Non-linear flexural–torsional dynamic analysis of beams of arbitrary cross section by BEM

Sapountzakis, E. J.; Dikaros, I. C.

doi:10.1016/j.ijnonlinmec.2011.02.012

Cited by 20 publications

(8 citation statements)

References 29 publications

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“…In [10], an elastic non-uniform torsion analysis of simply or multiply connected cylindrical bars with arbitrary cross-sections accounts for the effect of geometric non-linearity in the framework of the boundary-element method. In [11], the effect of rotary and warping inertia is considered. Nonlinear torsional vibrations of thin-walled beams, exhibiting primary and secondary warping, are investigated in [12].…”

Section: Introductionmentioning

confidence: 99%

Second-order torsional warping theory considering the secondary torsion-moment deformation-effect

Aminbaghai

Muŕın

Balduzzi

et al. 2017

Engineering Structures

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In this paper, the influence of the variable axial force and of the Secondary Torsion-Moment Deformation-Effect (STMDE) on the deformations of beams due to torsional warping is investigated. The investigation is based on the second-order torsional warping theory of doubly symmetric beams with thin-walled open or closed cross-sections. The effect of the axial force on the torsional stiffness of thinwalled beams is considered according to the second-order torsional warping theory. The solutions of the underlying differential equations are used for setting up the relations, needed for application of the transfer matrix method. They are derived, considering both static and dynamic action. This enables stablishing the local

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Section: Introductionmentioning

confidence: 99%

Second-order torsional warping theory considering the secondary torsion-moment deformation-effect

Aminbaghai

Muŕın

Balduzzi

et al. 2017

Engineering Structures

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“…Minghini et al [38] take into account shear strain effects due to both nonuniform bending and torsion in the analysis of thin walled cross sections. Some other researchers have employed the nonuniform torsion theory for beams with arbitrarily shaped cross sections with the rate of the angle of twist as an additional degree of freedom [39][40][41][42][43][44][45][46].Sapountzakis and Tsipiras [47] have taken into account nonouniform torsion in the analysis of beam with arbitrarily shaped doubly symmetric cross sections using a secondary warping function. On the other hand Li et al [48] developed an element that includes the effect of warping using a displacement field that is assumed to be cubic in the axial direction and quadratic in the transverse direction.…”

Section: Introductionmentioning

confidence: 99%

Generalized Warping Effect in the Dynamic Analysis of Beams of Arbitrary Cross Section

Dikaros¹,

Sapountzakis²,

Argyridi³

et al. 2015

Proceedings of the 5th International Conference on Computational Methods in Structural Dynamics and Earthquake Engineering (COM

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“…In [9], Ref. [7] is extended taking the geometrical nonlinearity into account, and in [10], the effect of rotary and warping inertia is implemented. In [11], the nonlinear torsional vibrations of thin-walled beams exhibiting primary and secondary warping are investigated.…”

Section: Introductionmentioning

confidence: 99%

Modelling of Warping Eigenvibration by Non-Uniform Torsion

Muŕın¹,

Aminbaghai²,

Hrabovský³

et al. 2015

Proceedings of the 5th International Conference on Computational Methods in Structural Dynamics and Earthquake Engineering (COM

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Abstract. This contribution contains a novel investigation of the influence of warping of the cross-section of twisted beams on their eigenvibrations. The investigation is based on the analogy of the bending beam theory and the non-uniform torsion theory of thin-walled open INTRODUCTIONBeam structures are often exposed to time-dependent loads. Commercial FEM codes allow performing modal and transient dynamic analysis by 3D beam finite elements with and without consideration of the warping effect. Very often the improved Saint-Venant theory of torsion is used and special mass matrices are proposed. Mostly, the bicurvature is chosen as an additional warping degree of freedom and the secondary torsion moment deformation effect (STMDE) is not considered.For example in [1], the beam element can be used with a lumped or a consistent mass matrix. The consistent mass matrix includes warping effects but does not include the effect of shear deformation. For the standard beam element, the consistent mass matrix is based on reference [2] with the exception that there are additional terms arising from the warping constant  I . For the warping element, lumped masses for the warping degree of freedom (bicurvature) are defined [3]. As stated in [1], for solid and closed thin-walled sections, the standard beam element can be used without significant error. However, for the open thinwalled sections, the warping beam element should be used. In [4], the warping beam finite element is recommended to be used only for open thin walled section beams. In [5], the finite beam element is implemented with unrestrained or restrained warping (BEAM188). In [6], the warping beam finite element can be used only for elastostatic analysis of straight beams. It should be noted that in technical practice as well as in the Eurocodes 3 (EC3) the effect of non-uniform torsion by the steel beams with closed cross-sections is not considered.In the most recent literature relatively little information can be found that refers to the solution for free and forced torsional vibration of beams with hollow cross-sections that include non-uniform torsion effects. In [7], a boundary element method is developed for the nonuniform torsional vibration problem of doubly symmetric composite bars of arbitrary variable cross-section. Dynamic analysis of 3-D beam elements, restrained at their edges, subjected to arbitrarily distributed dynamic loading, is presented in [8]. In [9], Ref. [7] is extended taking the geometrical nonlinearity into account, and in [10], the effect of rotary and warping inertia is implemented. In [11], the nonlinear torsional vibrations of thin-walled beams exhibiting primary and secondary warping are investigated. In [12], a solution for the vibrations of Timoshenko beams by the isogeometric approach is presented, but warping effects are not considered. In [13], geometrically non-linear free and forced vibrations of beams with non-symmetrical cross sections are investigated by the Saint-Venant theory of torsion. In [14], an axial-torsional vi...

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Non-linear flexural–torsional dynamic analysis of beams of arbitrary cross section by BEM

Abstract: In this paper, a boundary element method is developed for the nonlinear flexuraltorsional dynamic analysis of beams of arbitrary, simply or multiply connected,

Cited by 20 publications

References 29 publications

Second-order torsional warping theory considering the secondary torsion-moment deformation-effect

Second-order torsional warping theory considering the secondary torsion-moment deformation-effect

Generalized Warping Effect in the Dynamic Analysis of Beams of Arbitrary Cross Section

Modelling of Warping Eigenvibration by Non-Uniform Torsion

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