GBT-Based Buckling Analysis Using the Exact Element Method

Rui Bebiano, Moshe Eisenberger, Dinar Camotim, Rodrigo Gonçalves

Research output: Contribution to journalArticle

5 Citations (Scopus)

Abstract

Generalized Beam Theory (GBT), intended to analyze the structural behavior of prismatic thin-walled members and structural systems, expresses the member 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. This paper presents the formulation, implementation and application of the so-called "exact element method" in the framework of GBT-based linear buckling analyses. This method, originally proposed by Eisenberger (1990), uses the power series method to solve the governing differential equation and obtains the buckling eigenvalue problem from the boundary terms. A few illustrative numerical 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 shows that the GBT-based exact element method may lead to significant computational savings, particularly when the buckling modes exhibit larger half-wave numbers.

Original languageEnglish
Article number1750125
JournalInternational Journal of Structural Stability and Dynamics
Volume17
Issue number10
DOIs
Publication statusPublished - 1 Dec 2017

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Buckling
Finite Element
Differential equations
Power series
Eigenvalue Problem
Governing equation
Cross section
Express
Differential equation
Numerical Examples
Configuration
Formulation
Term

Keywords

  • exact element method
  • generalized beam theory (GBT)
  • linear buckling
  • power series solution
  • Thin-walled members

Cite this

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abstract = "Generalized Beam Theory (GBT), intended to analyze the structural behavior of prismatic thin-walled members and structural systems, expresses the member 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. This paper presents the formulation, implementation and application of the so-called {"}exact element method{"} in the framework of GBT-based linear buckling analyses. This method, originally proposed by Eisenberger (1990), uses the power series method to solve the governing differential equation and obtains the buckling eigenvalue problem from the boundary terms. A few illustrative numerical 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 shows that the GBT-based exact element method may lead to significant computational savings, particularly when the buckling modes exhibit larger half-wave numbers.",
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GBT-Based Buckling Analysis Using the Exact Element Method. / Bebiano, Rui; Eisenberger, Moshe; Camotim, Dinar; Gonçalves, Rodrigo.

In: International Journal of Structural Stability and Dynamics, Vol. 17, No. 10, 1750125, 01.12.2017.

Research output: Contribution to journalArticle

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