Skip to main content

Perturbation procedures in nonlinear finite element structural analysis

Lectures

Part of the Lecture Notes in Mathematics book series (LNM,volume 461)

Keywords

  • Limit Point
  • Perturbation Method
  • Bifurcation Point
  • Load Parameter
  • Tangent Stiffness

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.

This is a preview of subscription content, access via your institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   34.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   46.00
Price excludes VAT (Canada)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Stoker, J. J. Nonlinear Vibrations. Interscience Publ., N.Y., 1950.

    MATH  Google Scholar 

  2. Linstedt, A. Differentialgliechungen der Storungs Theorie. Mem. Acad. Sci. St. Petersburg, Vol. XXXI, 1883.

    Google Scholar 

  3. Bellman, R. Perturbation Techniques in Mathematics, Physics, and Engineering. Holt, Rhinehart, and Winston, N.Y., 1964.

    MATH  Google Scholar 

  4. Nayfeh, A. Perturbation Methods. J. Wiley, N.Y., 1974.

    Google Scholar 

  5. Koiter, W. T. On the Stability of Elastic Equilibrium. Ph.D. Thesis, Dalft, 1945. (Published as AFFDL-TR-70-25, U.S. Air Force Flight Dynamics Lab., Dayton, Ohio).

    Google Scholar 

  6. Thompson, J. M. T. “Discrete Branching Points in the General Theory of Elastic Stability”, J. Mech. Phys. Solids. V, 13, 1965, p. 295.

    CrossRef  Google Scholar 

  7. Sewell, M. J. “A General Theory of Equilibrium Paths Through Critical Points”, Proc. Royal Soc. A. 306, 1968, pp. 201–223.

    CrossRef  Google Scholar 

  8. Croll, J. G. and Walker, A. Elements of Structural Stability. Macmillan Publ., London, 1972.

    Google Scholar 

  9. Thompson, J. M. T. and Hunt, G. W. A General Theory of Elastic Stability, J. Wiley Publ., Ltd., London, 1973.

    MATH  Google Scholar 

  10. Hangai, Y. and Kawamata, S. “Perturbation Method in the Analysis of Geometrically Nonlinear and Stability Problems” in Advances in Computational Methods in Structural Mechanics and Design, J. T. Oden, et al (eds.). UAH Press, The University of Alabama in Huntsville, 1972, pp. 473–492.

    Google Scholar 

  11. Hangai, Y. and Kawamata, S. “Analysis of Geometrically Nonlinear and Stability Problems by Static Perturbation Method”, Report of the Institute of Industrial Science, The University of Tokyo, V. 22, No. 5, Jan. 1973.

    Google Scholar 

    Google Scholar 

  12. Connor, J. J. and Morin, N. “Perturbation Techniques in the Analysis of Geometrically Non-linear Shells” in High Speed Computing of Elastic Structures, B. Fraeujs de Veubeke, ed., University of Liege, 1971, Tome 2, pp. 683–706.

    Google Scholar 

  13. Mau, S. T. and Gallagher, R. H. A Finite Element Procedure for Nonlinear Prebuckling and Initial Postbuckling Analysis. NASA CR-1936, Jan. 1972.

    Google Scholar 

  14. Gallagher, R. H., Lien, S., and Mau, S. T. “Finite Element Plate and Shell Pre-and Post-Buckling Analysis”, Proc. of Third Conference on Matrix Methods in Structural Mechanics, Dayton, Ohio, 1971.

    Google Scholar 

  15. Hofmeister, L. D., Greenbaum, G., and Evenson, D. “Large Strain, Elastic Plastic Finite Element Analysis”, AIAA J., V. 9, No. 7, July, 1971, pp. 1248–1254.

    CrossRef  MATH  Google Scholar 

  16. Gallagher, R. H. and Thomas, G. R. “The Finite Element Method in Plate and Shell Instability Analysis”, Proc. 4th Australasian Conf. on the Mechanics of Structures and Materials, Brisbane, Aug. 1973.

    Google Scholar 

  17. Haisler, W., Stricklin, J. A., and Stebbins, F. “Development and Evaluation of Solution Procedures for Geometrically Nonlinear Structural Analysis”, AIAA J., V. 10, No. 3, Mar. 1972, pp. 264–272.

    CrossRef  MATH  Google Scholar 

  18. Mallett, R. H. and Haftka, R. T. “Progress in Nonlinear Finite Element Analysis using Asympototic Solution Techniques”, in Advances in Computational Methods in Structural Mechanics and Design, J. T. Oden, et al. (Eds.), UAH Press, The University of Alabama in Huntsville, 1972, pp. 357–374.

    Google Scholar 

  19. Butterworth, J. W. “Numerical Post-Buckling Analysis”, Ch. 8 in Structural Instability, W. J. Supple (Ed.), IPC Science and Technology Press, Guildford, Surrey, U.K., 1973.

    Google Scholar 

  20. Lang, T. E. and Hartz, B. J. Finite Element “Matrix Formulation of Post-Buckling Stability and Imperfection Sensitivity” in High Speed Computing of Elastic Structures, B. Fraeijs de Veubeke (Ed.), University of Liege, 1971, Tome 2, pp. 727–758.

    Google Scholar 

  21. Ecer, A. “Finite Element Analysis of the Postbuckling Behavior of Structures”, AIAA J., V. 11, Nov. 1973, pp. 1532–1538.

    CrossRef  MATH  Google Scholar 

  22. Endo, A., Kawamata, S., and Hangai, Y., “Post-Bifurcation Analysis of Shallow Spherical Shells Under Uniform Pressure”, Seisan-Kenkyu, Institute of Industrial Science, University of Tokyo, V. 26, No. 10, Oct. 1974.

    Google Scholar 

    Google Scholar 

  23. Haftka, R. T., Mallett, R. H., and Nachbar, W. A Koiter-Type Method for Finite Element Analysis of Nonlinear Structural Behavior, AFFDL TR 70-130, V. 1, Nov. 1970.

    Google Scholar 

  24. Thompson, J. M. T. and Walker, A. C. “The Non-Linear Perturbation Analysis of Discrete Structural Systems,” Int. J. Solids Struct., V. 4, 1968, pp. 757–768.

    CrossRef  MATH  Google Scholar 

Download references

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and Permissions

Copyright information

© 1975 Springer-Verlag

About this paper

Cite this paper

Gallagher, R.H. (1975). Perturbation procedures in nonlinear finite element structural analysis. In: Oden, J.T. (eds) Computational Mechanics. Lecture Notes in Mathematics, vol 461. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0074150

Download citation

  • DOI: https://doi.org/10.1007/BFb0074150

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-07169-3

  • Online ISBN: 978-3-540-37503-6

  • eBook Packages: Springer Book Archive