Advanced 3D beam element of arbitrary composite cross section including generalized warping effects

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

doi:10.1002/nme.4849

Cited by 18 publications

(7 citation statements)

References 36 publications

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“…It can confirm that the loading condition, which is not mentioned in the standard [2][3][4], is also one factor affecting shear lag [33,34]. Sapountzakis and Dikaros [40] analyzed the problem based on BEM with (Model B) and without (Model A) shear stress correction and compared with the result obtained from 3D solid simulation by FEMAP commercial software. It is emphasized that RWB is based on the theory of Model B, which gives more accuracy than Model A.…”

Section: Examplementioning

confidence: 86%

Shear Lag Analysis due to Flexure of Prismatic Beams with Arbitrary Cross-Sections by FEM

Tran¹,

Navrátil²

2021

Period. Polytech. Civil Eng.

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This paper presents the use of a finite element method (FEM) to analyze the shear lag effect due to the flexure of beams with an arbitrary cross-section and homogeneous elastic material. Beams are constrained by the most common types of supports, such as fixed, pinned, and roller. The transverse, concentrated, or distributed loads act on the beams through the shear center of the cross-section. The presented FEM transforms the 3D analysis of the shear lag phenomenon into separated 2D cross-sectional and 1D beam modeling. The characteristics of the cross-section are firstly derived from 2D FEM, which uses a 9-node isoparametric element. Then, a 1D FEM, which uses a linear isoparametric element, is developed to compute the deflection, rotation angle, bending warping parameter, and stress resultants. Finally, the stress field is obtained from the local analysis on the 2D-cross section. A MATLAB program is executed to validate the numerical method. The validation examples have proven the efficiency and reliability of the numerical method for analyzing shear lag flexure, which is a common problem in structural design.

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Section: Examplementioning

confidence: 86%

Shear Lag Analysis due to Flexure of Prismatic Beams with Arbitrary Cross-Sections by FEM

Tran¹,

Navrátil²

2021

Period. Polytech. Civil Eng.

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“…The kinematical and kinetic variables at node I are denoted by index i in (12). The terms A in (12) are established semi analytically using MATHEMATICA [21].…”

Section: Flexural Deformation About the Y And Z Axismentioning

confidence: 99%

“…The latest results of theoretical research on statics and vibration and loss of stability of FGM and composite beams are presented for example in the articles [1][2][3][4][5][6][7][8][9][10][11][12][13].The first significant feature of the references [1][2][3][4][5][6][7][8] (and also of those published in the previous period) is that variation of material properties is considered only in one direction, usually along the beam thickness, and exceptionally in the longitudinal direction of the beam. The second feature of these works is that they are analyzed only a simple planar beams with rectangular cross-section.…”

Section: Introductionmentioning

confidence: 99%

“…The third feature of most of these works is that their fundamental equations are based on the equations of plane stress state in a continuum with varying material properties which are simplified for the solution of the beams. In [9][10][11][12], general formulations for nonuniform shear warping are presented and an advanced 20 20 stiffness matrix and the corresponding nodal load vector of a member of arbitrary composite cross section is developed, taking shear lag effects into account due to both flexure and torsion. In [13], a static analysis of three-dimensional FGM beams by hierarchical modeling and a collocation meshless solution method is presented.…”

Section: Introductionmentioning

confidence: 99%

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Elastostatic and Modal and Buckling Analysis of Spatial FGM Beam Structures

Muŕın¹,

Aminbaghai²,

Hrabovský³

et al. 2016

Proceedings of the VII European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS Congress 2016)

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“…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%

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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Advanced 3D beam element of arbitrary composite cross section including generalized warping effects

Cited by 18 publications

References 36 publications

Shear Lag Analysis due to Flexure of Prismatic Beams with Arbitrary Cross-Sections by FEM

Shear Lag Analysis due to Flexure of Prismatic Beams with Arbitrary Cross-Sections by FEM

Elastostatic and Modal and Buckling Analysis of Spatial FGM Beam Structures

Modelling of Warping Eigenvibration by Non-Uniform Torsion

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