Modélisation et résolution du problème de contact mécanique et son application dans un contexte multi-physiques /

Bussetta, Philippe

doi:10.1522/030097727

Cited by 2 publications

(8 citation statements)

References 15 publications

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“…Actually, APM is not adapted for elastoplastical problems because, the important augmentation of the value of the normal penalty coefficient produce numerical oscillation and generally prevent the convergence of the algorithm [20].…”

Section: Penalty Methods (Pm)mentioning

confidence: 99%

“…On the contact boundary Γ 1 c , the field of virtual relative displacement between the two interfaces is split in the normal direction, δg and on the tangential plane, δξ β (for more information see [1] or [36]). In the same way, the contact stress is projected on the normal direction (normal contact stress, t n ) and on the tangential plane (tangential contact stress, t t = t t 1 + t t 2 ) [20]. The contact's laws are the unilateral contact (relations (4)) and the Coulomb's friction law (relations (5)), such that:…”

Section: Equations To Be Solvedmentioning

confidence: 99%

“…Like for the PM, large values of the penalty coefficients prevent convergence of the algorithm. In addition, the quality of the solution can be controlled by the tolerance on the gap, the tolerance on the reversible tangential displacement and the number of augmentation of the Lagrange multipliers [20]. So, the larger value of the penalty coefficients, the smaller the number of augmentation of the Lagrange multipliers will be.…”

Section: Algorithm 1 Computation Of Lagrange Multipliersmentioning

confidence: 99%

“…The value of the tangential penalty coefficient is based on an empirical study that shows that the overvaluation of the tangential stress has a bad influence on the resolution of the problem [20]. When the contact takes place, the value of the tangential penalty coefficient leads to a tangential stress equal to the half of the stress value corresponding to sliding threshold.…”

Section: Algorithm 3 Adaptation Of Normal Penalty Coefficientmentioning

confidence: 99%

“…The value of the tangential penalty coefficient is still user chosen. In addition, this method is not appropriate to elastoplastic problems [20] (it is proved in the Sect. 4 by one example).…”

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confidence: 99%

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The adapted augmented Lagrangian method: a new method for the resolution of the mechanical frictional contact problem

2011

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The aim of this work is to propose a new numerical method for solving the mechanical frictional contact problem in the general case of multi-bodies in a three dimensional space. This method is called adapted augmented Lagrangian method (AALM) and can be used in a multi-physical context (like thermo-electro-mechanical fields problems). This paper presents this new method and its advantages over other classical methods such as penalty method (PM), adapted penalty method (APM) and, augmented Lagrangian method (ALM). In addition, the efficiency and the reliability of the AALM are proved with some academic problems and an industrial thermo-electromechanical problem.

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Section: Penalty Methods (Pm)mentioning

confidence: 99%

Section: Equations To Be Solvedmentioning

confidence: 99%

Section: Algorithm 1 Computation Of Lagrange Multipliersmentioning

confidence: 99%

Section: Algorithm 3 Adaptation Of Normal Penalty Coefficientmentioning

confidence: 99%

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confidence: 99%

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The adapted augmented Lagrangian method: a new method for the resolution of the mechanical frictional contact problem

2011

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A new fluid-structure coupling model: Case of a pipe under internal pressure

Hicham

Hadjoui

2023

Advances in Mechanical Engineering

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This work presents the eigenfrequencies of a study on the fluid-structure interaction for a pipe with a circular section, under pressure constraints in laminar, incompressible and irrotational flow, followed by a comparison between stiffness coupling and bar coupling with different geometric ratio Radius/Length; Radius/Thickness, as a frequency geometric identity of the pipe in the industry. The realization of this study is to have better coupling, where we use the relations of mechanical behaviour of the solid on displacement-stress and for the fluid, we use the Navier-Stokes equations in cylindrical coordinates under the speed-stress form transformed into displacement by the Galerkin-Temp theory. Either the force of the fluid will be distributed on the internal surface of the cylinder by the coupling (interface) between fluid and solid. To obtain the results of the eigenfrequencies we used the hierarchical finite element method (HFEM) for both mechanical and fluid entities. For the natural frequencies, we apply the hierarchical finite elements of the Legendre polynomial which is defined in a well-known interval, thanks to this mathematical calculation we arrive at the general equations of motion matrix form of the solid, the interface and the fluid. The calculation was carried out by a MATLAB programme which determines the eigenfrequencies of the evolved system by different geometric and physical parameters mentioned. We validated this work by a table of comparison between the experimental values and the values of the programme.

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Modélisation et résolution du problème de contact mécanique et son application dans un contexte multi-physiques /

Cited by 2 publications

References 15 publications

The adapted augmented Lagrangian method: a new method for the resolution of the mechanical frictional contact problem

The adapted augmented Lagrangian method: a new method for the resolution of the mechanical frictional contact problem

A new fluid-structure coupling model: Case of a pipe under internal pressure

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