A 3D cracked beam model with unilateral contact. Application to rotors

Andrieux, Stéphane; Varé, Christophe

doi:10.1016/s0997-7538(02)01225-1

Cited by 33 publications

(51 citation statements)

References 18 publications

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“…The crack breathing phenomenon is finely described since the flexibility due to the presence of the cracks is deduced from threedimensional finite element calculations taking into account the conditions of unilateral contact between the crack lips as originally developed by Andrieux and Varé [2002]. The precise descriptions of the loss of stiffness and of the progressive closure or opening of the cracks are of fundamental importance.…”

Section: Discussionmentioning

confidence: 99%

“…However, for finite element computational codes in rotordynamics, the compliance function s( ) is of low interest and a nonlinear relation of the form and Varé [2002] introduced some properties of the additional strain energy due to the cracked section, w([θ ]). Thus, w could be written as a quadratic function of the rotations jumps as…”

Section: Cracked Rotors Modeling: State Of the Artmentioning

confidence: 99%

“…As described in [Andrieux and Varé 2002], the behavior law is finally deduced from differentiation of w([θ ]) with respect to [θ ] as…”

Section: Cracked Rotors Modeling: State Of the Artmentioning

confidence: 99%

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A cracked beam finite element for rotating shaft dynamics and stability analysis

Arem

Maïtournam

2008

JOMMS

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In this paper, a method for the construction of a cracked beam finite element is presented. The additional flexibility due to the cracks is identified from three-dimensional finite element calculations taking into account the unilateral contact conditions between the crack lips. Based on this flexibility, which is distributed over the entire length of the element, a cracked beam finite element stiffness matrix is deduced. Considerable gain in computing efforts is reached compared to the nodal representation of the cracked section when dealing with the numerical integration of differential equations in structural dynamics. The stability analysis of a cracked shaft is carried out using the Floquet theory.

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Section: Discussionmentioning

confidence: 99%

Section: Cracked Rotors Modeling: State Of the Artmentioning

confidence: 99%

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A cracked beam finite element for rotating shaft dynamics and stability analysis

Arem

Maïtournam

2008

JOMMS

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“…An original method for deriving a lumped model for a cracked beam section was proposed by Andrieux and Varé [2002]. Based on three-dimensional computations, the procedure incorporates more realistic behavior of the cracks than the previous models, namely the unilateral contact conditions on the crack lips and their breathing mechanism under variable loading.…”

Section: Review Of the Andrieux And Varé Modelmentioning

confidence: 99%

“…The experimental validation allows the use of the model, with confidence and reliability, for the determination of the dynamics of supposed cracked rotors. Based on the approach of Andrieux and Varé [2002], El Arem andMaitournam [2008, 2007] presented a method of construction of a cracked beam finite element which they used afterwards for the stability analysis of cracked shafts. The authors distributed the additional energy due to the cracked section on the entire length of the cracked beam finite element.…”

Section: Review Of the Andrieux And Varé Modelmentioning

confidence: 99%

Shearing effects on the breathing mechanism of a cracked beam section in bi-axial flexure

Arem

2009

European Journal of Mechanics - A/Solids

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To cite this version:Saber El Arem. Shearing effects on the breathing mechanism of a cracked beam section in bi-axial flexure. European Journal of Mechanics -A/Solids, Elsevier, 2009Elsevier, , 28 (6), pp.1079Elsevier, -1087 Shearing effects on the breathing mechanism of a cracked beam section in bi-axial flexure Saber El AremLaboratoire Sols Solides Structures-Risques, Domaine Universitaire BP53 38041Grenoble, France AbstractThe main purpose of this paper is to complete the works presented by Andrieux and Varé [2002] and El Arem et al. [2003] by taking into account the effects of shearing in the constitutive equations of a beam cracked section in bi-axial flexure. The paper describes the derivation of a lumped cracked beam model from the three-dimensional formulation of the general problem of elasticity with unilateral contact conditions on the crack lips. Properties of the potential energy and convex analysis are used to reduce the three-dimensional computations needed for the model identification, and to derive the final form of the elastic energy that determines the nonlinear constitutive equations of the cracked transverse section. We aim to establish a relation of behavior between the applied forces and the resulting displacements field vectors, which is compatible with the beams theory in order to allow the model exploitation for shafts dynamics analysis. The approach has been applied to the case of a cracked beam with a single crack covering the half of its circular cross section.

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