Warping Transmission in 3-D Beam Element Including Secondary Torsional Moment Deformation Effect

Sapountzakis, E. J.; Tsipiras, V.J.; Gkesos, Pavlos G.

doi:10.7712/seeccm-2013.2030

Cited by 2 publications

(2 citation statements)

References 11 publications

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“…Z/ at any interior point of each domain m (m D 1; : : :; M / of the cross section having continuous partial derivatives up to the second order with respect to y;´, satisfying the boundary value problems described by Equations (18), (19), (21), (23), (24), and (26). The numerical solution of these problems is similar and is accomplished using BEM within the context of the method of subdomains [42,43].…”

Section: Bem For the Warping Functionsmentioning

confidence: 99%

“…Toward improving conventional beam elements in order to include nonuniform warping effects, 14 14 stiffness matrices have been proposed incorporating nonuniform torsion. The additional DOF in each element node concerns either the rate of change of the total angle of twist [20] or an independent warping parameter, thus taking into account STSDE as well [21][22][23][24][25][26]. As far as shear lag effects in flexure are concerned, expanded stiffness matrices have been proposed as well, most of which employ the assumptions of thin tube theory (TTT) [11].…”

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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: Bem For the Warping Functionsmentioning

confidence: 99%

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confidence: 99%

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

Sapountzakis

Dikaros

2015

Numerical Meth Engineering

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The impact of section properties on thin walled beam sections with restrained torsion

Gebre

Galishnikova

2020

J. Phys.: Conf. Ser.

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In this paper the influence of section properties on thin walled beam sections with restrained torsion is studied by considering the angle of twisting for non-uniform torsion. The study is based on the governing equation for non-uniform torsion of thin-walled beam of open and closed cross-sections, including the restrained behavior. The hyperbolic shape functions is used to generate the general solution for homogenous equation as it gives the exact results in accordance with the analytical solution. This study is focused on a bar subjected to torsion with warping of wide-ranging open and closed cross-sections with different value of characteristics number for torsion. The impact of the characteristics number for torsion on different section type is studied and evaluated. The obtained results are compared based on the influence of section properties on the components of the total applied torsion and presented graphical for different value of characteristics number for torsion.

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Warping Transmission in 3-D Beam Element Including Secondary Torsional Moment Deformation Effect

Cited by 2 publications

References 11 publications

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

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

The impact of section properties on thin walled beam sections with restrained torsion

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