Skip to main content
SpringerLink
Log in

Fundamental equations of large spatial deflection problems of rods and its application to drilling engineering

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

Abstract

The fundamental equations for analysis of a straight slender rod which deform at large deflections of order of several times of the dimension of the cross section of the rod are derived by using convected coordinate system. In accordance with the practice of oil drilling, an effective method of three dimensional static analysis of bottom-hole assemblies is simply described. Errors in reference [8] are pointed out.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Naghdi, P. M. and M. B. Rubin, On the significance of normal cross-sectional extension in beam theory with application to contact problems,Int. J. Solids Structures,25, 3 (1989).

    Google Scholar 

  2. Saje, M., A variational principle for finite planar deformation of straight slender elastic beams,Int. J. Solids Structures,26, 8 (1990).

    Article  MATH  Google Scholar 

  3. Iwakuma, T., Timoshenko beam theory with extension effect and its stiffness equation for finite rotation,Comput. Struct.,34, 2 (1990).

    MATH  Google Scholar 

  4. Cardona, A., Beam finite element nonlinear theory with finite rotations,Int. J. Numer. Methods Eng.,26, 11 (1988).

    Article  MATH  MathSciNet  Google Scholar 

  5. Argyris, J. H., P. C. Dunne and D. W. Scharpf, On large displacement small strain analysis of structures with rotational degrees of freedom,Computer Methods in Applied Mechanics and Engineering,14 (1978).

  6. Bathe, K. J. and S. Bolourch, Large displacement analysis of three-dimensional beam structures,Int. J. Numerical Methods in Engineering,14 (1979).

  7. Bathe, K. J. and S. Mijailovich, Finite element analysis of frictional contact problems,J. Theoretical and Applied Mechanics,17 (1988).

  8. Walker, B. H. and M. B. Friedman, Three-dimensional, force and deflection analysis of a variable cross section drill-string.J. Pressure Vessel Technology,99, 2 (1977).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Tianjin University, Tianjin

    Cai Zong-xi

Authors
  1. Cai Zong-xi
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Communicated by Zhao Zhu-wu

Rights and permissions

Reprints and permissions

About this article

Cite this article

Zong-xi, C. Fundamental equations of large spatial deflection problems of rods and its application to drilling engineering. Appl Math Mech 14, 1103–1111 (1993). https://doi.org/10.1007/BF02456648

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02456648

Key words

Search

Navigation