A non-linear model for the dynamics of open cross-section thin-walled beams—Part I: formulation

Egidio, Angelo Di; Luongo, Angelo; Vestroni, Fabrizio

doi:10.1016/s0020-7462(02)00053-7

Cited by 39 publications

(24 citation statements)

References 9 publications

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“…The papers [44][45][46][47][48][49][50][51][52] are specifically devoted to modeling problems of structural interest; the main original results are summarized in the following.…”

Section: Structural Modelingmentioning

confidence: 99%

“…A nonlinear one-dimensional model of a thin-walled beam with generic, non-symmetric open cross-section is developed as an internally constrained three-dimensional continuum [44], subject to axial and shear undeformability. Thanks to cross-section constraints, the warping is expressed in terms of displacements of the shear center by extending the Vlasov theory to the nonlinear field; in particular, the in-plane displacements, which arise as a second-order effect of the out-of-plane classic warping, have been accounted for.…”

Section: Structural Modelingmentioning

confidence: 99%

See 1 more Smart Citation

On the contribution of Angelo Luongo to Mechanics: in honor of his 60th birthday

Piccardo

D’Annibale

Zulli

2014

Continuum Mech. Thermodyn.

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This paper intends to summarize the scientific production of Angelo Luongo on the occasion of his Sixtieth Birthday, focusing on his main contributions in the field of Mechanics. The task will not be easy because of the breadth of his scientific production, only apparently attributable to a restricted number of keywords. In fact, even when the work seems purely algorithmic, speculation on the physical and mechanical aspects of the problem is always present, providing new interpretations and innovative openings to a careful reader. Similarly, also the works, which apparently seem to be high-level applications, always reserve methodological aspects that are not negligible. The editorial choice to divide his papers through a small number of keywords is certainly simplistic, but offers the possibility to better highlight all the connections among his variegated production. The most original contributions of Angelo Luongo in the context of perturbation methods, linear and nonlinear dynamics and control, elastic buckling and structural analysis, bifurcation and stability of non-conservative systems, are discussed in detail. Finally, the Angelo Luongo's central role in the creation and development of activities of the international research center M&MoCS is pointed out.

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“…The papers [44][45][46][47][48][49][50][51][52] are specifically devoted to modeling problems of structural interest; the main original results are summarized in the following.…”

Section: Structural Modelingmentioning

confidence: 99%

Section: Structural Modelingmentioning

confidence: 99%

On the contribution of Angelo Luongo to Mechanics: in honor of his 60th birthday

Piccardo

D’Annibale

Zulli

2014

Continuum Mech. Thermodyn.

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show abstract

“…Pai and Nayfeh in [104][105][106] studied also the nonlinear flexuraltorsional-extensional vibrations of metallic and composite slewing or rotating closed cross section beams, primarily focusing on flexural vibrations and neglecting again the effect of torsional warping. Di Egidio et al in [107,108] presented also a FEM solution to the nonlinear flexuraltorsional vibrations of shear undeformable thin-walled open beams taking into account in-plane and out-of-plane warpings and neglecting warping inertia. In these papers, the torsional-extensional coupling is taken into account but the inextensionality assumption leads to the fact that the axial boundary conditions are not general.…”

Section: Nonlinear Elastic Torsional Vibrations Of Barsmentioning

confidence: 99%

Bars under Torsional Loading: A Generalized Beam Theory Approach

Sapountzakis

2013

ISRN Civil Engineering

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In this paper both the static and dynamic analyses of the geometrically linear or nonlinear, elastic or elastoplastic nonuniform torsion problems of bars of constant or variable arbitrary cross section are presented together with the corresponding research efforts and the conclusions drawn from examined cases with great practical interest. In the presented analyses, the bar is subjected to arbitrarily distributed or concentrated twisting and warping moments along its length, while its edges are supported by the most general torsional boundary conditions. For the dynamic problems, a distributed mass model system is employed taking into account the warping inertia. The analysis of the aforementioned problems is complete by presenting the evaluation of the torsion and warping constants of the bar, its displacement field, its stress resultants together with the torsional shear stresses and the warping normal and shear stresses at any internal point of the bar. Moreover, the construction of the stiffness matrix and the corresponding nodal load vector of a bar of arbitrary cross section taking into account warping effects are presented for the development of a beam element for static and dynamic analyses. Having in mind the disadvantages of the 3D FEM solutions, the importance of the presented beamlike analyses becomes more evident.

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“…In Tatone et al [9], the sensitivity to imperfections for thin-walled beams, where warping is considered, were studied in the case of buckling. In Di Egidio et al [10], a non-linear model of a thin-walled, nonsymmetric open-section beam were studied including both non-linear warping and torsional elongation effects. It was also shown that, in beams with doublesymmetric sections, these two last contributions are negligible.…”

Section: Introductionmentioning

confidence: 99%

“…The initial curvature terms, assumed as uniform, are considered as explicit parameters characterizing the initial configuration. The deformation field, the inertia terms, and then the equations of motion are explicitly derived as function of such parameters, without considering the contributions due to the warping (Di Egidio et al [10]). …”

Section: Introductionmentioning

confidence: 99%

Non-linear dynamics of curved beams. Part 1: Formulation

Zulli¹,

Alaggio²,

Benedettini³

2009

International Journal of Non-Linear Mechanics

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The non-linear dynamics of elastic beams with uniform initial curvature and doublesymmetric cross-section are considered in this work. In particular, the work is divided in two parts. In Part 1, the interest is oriented to the formulation of an accurate model, able to describe the finite dynamics of initially curved beams as to obtain a parameterization of the initial configuration and the weak expression of the equations of motion. To this end, an explicit description of the deformation field and inertia terms is presented. The equations of motion can be used, with slight modifications, for extensible and inextensible, or shear-deformable and shearindeformable, beams. A description of the free dynamics, of the possible classes of motion under a sinusoidally varying shear tip force, and of bifurcation phenomena is presented in Part 2 for a case-study, together with the results of experimental tests on an aluminum prototype.

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A non-linear model for the dynamics of open cross-section thin-walled beams—Part I: formulation

Cited by 39 publications

References 9 publications

On the contribution of Angelo Luongo to Mechanics: in honor of his 60th birthday

On the contribution of Angelo Luongo to Mechanics: in honor of his 60th birthday

Bars under Torsional Loading: A Generalized Beam Theory Approach

Non-linear dynamics of curved beams. Part 1: Formulation

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