A new 3D Timoshenko finite beam element including non-uniform torsion of open and closed cross sections

Muŕın, Just́ın; Aminbaghai, Mehdi; Kutiš, Vladimı́r; Kralovic, V.; Sedlár, Tibor; Goga, Vladimír; Mang, Herbert A.

doi:10.1016/j.engstruct.2013.10.036

Cited by 28 publications

(33 citation statements)

References 10 publications

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“…This fact was yet also experimentally proved by elastostatic torsional loading of hollow section beams [17]. It was also shown that the effect of the secondary torsion moment has to be taken into account especially by closed-section beams.…”

Section: Introductionmentioning

confidence: 78%

“…It is seen that the cross-section satisfies the deformation conditions for nonuniform torsion of thin-walled cross-sections, as given by the thin tube theory (TTT). The torsional eigenmodes can be evaluated by means of the transfer relations (17), but the graphical representation is quite cumbersome (as it is also the case for the beam finite elements). This problem will be treated in our future work.…”

Section: Cantilever Beam With An I Cross-sectionmentioning

confidence: 99%

“…As follows from the above overview of research papers on the area of nonuniform torsion and of the papers [16], [17], [18], the effect of warping should be considered also by torsion of closed thin-walled section beams. This fact was yet also experimentally proved by elastostatic torsional loading of hollow section beams [17].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

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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Section: Introductionmentioning

confidence: 78%

Section: Cantilever Beam With An I Cross-sectionmentioning

confidence: 99%

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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

View full text Add to dashboard Cite

show abstract

“…Beam models based on a cross-section discretization that considers warping functions of thin-walled cross-sections were presented in Laudiero [29], Razaqpur and Li [41], Prokić [37], Razaqpur and Li [42], Prokić [38,39], Kim and Kim [25], Prokić [40], Kim and Kim [26], Saadé et al [44]. A new finite beam model for the analysis of non-uniform torsion of beams that considers the cross-section warping through an additional degree of freedom and includes secondary torsional phenomena and shear effects has been proposed in Murin [34]. An alternative procedure, cast within the boundary element method, for the analysis of nonuniform torsion of bars considering secondary warping was put forward in Tsipiras [50], Sapountzakis et al [45], Dikaros et al [11].…”

Section: Introductionmentioning

confidence: 97%

A higher order beam model for thin-walled structures with in-plane rigid cross-sections

Vieira

Virtuoso

Pereira

2015

Engineering Structures

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“…And some other researchers mainly devoted themselves to studying the response [9][10][11][12][13][14] of the beams, consisting of different materials, under special load and their fatigue behavior [15], etc. In addition, some scholars have put forward some methods, based on the displacement monitoring, that can be good for obtaining the internal force of different engineering structures [16], and someone even proposed a new finite element model of beam [17]. Although beams have been deeply studied, scholars always concentrate more on special beams, such as concrete-filled steel plate composite coupling beams [18], tapered thin-walled box beams [19], steel-concrete composite beams [20] and corbels [21], rather than SBWCCS.…”

Section: Introductionmentioning

confidence: 99%

An Improved Method for Calculating Bending Moment and Shearing Force of Beam in Numerical Modelling

Yuan

Wang

et al. 2018

Teh. vjesn.

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Abstract:In view of the problem that it is difficult to obtain the displacement, internal force and damage status from one beam model established in most numerical analysis models, an improved method for calculating bending moment and shearing force is presented in this paper, which can change this situation. This method portrays how to obtain the internal force from model established using 3-D solid element which can be able to show the failure process easily. The research results are as follows:(1) Deflection equation of beam established using 3-D solid element can be fitted by extracting displacement value of each node on the axis, thus bending moment and shearing force value can be directly figured out by putting the equation of deflection curve into approximately differential equation of deflection curve. (2) The reliability of the results calculated in this method would be easily affected by force, shape of cross section and the highest degree of polynomial, etc. When the beam is in a state of small deformation and the highest degree of polynomial is kept between 20 and 30, the results will be more reliable, besides, beam model whose shape of the cross section is rectangular is more suitable for the method than the circular one. (3) This method can always be applied to beam model, no matter its constraint conditions and loading conditions are complex or not.

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A new 3D Timoshenko finite beam element including non-uniform torsion of open and closed cross sections

Cited by 28 publications

References 10 publications

Modelling of Warping Eigenvibration by Non-Uniform Torsion

Modelling of Warping Eigenvibration by Non-Uniform Torsion

A higher order beam model for thin-walled structures with in-plane rigid cross-sections

An Improved Method for Calculating Bending Moment and Shearing Force of Beam in Numerical Modelling

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