equilibrium conditions, Underground Engineering, (1981). (in Chinese)

  11. Chien, W. Z.,Variational calculus and finite element methods, Science Publishers, Beijing, (1980). (in Chinese)

  12. Wai-fah Chen,Limit Analysis and Soil Plasticity, (1975).

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Jia-yi, Z., Dah-wei, H. 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. Appl Math Mech 4, 465–480 (1983). https://doi.org/10.1007/BF01874661

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01874661

Keywords

Navigation