Unstable perturbation of the equilibrium under Coulomb friction: Nonlinear eigenvalue analysis

Hassani, Riad; Ionescu, Ioan R.; Sakki, Nour-Dine

doi:10.1016/j.cma.2006.11.020

Cited by 3 publications

(9 citation statements)

References 12 publications

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“…6 depicts the polar representation of the contact variables of problem MCEIP-l 2 for the more refined mesh. Non-all-slip divergence instability modes in the context of plane obstacles were obtained in [29,8].…”

Section: Searching For Non-all-slip Instability Modesmentioning

confidence: 99%

“…Moirot [22] dedicated attention to frictional instabilities of the divergence and flutter types; special emphasis was given to discretized structures with many degrees of freedom with industrial applications in the automotive industry. More recently Ionescu et al [11,8] have also done a research effort on frictional instabilities; they deal with discrete nonlinear eigenvalue analyses and propose an algorithm that, in case of convergence, generates a sequence whose limit is a solution of the eigenvalue problem (a divergence instability mode). The complementarity eigenvalue behind these instability analyses problem has also been attracting mathematicians that have developed algorithms for its numerical resolution [12,30,31].…”

Section: Introductionmentioning

confidence: 99%

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Frictional instabilities in orthotropic hollow cylinders

Costa

Agwa

2009

Computers & Structures

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Section: Searching For Non-all-slip Instability Modesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Frictional instabilities in orthotropic hollow cylinders

Costa

Agwa

2009

Computers & Structures

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“…The theoretical interest of wedged configurations is related to the non uniqueness of the equilibrium problem with Coulomb friction in linear elasticity (see for instance Ballard, 1999;Janovský, 1981;Klarbring, 1990;Hassani et al, 2003Hassani et al, , 2006. The wedged states concern a special type of non-uniqueness in which one of the solution is the trivial one.…”

Section: Introductionmentioning

confidence: 98%

Critical friction for wedged configurations

Hassani¹,

Ionescu²,

Oudet³

2007

International Journal of Solids and Structures

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International audienceA wedged configuration with Coulomb friction is a nontrivial equilibrium state of a linear elastic body in a frictional unilateral contact with a rigid body under vanishing external loads. We analyze here the relation between the geometry of the elastic body and the friction coefficient for which wedged configurations exist in a 3-D context. The critical friction coefficient, μw, is defined as the infimum of a supremal functional defined on the set of admissible normal displacement and tangential stresses. For friction coefficients μ with μ > μw the wedged problem has at least a solution and for μ < μw there exits no wedged configurations. For the in-plane problem we discuss the link between the critical friction and the smallest real eigenvalue μs which is related to the loss of uniqueness. The wedged problem is stated in a discrete framework using a mixed finite element approach and the (discrete) critical friction coefficient View the MathML source is introduced as the solution of a global minimization problem involving a non differentiable and non-convex functional. The existence of View the MathML source, the displacement field of a critical wedged state, is proved and a specific numerical method, based on a genetic algorithm, was developed to compute the critical wedged configurations. Some techniques to handle the discontinuities of the normal vector on the contact surface are presented and the analysis is illustrated with three numerical simulations

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“…A study dealing with stability properties of equilibrium configurations in the continuous context can be found in [8].…”

Section: The Equilibrium Problemmentioning

confidence: 99%

“…On Γ C × [0, T ], the three conditions representing unilateral contact are as follows 5) and the Coulomb friction law on Γ C × [0, T ] is described by the following conditions (see e.g., [4], p. 21, or [8]):…”

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confidence: 99%

Weak Formulations and Solution Multiplicity of Equilibrium Configurations with Coulomb Friction

Bostan

Hild²

2009

Math. Model. Nat. Phenom.

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Abstract. This work is concerned with the equilibrium configurations of elastic structures in contact with Coulomb friction. We obtain a variational formulation of this equilibrium problem. Then we propose sufficient conditions for the existence of an infinity of equilibrium configurations with arbitrary small friction coefficients. We illustrate the result in two space dimensions with a simple example.

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Unstable perturbation of the equilibrium under Coulomb friction: Nonlinear eigenvalue analysis

Cited by 3 publications

References 12 publications

Frictional instabilities in orthotropic hollow cylinders

Frictional instabilities in orthotropic hollow cylinders

Critical friction for wedged configurations

Weak Formulations and Solution Multiplicity of Equilibrium Configurations with Coulomb Friction

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