A novel straightforward dynamic approach for the evaluation of extensional modes within GBT ‘cross-section analysys’

Ferrarotti, Alberto; Piccardo, Giuseppe; Luongo, Angelo

doi:10.1016/j.tws.2017.01.001

Cited by 7 publications

(5 citation statements)

References 35 publications

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“…The newly introduced material constants A 1i , A 2i , H 1i , and H 2i affect the deformation of the crosssection. The constraint (20b) still can be employed with the Lagrange multipliers or substituted with an equivalent term in the energy (48), involving the change of the angle between e i and m i respect to π/2, like this: It is worthy to remark that many other kinds of generalization may be done; for example, one can think about generalized beam theory (GBT) (Ferrarotti et al 2017;Eugster 2015;Piccardo et al 2014).…”

Section: A Generalization To An Orthotropic Rod With Poisson's Effectmentioning

confidence: 99%

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A discrete formulation of Kirchhoff rods in large-motion dynamics

Giorgio¹

2020

Mathematics and Mechanics of Solids

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A nonlinear model for the dynamics of a Kirchhoff rod in the three-dimensional space is developed in the framework of a discrete elastic theory. The formulation avoids the use of Euler angles for the orientation of the rod cross-sections to provide a computationally singularity-free parameterization of rotations along the motion trajectories. The material directions related to the principal axes of the cross-sections are specified using auxiliary points that must satisfy constraints enforced by the Lagrange multipliers method. A generalization of this approach is presented to take into account Poisson’s effect in an orthotropic rod. Numerical simulations are performed to test the presented formulation.

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Section: A Generalization To An Orthotropic Rod With Poisson's Effectmentioning

confidence: 99%

“…It is worth remarking that many other kinds of generalization may be done; for example, one can think about generalized beam theory (GBT) [27][28][29].…”

Section: A Generalization To An Orthotropic Rod With Poisson's Effectmentioning

confidence: 99%

A discrete formulation of Kirchhoff rods in large-motion dynamics

Giorgio¹

2020

Mathematics and Mechanics of Solids

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“…Having found the in-plane deformation modes, at the next stage the third trial function W j (s) is determined. This represents the component relevant to the out-of-plane warping of the cross-section and it is consistently evaluated by integration of Equation (24). The emerging unknown integration constant is obtained by imposing the orthogonality condition of W j (s) to the uniform axial extension, i.e., γ W j (s)ds = 0.…”

Section: Trial Functions and Vlasov's Constraintsmentioning

confidence: 99%

Generalized Beam Theory for Thin-Walled Beams with Curvilinear Open Cross-Sections

Latalski

Zulli

2020

Applied Sciences

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The use of the Generalized Beam Theory (GBT) is extended to thin-walled beams with curvilinear cross-sections. After defining the kinematic features of the walls, where their curvature is consistently accounted for, the displacement of the points is assumed as linear combination of unknown amplitudes and pre-established trial functions. The latter, and specifically their in-plane components, are chosen as dynamic modes of a curved beam in the shape of the member cross-section. Moreover, the out-of-plane components come from the imposition of the Vlasov internal constraint of shear indeformable middle surface. For a case study of semi-annular cross-section, i.e., constant curvature, the modes are analytically evaluated and the procedure is implemented for two different load conditions. Outcomes are compared to those of a FEM model.

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“…It had in Camotim and its school [23][24][25] a huge impulse in the last two decades, through a series of papers in which the choice of modes (cross-section analysis) and various algorithmic aspects were progressively refined. Luongo, Ranzi, and coworkers [26][27][28][29][30] launched the idea to combine GBT with a dynamic boundary value problem to automatize the cross-sectional analysis. De Miranda et al [31,32] analyzed, in particular, the shear effects.…”

Section: Introductionmentioning

confidence: 99%

A Minimal GBT Model for Distortional-Twist Elastic Analysis of Box-Girder Bridges

Pancella

Luongo

2021

Applied Sciences

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A simple and efficient method is proposed for the analysis of twist of rectangular box-girder bridges, which undergo distortion of the cross section. The model is developed in the framework of the Generalized Beam Theory and oriented towards semi-analytical solutions. Accordingly, only two modes are accounted for: (i) the torsional mode, in which the box-girder behaves as a Vlasov beam under nonuniform torsion, and, (ii) a distortional mode, in which the cross section behaves as a planar frame experiencing skew-symmetric displacements. By following a variational approach, two coupled, fourth-order differential equations in the modulating amplitudes are obtained. The order of magnitude of the different terms is analyzed, and further reduced models are proposed. A sample system, taken from the literature, is considered, for which generalized displacement and stress fields are evaluated. Both a Fourier solution for the coupled problem and a closed-form solution for the uncoupled problem are carried out, and the results are compared. Finally, the model is validated against finite element analyses.

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A novel straightforward dynamic approach for the evaluation of extensional modes within GBT ‘cross-section analysys’

Cited by 7 publications

References 35 publications

A discrete formulation of Kirchhoff rods in large-motion dynamics

A discrete formulation of Kirchhoff rods in large-motion dynamics

Generalized Beam Theory for Thin-Walled Beams with Curvilinear Open Cross-Sections

A Minimal GBT Model for Distortional-Twist Elastic Analysis of Box-Girder Bridges

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