A cross-section analysis procedure to rationalise and automate the performance of GBT-based structural analyses

Bebiano, Rui; Gonçalves, Rodrigo; Camotim, Dinar

doi:10.1016/j.tws.2015.02.017

Cited by 109 publications

(34 citation statements)

References 26 publications

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“…The GBT cross-section analysis involves a lengthy set of fairly complex operations which has been reported in the literature, with emphasis on the recent works of Gonçalves et al (2014) and Bebiano et al (2015)  the interested reader can find detailed acounts in these references, which provide the fundamentals of the procedure implemented in version 2.0 of code GBTUL (Bebiano et al 2016). The deformation modes obtained can be divided into three main sets/families, namely the (i) conventional (or Vlasov modes), (ii) shear modes and (iii) transverse extensions modes.…”

Section: Cross-section Analysismentioning

confidence: 99%

On the mechanics of local-distortional interaction in thin-walled lipped channel beams

Martins

Camotim

Gonçalves

et al. 2018

Thin-Walled Structures

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This paper investigates the elastic post-buckling behavior of simply supported thin-walled lipped channel beams undergoing local-distortional (L-D) interaction. The beams are uniformly bent about the major-axis and experience flange-triggered local buckling (most common situation in practice). Three beams are analyzed, each exhibiting a different type of L-D interaction, namely (i) "true L-D interaction" (close local and distortional critical buckling moments), (ii1) "secondary local-bifurcation interaction" and (ii2) "secondary distortional-bifurcation interaction" (critical distortional/local buckling moments and high enough yield stresses). The results presented and discussed are obtained through geometrically non-linear Generalized Beam Theory (GBT) analyses and provide the evolution, along given equilibrium paths, of the beam deformed configuration (expressed in GBT modal form) and relevant displacement profiles, making it possible to acquire in-depth knowledge on the beam L-D interaction mechanics. Particular attention is devoted to interpreting the quantitative and qualitative differences exhibited by the beam post-buckling behaviors associated with the three aforementioned L-D interaction types.

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Section: Cross-section Analysismentioning

confidence: 99%

On the mechanics of local-distortional interaction in thin-walled lipped channel beams

Martins

Camotim

Gonçalves

et al. 2018

Thin-Walled Structures

View full text Add to dashboard Cite

show abstract

“…This work is based on a recently developed version of this procedure, applicable to arbitrary flat-walled members and described in detail in [6][7]  therefore, only a very brief overview is provided here.…”

Section: Cross-section Analysismentioning

confidence: 99%

“…It is necessary to begin by defining the cross-section nodal discretisation, which involves (i) natural internal nodes, (ii) natural end nodes and (iii) intermediate nodes [7]  while the first two sets of nodes are compulsory, the last one is optional and user-defined 9 . Three elementary deformation modes are associated with each node, leading to a total of = 3 × elementary modes.…”

Section: Cross-section Analysismentioning

confidence: 99%

“…Recent progress concerning the cross-section analysis has made GBT applicable in the context of members exhibiting arbitrary flat-walled cross-sections [6][7] or circular/elliptical tubular cross-sections [8][9][10]. Concerning the member analysis, formulations/studies have been reported for various types of structural analysis, namely first-order [11,12], buckling [3,[13][14][15][16], vibration [17][18][19], post-buckling [20][21][22] and dynamic [23] analyses involving elastic members (mostly), frames and trusses.…”

Section: Introductionmentioning

confidence: 99%

“…This finite element is based on the technique originally developed by Eisenberger (e.g., [28][29][30]) and already successfully employed to solve firstorder [31][32], buckling [33][34] and vibration [35][36]) problems involving prismatic and tapered thin-walled members 7 . The exact element is employed to solve GBT fourth order differential equilibrium equation system and associated boundary conditions, characterising the strong formulation of the buckling eigenvalue problem.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

GBT-Based Buckling Analysis Using the Exact Element Method

Bebiano

Eisenberger

Camotim

et al. 2017

Int. J. Str. Stab. Dyn.

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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 , approximates the modal longitudinal amplitude functions by means of power series, whose coefficients are obtained by means of a recursive formulasince 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.

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Combining Shell and GBT‐based Finite Elements – the Best of Both Worlds?

Manta¹,

Gonçalves²,

Camotim³

2022

ce papers

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A general and efficient approach to model thin‐walled members and frames with complex geometries (including tapered and perforated members) is proposed, combining standard shell and GBT‐based (beam) finite elements. Each element type is employed where it is most effective: (i) shell elements in plastic and geometrically complex zones, and (ii) GBT elements in prismatic and elastic zones. After providing a brief overview of the finite elements employed, several illustrative numerical examples are presented and discussed, in order to show the capabilities and potential of the proposed approach – they concern linear static, bifurcation (linear stability – calculation of buckling loadings and mode shapes), vibration (calculation of natural frequencies and vibration mode shapes), dynamic and first‐order plastic zone analyses. These numerical examples involve members with tapered segments and/or perforations and frames with complex joint geometries. For validation and comparison purposes, full shell finite element results are provided – in all cases, an excellent match is obtained.

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A cross-section analysis procedure to rationalise and automate the performance of GBT-based structural analyses

Cited by 109 publications

References 26 publications

On the mechanics of local-distortional interaction in thin-walled lipped channel beams

On the mechanics of local-distortional interaction in thin-walled lipped channel beams

GBT-Based Buckling Analysis Using the Exact Element Method

Combining Shell and GBT‐based Finite Elements – the Best of Both Worlds?

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