GBTUL 2.0 – A Second-Generation Code for GBT-Based Buckling and Vibration Analysis of Thin-Walled Members

Bebiano, Rui; Camotim, Dinar; Gonçalves, Rodrigo

doi:10.3850/978-981-07-7137-9_119

Cited by 28 publications

(47 citation statements)

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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

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“…The numerical illustrative examples presented and discussed in the next subsections concern cold-formed steel lipped channel columns with the cross-section dimensions given in Figure 2 employing either "analytical solutions" ("AS"), conventional GBT-based finite elements ("CE") or exact GBTbased elements ("EE"), with the objective of comparing the three sets of results -note that the first two sets of results are obtained by means of program GBTUL [24], while the last one stems from a FORTRAN code written specifically to implement the "EE" approach.…”

Section: Illustrative Examplesmentioning

confidence: 99%

“…For the discretisation considered (involving 15 nodes), a total of = 3 × 15 = 45 deformation modes are obtained  the in-plane or out-of-plane configurations of the most relevant ones are depicted in Figure 3. They comprise: (i) the four classical rigid-body (or "global") modes (axial extension (1), major-and minor-axis bending (2-3) and torsion (4)), (ii) two distortional modes, associated with quasi-rigid body flange-lip motions (5-6), (iii) a sequence of local modes, involving transverse plate bending with increasing curvature (7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17), (iv) five global shear modes (18)(19)(20)(21)(22), consisting of the warping components of the Vlasov modes 2-6, (v) a set of local shear modes, (23)(24)(25)(26)(27)(28)(29)(30)(31), (vi) five global transverse extension modes (32)(33)(34)(35)(36) and (vii) the local transverse extension modes (37-45).…”

Section: Cross-section Analysismentioning

confidence: 99%

“…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. Recently, the second version of GBTUL [24], a GBT-based freeware code which performs linear buckling and vibration analyses of general thin-walled bars, has been released online [25].…”

Section: Introductionmentioning

confidence: 99%

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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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“…In Section 5 trigonometric solutions of the eigenvalue problem are considered. Finally Section 6 is devoted to illustrative examples including development of classic buckling curves and comparison of results with finite element results found using Abaqus, [20], as well as with FSM and conventional GBT results found using the freely available software packages CUFSM and GBTUL, see [21] and [22].…”

Section: Introductionmentioning

confidence: 99%

Distortional buckling modes of semi-discretized thin-walled columns

Andreassen¹,

Jönsson²

2012

Thin-Walled Structures

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This paper presents distorting buckling solutions for semi-discretized thin-walled columns using the coupled differential equations of a Generalized Beam Theory (GBT). In two related papers recently published by the authors a novel semi-discretization approach to GBT has been presented. The cross section is discretized and analytical solutions are sought for the variation along the beam. With this new approach the general GBT equations for identification of a full set of deformation modes corresponding to both homogeneous and non-homogenous equations are formulated and solved. Thereby giving the (complex) deformation modes of GBT which decouple the state space equations corresponding to the reduced order differential equations.In this paper the developed semi-discretization approach to Generalized Beam Theory (GBT) is extended to include the geometrical stiffness terms, which are needed for column buckling analysis and identification of buckling modes. The extension is based on an initial stress approach by addition of the related potential energy terms. The potential energy of a single deformation mode is formulated based on a discretization of the cross section. Through variations in the potential energy and the introduction of the constraints related to beam theory this leads to a modified set of coupled homogeneous differential equations of GBT with initial stress for identification of distortional displacement modes. In this paper we seek instability solutions using these GBT initial stress equations for simply supported columns with constrained transverse displacements at the end sections and a constant axial initial stress. Based on the known boundary conditions the reduced order differential equations are solved by using the trigonometric solution functions and solving the related eigenvalue problem. This gives the buckling mode shapes and the associated eigenvalues corresponding to the bifurcation load factors. Thus the buckling modes are found directly by the analytical solution of the coupled GBT-equations without modal decomposition. Illustrative examples showing global column buckling, distortional buckling and local buckling are given and it is shown how the novel approach may be used to develop signature curves and elastic buckling curves. In order to assess the accuracy of the method some of the results are compared to results found using the commercial FE program Abaqus as well as the conventional GBT and FSM methods using the software packages GBTUL and CUFSM.

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GBTUL 2.0 – A Second-Generation Code for GBT-Based Buckling and Vibration Analysis of Thin-Walled Members

Cited by 28 publications

References 0 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

Distortional buckling modes of semi-discretized thin-walled columns

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