Large torsion finite element model for thin-walled beams

Mohri, Foudil; Damil, Noureddine; Ferry, Michel

doi:10.1016/j.compstruc.2007.07.007

Cited by 53 publications

(50 citation statements)

References 29 publications

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“…(11b-11d), can be established by solving Eq. (17) under the same boundary conditions (13)(14)(15), provided that the fictitious load distributions q i (x) (i = 2, 3, 4) are first established. These distributions are determined using the BEM.…”

Section: For the Transverse V W Displacements And The Angle Of Twistmentioning

confidence: 99%

“…Following the procedure presented in [26,27] and employing the constant element assumption for the load distributions q i along the L internal beam elements (as the numerical implementation becomes very simple and the obtained results are of high accuracy), the integral representations of the displacement components u i (i = 2, 3, 4) and their first derivatives with respect to x when applied for the beam ends (0, l), together with the boundary conditions (13)(14)(15) are employed to express the unknown boundary…”

Section: For the Transverse V W Displacements And The Angle Of Twistmentioning

confidence: 99%

“…are functions specified at the beam ends x = 0, l. Equations (12)- (15) describe the most general boundary conditions associated with the problem at hand and can include elastic support or restraint. It is apparent that all types of the conventional boundary conditions (clamped, simply supported, free or guided edge) can be derived from these equations by specifying appropriately these functions (e.g.…”

Section: Statement Of the Problemmentioning

confidence: 99%

“…Mohri et al [14] studied the lateral post-buckling analysis of simply supported thin-walled open section beams employing the Galerkin method after applying sinusoidal functions. Finally, Mohri et al [15] developed a large torsion finite element model for elastic thin-walled Bernoulli beams without any assumption for the torsion angle amplitude and any approximation for the trigonometric terms. Nevertheless, in all of the aforementioned research efforts the analysis is not general since either the analysis is restricted to the thinwalled theory assumptions or to mono-or doubly-symmetric cross sections, or the beam boundary conditions are not general or linear expressions for the curvature have been employed or the Wagner's coefficients [16][17][18][19] have been ignored.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Lateral buckling analysis of beams of arbitrary cross section by BEM

Sapountzakis

Dourakopoulos

2009

Comput Mech

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In this paper, the lateral buckling analysis of beams of arbitrary cross section is presented taking into account moderate large displacements and employing nonlinear relationships between bending moments and curvatures. The beam is supported by the most general boundary conditions including elastic support or restraint. Starting from a displacement field without any simplifying assumptions about the angle of twist amplitude and based on the total potential energy principle, the stability criterion is formulated taking into account the warping effects, the prebuckling displacements and the Wagner's coefficients due to the asymmetric character of the cross section. The stability criterion is based on the positive definiteness of the second variation of the total potential energy and is established using the Analog Equation Method (AEM), a BEM based method. The proposed formulation does not stand on the assumption of a thin-walled structure and therefore the cross section's torsional rigidity is evaluated exactly without using the so-called Saint-Venant's torsional constant. Numerical examples are worked out to illustrate the efficiency, the accuracy and the range of applications of the developed method. The effects of both the load height and prebuckling deflections as well as the discrepancy of the Eurocode 3 standard solutions are discussed.

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Section: For the Transverse V W Displacements And The Angle Of Twistmentioning

confidence: 99%

Section: For the Transverse V W Displacements And The Angle Of Twistmentioning

confidence: 99%

Section: Statement Of the Problemmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Lateral buckling analysis of beams of arbitrary cross section by BEM

Sapountzakis

Dourakopoulos

2009

Comput Mech

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“…The presented numerical examples in these studies are concerned only with uniform torsion of either mono-or doubly symmetric cross sections. Finally, Trahair in [94] employing the finite element method and presenting examples of only doubly symmetric cross sections and Mohri et al in [95] employing similar equations to those established by Attard in [92] and presenting examples of either doubly symmetric cross sections subjected in nonuniform torsion or buckling or postbuckling behavior of arbitrary cross section beams also analyze the nonlinear nonuniform torsional problem. Nevertheless, all of the aforementioned studies, which are the only one considering finite angles of twist in asymmetrical bars (and taking into account all of the arising nonlinear terms) are not general since they are restricted to thin-walled beams.…”

Section: Nonlinear Elastic Nonuniform Torsion Of Barsmentioning

confidence: 99%

Bars under Torsional Loading: A Generalized Beam Theory Approach

Sapountzakis

2013

ISRN Civil Engineering

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In this paper both the static and dynamic analyses of the geometrically linear or nonlinear, elastic or elastoplastic nonuniform torsion problems of bars of constant or variable arbitrary cross section are presented together with the corresponding research efforts and the conclusions drawn from examined cases with great practical interest. In the presented analyses, the bar is subjected to arbitrarily distributed or concentrated twisting and warping moments along its length, while its edges are supported by the most general torsional boundary conditions. For the dynamic problems, a distributed mass model system is employed taking into account the warping inertia. The analysis of the aforementioned problems is complete by presenting the evaluation of the torsion and warping constants of the bar, its displacement field, its stress resultants together with the torsional shear stresses and the warping normal and shear stresses at any internal point of the bar. Moreover, the construction of the stiffness matrix and the corresponding nodal load vector of a bar of arbitrary cross section taking into account warping effects are presented for the development of a beam element for static and dynamic analyses. Having in mind the disadvantages of the 3D FEM solutions, the importance of the presented beamlike analyses becomes more evident.

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Incorporation of wall finite relative rotations in a geometrically exact thin-walled beam element

Gonçalves

Ritto‐Corrêa²,

Camotim³

2011

Comput Mech

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In this paper, a large displacement and finite rotation thin-walled beam element previously developed by the authors, which accounts for cross-section deformation, is extended by including finite relative rotations of the beam walls in the in-plane kinematic description of the crosssections. The inclusion of these relative rotations is motivated by the fact that it enables a simple and meaningful representation of the cross-section in-plane distortion and allows for a co-rotational description of the wall "local-plate" behavior, which leads to a computationally efficient numerical implementation. The present extension preserves all features of the original formulation, namely the geometrically exact description of the beam mid-surface and the allowance for arbitrary cross-section deformation modes complying with Kirchhoff's assumption. The efficiency of the resulting beam finite element is demonstrated by means of numerical examples, which include comparisons with solutions obtained by means of the previous beam finite element and standard shell finite elements.

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Large torsion finite element model for thin-walled beams

Cited by 53 publications

References 29 publications

Lateral buckling analysis of beams of arbitrary cross section by BEM

Lateral buckling analysis of beams of arbitrary cross section by BEM

Bars under Torsional Loading: A Generalized Beam Theory Approach

Incorporation of wall finite relative rotations in a geometrically exact thin-walled beam element

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