GBT-based buckling analysis using the exact element method

Rui Bebiano, Moshe Eisenberger, Dinar Camotim, Rodrigo de Moura Gonçalves

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review


Generalised Beam Theory (GBT), intended to analyse the structural behaviour of prismatic thin-walled
members and structural systems, expresses the member local and/or global deformed configuration as a
combination of cross-section deformation modes multiplied by the corresponding longitudinal amplitude
functions. The determination of the latter, usually the most computer-intensive step of the analysis, is almost
always performed by means of GBT-based conventional 1D (beam) finite elements, using Hermite cubic
polynomials as shape functions. This paper presents the formulation, implementation and application of
a new GBT-based exact element, developed in the context of member (linear) buckling analyses. This exact
element, originally proposed by Eisenberger (1990), approximates the modal longitudinal amplitude
functions by means of power series, whose coefficients are obtained by means of a recursive formula –
since the higher-order coefficients tend to vanish, the method has the potential to become exact (up to computer precision). The buckling load parameters are the solutions of the (highly) non-linear characteristic equation associated with the buckling eigenvalue problem. A few numerical illustrative examples are presented, focusing mainly on the comparison between the combined accuracy and computational effort associated with the determination of buckling solutions with the exact and standard GBT-based (finite) elements. This comparison provides evidence that the exact element leads to equally accurate results with less degrees of freedom and, moreover, without the need to define a (longitudinal) mesh the relative efficiency of the exact element is higher when the buckling modes exhibit larger half-wave numbers.
Original languageEnglish
Title of host publicationProceedings of the Coupled Instabilities in Metal Structures Conference
Number of pages24
Publication statusPublished - 2016
EventCoupled Instabilities in Metal Structures Conference 2016 - Baltimore, United States
Duration: 7 Nov 20168 Nov 2016

Publication series

NameInternational Journal of Structural Stability and Dynamics
PublisherWorld Scientific Publishing Co. Pte Ltd
ISSN (Print)0219-4554


ConferenceCoupled Instabilities in Metal Structures Conference 2016
CountryUnited States


Dive into the research topics of 'GBT-based buckling analysis using the exact element method'. Together they form a unique fingerprint.

Cite this