3D Beam Finite Element Including Nonuniform Torsion

Muŕın, Just́ın; Kutiš, Vladimı́r; Kralovic, V.; Sedlár, Tibor

doi:10.1016/j.proeng.2012.09.537

Cited by 8 publications

(11 citation statements)

References 8 publications

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“…In Table , the geometric constants of the cross section corresponding to models A, B as computed employing BEM are presented. In Figure , the distribution of the angle of twist | θ x |( x ) is presented as compared with the ones obtained by the 14 × 14 stiffness matrix of Murín et al , , commercial software ANSYS employing either TTT‐based 14 × 14 stiffness matrix or a shell model as well as experimental measurement conducted in . From this figure, the accuracy of the developed models A, B can be verified.…”

Section: Numerical Examplesmentioning

confidence: 87%

“…Furthermore, in Figure , the warping moment

M_{ϕ_{x}^{P}} ((), x)

M_{ϕ_{x}^{S}} (x)

diagrams along the beam length are given. In order to assess the behavior of the developed models A, B of the present beam element in normal stress computation, in Figure , the variation of normal stresses

σ_{xx}^{C 1}

σ_{xx}^{C 2}

, x ∈[0.0,8.0] at points C 1( y C 1 =2.9, z C 1 =0.9) (mid‐line corner), C 2( y C 2 =3.0, z C 2 =1.0) (upper outer corner) (Figure b) is presented as compared with the results of the literature as well as to the ones obtained using classical 12 × 12 stiffness matrix (uniform torsion) and 14 × 14 stiffness matrix based on classical nonuniform torsion theory as presented in . Moreover, in Table , the values of rotation angle, warping moment, and normal stress

σ_{xx}^{C 1}

at various x positions are also given as compared with the ones retrieved from the literature .…”

Section: Numerical Examplesmentioning

confidence: 99%

“…In order to assess the behavior of the developed models A, B of the present beam element in normal stress computation, in Figure , the variation of normal stresses

σ_{xx}^{C 1}

σ_{xx}^{C 2}

σ_{xx}^{C 1}

at various x positions are also given as compared with the ones retrieved from the literature . From this figure and table, the satisfactory convergence of the present results obtained from model B to the shell model retrieved from the literature can be verified, whereas the results obtained from model A are closer to those obtained using classical nonuniform torsion and 14 × 14 stiffness matrix of ANSYS , which exhibits discrepancies from the actual stress state.…”

Section: Numerical Examplesmentioning

confidence: 99%

“…Finally, in Table , the primary and secondary normal stress components

σ_{xx}^{PC 2}

σ_{xx}^{SC 2}

at x = 0,80 cm are given. From this table, the influence of torsional shear lag effect (indicated by the magnitude of

σ_{xx}^{SC 2}

), which in is ignored, can be observed.…”

Section: Numerical Examplesmentioning

confidence: 99%

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

Sapountzakis

Dikaros

2015

Numerical Meth Engineering

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SummaryIn this paper, an advanced 20 × 20 stiffness matrix and the corresponding nodal load vector of a member of arbitrary composite cross section is developed taking into account shear lag effects due to both flexure and torsion (the case of the three‐dimensional beam element of arbitrary homogeneous cross section is treated as a special one). The composite member consists of materials in contact each of which can surround a finite number of inclusions. Nonuniform warping distributions are taken into account by employing four independent warping parameters multiplying a shear warping function in each direction and two torsional warping functions. Ten boundary value problems with respect to the kinematical components are formulated and solved employing the analog equation method, a BEM‐based technique. The aforementioned boundary value problems are formulated employing either an improved stress field arising from the correction of shear stress components or the stress field arising directly from displacement considerations. The warping functions and the geometric constants including the additional ones due to warping are evaluated employing a pure BEM approach, that is, only boundary discretization of the cross section is used. Numerical results are presented to illustrate the method and demonstrate its efficiency and accuracy. The deviations arising from the use of the advanced 20 × 20 stiffness matrix and the classical 12 × 12 or 14 × 14 ones employed in commercial software packages are illustrated through examples of great practical interest. Moreover, the influence of nonuniform warping effects necessitating the use of the aforementioned ‘advanced’ stiffness matrix is also demonstrated. Copyright © 2015 John Wiley & Sons, Ltd.

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Section: Numerical Examplesmentioning

confidence: 87%

“…Furthermore, in Figure , the warping moment

M_{ϕ_{x}^{P}} ((), x)

M_{ϕ_{x}^{S}} (x)

σ_{xx}^{C 1}

σ_{xx}^{C 2}

σ_{xx}^{C 1}

at various x positions are also given as compared with the ones retrieved from the literature .…”

Section: Numerical Examplesmentioning

confidence: 99%

“…In order to assess the behavior of the developed models A, B of the present beam element in normal stress computation, in Figure , the variation of normal stresses

σ_{xx}^{C 1}

σ_{xx}^{C 2}

σ_{xx}^{C 1}

Section: Numerical Examplesmentioning

confidence: 99%

“…Finally, in Table , the primary and secondary normal stress components

σ_{xx}^{PC 2}

σ_{xx}^{SC 2}

at x = 0,80 cm are given. From this table, the influence of torsional shear lag effect (indicated by the magnitude of

σ_{xx}^{SC 2}

), which in is ignored, can be observed.…”

Section: Numerical Examplesmentioning

confidence: 99%

See 2 more Smart Citations

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

Sapountzakis

Dikaros

2015

Numerical Meth Engineering

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“…The effect of warping in all thin-walled cross section loaded by torsion must be assumed in stress and deformation analyses of structures [10]. During the analysis, the secondary torsion moment deformation effect was included into the stiffness matrix [11].…”

Section: Introductionmentioning

confidence: 99%

Optimum Shapes and Sizes on Torsion Behaviour of I-Beam with Web Opening

De’nan

Hashim

2016

MATEC Web of Conferences

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Abstract. Numerical study on torsion behaviour of I-beam with web opening was carried out and presented in this paper. Optimum shapes and sizes which enhance the torsion behaviour of the I-beam with web opening as well as lead to economic design in terms of both manufacture and usage.Comparison is made between I-beam without web opening and I-beam with various shapes and sizes of web opening. Different types of finite elements model, sizes and types of web opening were used to investigate the effect of various shapes and sizes of web opening on the torsion behaviour. The results are expressed in terms of torsional rotation. It is concluded that I-beam without web opening has lower torsional resistance compared to that of I-beam with various shapes of web opening. Meanwhile, the model 2 is the optimum model compare to model 1.The size of opening has slightly effect on the torsional angles values. It was noted that the optimum web opening size is 0.5D due to the low values of the torsional angle values compared with 0.6D and 0.7D.

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