Mechanical Modeling and General Analytical Solution for the Dynamic Buckling of Plane Structures Using a Beam-Column Element with Varying End Restraints

Aissam Beldjazia, Redouane Adman, Adel Slimani, Messaoud Saidani, Toufik Belaid, Fatiha Ammari

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)
111 Downloads (Pure)


The stability of structures is an important aspect that the designer must pay particular attention to in order to ensure safety against collapse. This investigation is concerned with analytical and numerical analyses of the dynamic buckling of plane structures. A rigorous mechanical model is proposed, consisting of a beam-column element with nodal ends possessing two rotational springs of rigidities acting in parallel with the bending stiffness of the beam-column. The model is first analyzed with respect to the dynamic behavior by investigating the influence of the variation in the stiffness of the nodal springs on the fundamental frequency of the proposed mechanical model. Compression axial loading is applied to the beam-column in order to study the nonlinear dynamic behavior by introducing buckling. This novel approach is used to highlight the interaction between the fundamental frequency and the critical buckling load. Simple examples are treated using the approach and the results are compared with those obtained from a global analysis. The results revealed that it is possible to reproduce the stability analysis of a global structure by simply analyzing a target element, taking into account all elements adjacent to it with less than 1% error on the results.

Original languageEnglish
Article number2250019
Number of pages23
JournalInternational Journal of Structural Stability and Dynamics
Issue number2
Early online date23 Oct 2021
Publication statusPublished - 22 Feb 2022

Bibliographical note

Electronic version of an article published in International Journal of Structural Stability and Dynamics, vol. 22, no. 2, 2250019. 10.1142/S0219455422500195 © copyright World Scientific Publishing Company

Copyright © and Moral Rights are retained by the author(s) and/ or other copyright owners. A copy can be downloaded for personal non-commercial research or study, without prior permission or charge. This item cannot be reproduced or quoted extensively from without first obtaining permission in writing from the copyright holder(s). The content must not be changed in any way or sold commercially in any format or medium without the formal permission of the copyright holders.


  • Stability domain
  • beam-column
  • dynamic buckling
  • lateral vibration
  • semi-rigid connection

ASJC Scopus subject areas

  • Civil and Structural Engineering
  • Building and Construction
  • Aerospace Engineering
  • Ocean Engineering
  • Mechanical Engineering
  • Applied Mathematics


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