Exact solutions for buckling of some divergence-type nonconservative systems in terms of bessel and lommel functions

https://doi.org/10.1016/0045-7825(88)90062-XGet rights and content

Abstract

Closed-form solutions for a divergence-type nonconservative system, that of the column under follower distributed forces, is given for three types of boundary conditions. The solution generalizes the previous classical studies by Pflüger, who found the solution for the column simply supported at its ends in terms of Bessel functions, as well as by Leipholz and Madan, who formulated the series solutions for the column clamped at one end, and simply supported or clamped at the other.

In the present work the solution is formulated in terms of Bessel and Lommel functions, yielding exact characteristics equations, with attendant buckling loads found within any desired numerical accuracy.

References (13)

  • I. Elishakoff et al.

    Axisymmetric buckling of certain composite plates

    Internat. J. Solids and Structures

    (1975)
  • A. Pflüger

    Stabilitätsprobleme der Elastostatik

  • H.H.E. Leipholz

    Die Knicklast des einseitig eingespannten Stabes mit gleichmaesig verteilter, tangentialer Laengsbelastung

    Z. Angew. Math. Phys.

    (1962)
  • Y. Sugiyama et al.

    Studies on nonconservative problems of instability of columns by means of analog computer

  • Y. Sugiyama et al.

    Studies on nonconservative problems of instability of columns by difference methods

  • H.H.E. Leipholz et al.

    On the solution of the stability problem of elastic rods subjected to uniformly distributed, tangetial follower forces

    Ingenieur Arch.

    (1975)
There are more references available in the full text version of this article.

Cited by (0)

On leave from the Technion-Israel Institute of Technology, Haifa 32000, Israel.

View full text