Skip to main content
SpringerLink
Log in

On an optimization problem for elastic rods

  • Research Paper
  • Published:
Structural and Multidisciplinary Optimization Aims and scope Submit manuscript

Abstract

Optimal shape of an elastic rod loaded by extensional force is determined. It is assumed that the rod is described by a classical Bernoulli–Euler rod theory. The optimality conditions are obtained by using Pontriyagin's maximum principle. It is shown that the optimal shape (cross-sectional area as a function of an arc length) is determined from the solution of a nonlinear second-order differential equation. The solution of this equation is given in the closed form. It is shown that for the same buckling force, the savings of the material are of the order of 30%. An interesting feature of the problem is that for certain values of parameters, there is no optimal solution.

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

  • Alekseev VM, Tihomirov VM, Fomin SV (1979) Optimal control. Nauka, Moscow (in Russian)

  • Antman SS (1995) Nonlinear problems of elasticity. Springer, Berlin Heidelberg New York

    MATH  Google Scholar 

  • Atanackovic TM (1997) Stability theory of elastic rods. World Scientific, River Edge, NJ

    MATH  Google Scholar 

  • Atanackovic TM, Djukic DS (1989) Buckling by extension: stability boundary and post-critical behavior. Dyn Stab Syst 4:81–94

    MathSciNet  MATH  Google Scholar 

  • Atanackovic TM, Djukic DS, Strauss AM (1992) Instability by extension of an extensible elastic column. ZAMM 72:209–218

    Article  MathSciNet  MATH  Google Scholar 

  • Bizeno CB, Grammel R (1953) Technische dynamik. Springer, Berlin Heidelberg New York

    Google Scholar 

  • Chow S-N, Hale JK (1982) Methods of bifurcation theory. Springer, Berlin Heidelberg New York

    MATH  Google Scholar 

  • Greenev VB, Filippov AP (1979) Optimization of rods. Naukova Dumka, Kiev

    Google Scholar 

  • Sage AP, White CC (1977) Optimum control systems. Prentice-Hall, New Jersey

    MATH  Google Scholar 

  • Vujanovic BD, Atanackovic TM (2004) An introduction to modern variational methods in mechanics and engineering. Birkhaüser, Boston, MA

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Faculty of Technical Sciences, University of Novi Sad, 21000, Novi Sad, Serbia

    Z. D. Jelicic & T. M. Atanackovic

Authors
  1. Z. D. Jelicic
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. T. M. Atanackovic
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Jelicic, Z.D., Atanackovic, T.M. On an optimization problem for elastic rods. Struct Multidisc Optim 32, 59–64 (2006). https://doi.org/10.1007/s00158-005-0583-4

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00158-005-0583-4

Keywords

Search

Navigation