Skip to main content
Log in

Complementary energy principle for large elastic deformation

  • Published:
Science in China Series G Aims and scope Submit manuscript

Abstract

Using the “base forces” as the fundamental unknowns to determine the state of an elastic system, the complementary energy principle for large elastic deformation is constructed for the conjugate quantities being displacement gradients, which possesses exactly the same form as that of classical linear elasticity. It is revealed that the complementary energy contains deformation part and rotation part.

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. Hellinger E. Der allgemein Ansatz der Machanik der Kontinua. Encyclopqdia der Mathematischen Wissenschaften, 1914, 4: 602

    Google Scholar 

  2. Reissner E. On a variational theorem for finite elastic deformation. J Math Phys, 1953, 32: 129–135

    MATH  MathSciNet  Google Scholar 

  3. Levinson M. The complementary energy theorem in finite elasticity. J Appl Mech, 1965, 32: 826–828

    MathSciNet  Google Scholar 

  4. Washizu K. Variational Methods in Elasticity and Plasticity. Oxford: Pergamon press, 1968

    MATH  Google Scholar 

  5. Zubov L M. The stationary principle of complementary work in nonlinear theory of elasticity. Prikl Mat Mech, 1970, 34: 228–232

    Article  MATH  Google Scholar 

  6. Koiter W T. On the principle of stationary complementary energy in the nonlinear theory of elasticity. SIAM J Appl Math, 1973, 25: 424–434

    Article  MATH  MathSciNet  Google Scholar 

  7. Ogden R W. A note on variational theorems in non-linear elastostatics. Math Proc Camb Philos Soc, 1975, 77: 609–615

    MATH  MathSciNet  Google Scholar 

  8. Ogden R W. Inequalities associated with the inversion of elastic stress deformation relation and their implications. Math Proc Camb Philos Soc, 1977, 81: 313–324

    Article  MATH  MathSciNet  Google Scholar 

  9. Guo Z H. Non-linear Theory of Elasticity (in Chinese). Beijing: Science Press, 1980. 218–240

    Google Scholar 

  10. Atluri S N. On some new general and complementary energy theorems for the rate problems in finite strain, classical elasticity. J Struct Mech, 1980, 8: 62–91

    Google Scholar 

  11. Gao D Y, Strang G. Geometric nonlinearity: Potential energy, complementary energy and the gap function. Q Appl Math, 1989, 47(3): 487.

    MathSciNet  MATH  Google Scholar 

  12. Gao D Y. Pure complementary energy principle and triality theory in finite elasticity. Mech Res Commun, 1999, 26: 31–37

    Article  MATH  Google Scholar 

  13. Fraeijs de Veubeke B M. A new variational principle for finite elastic displacements. Int J Eng Sci, 1972, 10: 745–763

    Article  MathSciNet  MATH  Google Scholar 

  14. Gao Y C. A new description of stress state at a point with applications. Arch Appl Mech, 2003, 73: 171–183

    Article  MATH  Google Scholar 

  15. Gao Y C, Gao T J. Large deformation contact of a rubber notch with a rigid wedge. Int J Solids Struct, 2000, 37: 4319–4334

    Article  MATH  Google Scholar 

  16. Gao Y C. Asymptotic analysis of the nonlinear Boussinesq problem for a kind of incompressible rubber material (compression case). J Elast, 2001, 64: 111–130

    Article  MATH  Google Scholar 

  17. Gao Y C. Foundation of Solid Mechanics (in Chinese). Beijing: Railway Publisher of China, 1999

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Gao, Y. Complementary energy principle for large elastic deformation. SCI CHINA SER G 49, 341–356 (2006). https://doi.org/10.1007/s11433-006-0341-7

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11433-006-0341-7

Keywords

Navigation