Generalized warping effect in the dynamic analysis of beams of arbitrary cross section

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

doi:10.1016/j.jsv.2016.01.022

Cited by 14 publications

(17 citation statements)

References 43 publications

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“…The maximum axial stress caused by the bimoment occurs at the points of action of external torques (except for free ends of beams) and at cross-sections of restrained warping (for example clamped cross-sections). A broad comprehensive overview of the literature dealing with the issue of non-uniform torsion can be found, for example, in [1] and [2]. Recent research results have shown that for non-uniform torsion of beams with closed cross-sections the influence of the Secondary Torsion-Moment Deformation-Effect (STMDE) is particularly significant.…”

Section: Introductionmentioning

confidence: 99%

“…Other very recent aspects in the area of numerical solutions of non-uniform torsion are treated in [20]- [24]. Finally, in [2], a boundary element solution is developed for dynamic analysis, considering warping of beams with arbitrary cross-sections, including shear lag effects due to both flexure and torsion. High accuracy of the results in comparison to the ones obtained by solid finite element solution is obtained.…”

Section: Introductionmentioning

confidence: 99%

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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%

Section: Introductionmentioning

confidence: 99%

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

Aminbaghai

Muŕın

Balduzzi

et al. 2017

Engineering Structures

View full text Add to dashboard Cite

show abstract

“…The actual research results show that for nonuniform torsion of beams with closed cross-sections the impact of the Secondary Torsion Moment Deformation Effect (STMDE) is especially significant [3,9]. It is also shown [10,11], that not only warping, but also a cross-section distortion plays very important role. Consideration of this effect leads to developing of new approaches with definition of more than 7 degrees of freedom in the beam cross-section, what an usual case is.…”

Section: Introductionmentioning

confidence: 98%

“…The warping effect was included through an additional degree of freedom at each nodal point in form of the first derivative of the angle of twist of the cross-section of the beam. Comprehensive overview of the literature dealing with the issue of a non-uniform torsion in elastostatics and elastodynamics of thin-walled beams can be found in the articles [7,8], for example. The actual research results show that for nonuniform torsion of beams with closed cross-sections the impact of the Secondary Torsion Moment Deformation Effect (STMDE) is especially significant [3,9].…”

Section: Introductionmentioning

confidence: 99%

Effect of Non-Uniform Torsion on Elastostatics of a Frame of Hollow Rectangular Cross-Section

Muŕın

Aminbaghai

Goga

et al. 2018

Strojnícky Časopis - Journal of Mechanical Engineering

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In this paper, results of numerical simulations and measurements are presented concerning the nonuniform torsion and bending of an angled members of hollow cross-section. In numerical simulation, our linearelastic 3D Timoshenko warping beam finite element is used, which allows consideration of non-uniform torsion. The finite element is suitable for analysis of spatial structures consisting of beams with constant open and closed cross-sections. The effect of the secondary torsional moment and of the shear forces on the deformation is included in the local finite beam element stiffness matrix. The warping part of the first derivative of the twist angle due to bimoment is considered as an additional degree of freedom at the nodes of the finite elements. Standard beam, shell and solid finite elements are also used in the comparative stress and deformation simulations. Results of the numerical experiments are discussed, compared, and evaluated. Measurements are performed for confirmation of the calculated results.

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“…In the majority of works made in recent years, the effects of nonuniform shear warping distribution or, in other words, shear lag phenomenon in flexure, have not been extensively considered in the dynamic problems of beams by the inclusion of the corresponding inertia effects (Dikaros et al., 2016). The same case holds for the problem of torsion (Dikaros et al., 2016; Sapountzakis et al., 2016).…”

Section: Introductionmentioning

confidence: 99%

Generalized vibration analysis of beams including warping effects by isogeometric methods

Sapountzakis

Tsiptsis

2017

Journal of Vibration and Control

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In this paper, the Isogeometric tools, either integrated in the Finite Element Method (FEM) or in a Boundary Element based Method (BEM) called Analog Equation Method (AEM), are employed for the vibration analysis of homogeneous beams of arbitrary cross section (thin- or thick- walled) taking into account nonuniform warping and shear deformation effects (shear lag due to both flexure and torsion). The beam is subjected to the combined action of arbitrarily distributed or concentrated axial and transverse loading, as well as to bending, twisting and warping moments. Its edges are subjected to the most general boundary conditions. By employing a distributed mass model system accounting for longitudinal, transverse, rotatory, torsional and warping inertia, ten boundary value problems with respect to the variable along the beam time-dependent 1-D kinematical components are formulated. The numerical solution or the spectrum analysis of the aforementioned problems is performed through IGA, FEM and AEM, leading to a system of second-order differential equations, which are quasi-static and solved for the free vibration case, formulating a generalized eigenvalue problem. Special cases of the generalized problem have also been studied in order to demonstrate the efficiency of AEM in reducing computational effort and improving accuracy, especially when combined to Isogeometric tools, such as NURBS and B-splines.

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Generalized warping effect in the dynamic analysis of beams of arbitrary cross section

Cited by 14 publications

References 43 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

Effect of Non-Uniform Torsion on Elastostatics of a Frame of Hollow Rectangular Cross-Section

Generalized vibration analysis of beams including warping effects by isogeometric methods

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