Inequalities in Mechanics and Physics

Duvaut, Georges; Lions, J. L.

doi:10.1007/978-3-642-66165-5

Cited by 1,603 publications

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“…First, note that using Korn's Inequality [2], we have that there exist constants α, β > 0 such that (see [7])…”

Section: Polynomial Stabilitymentioning

confidence: 99%

On the stability of Mindlin–Timoshenko plates

Sare

2009

Quart. Appl. Math.

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Abstract. We consider a Mindlin-Timoshenko model with frictional dissipations acting on the equations for the rotation angles. We prove that this system is not exponentially stable independent of any relations between the constants of the system, which is different from the analogous one-dimensional case. Moreover, we show that the solution decays polynomially to zero, with rates that can be improved depending on the regularity of the initial data.

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“…First, note that using Korn's Inequality [2], we have that there exist constants α, β > 0 such that (see [7])…”

Section: Polynomial Stabilitymentioning

confidence: 99%

On the stability of Mindlin–Timoshenko plates

Sare

2009

Quart. Appl. Math.

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“…This is proved in [11], and also used in for example [6]. Moreover, the set of rigid body motions N is finite dimensional, and thus the H 1 -norm and the L 2 -norm are equivalent on N , that is…”

Section: Variational Formulationmentioning

confidence: 85%

“…Like [11], we can now formulate (1.5) as a variational inequality. This is the content of the next lemma.…”

Section: Notation and Problem Formulation 11mentioning

confidence: 99%

“…The orthogonal projection map onto N in L 2 (Ω) is denoted by P. The following inequality is proved in [11],…”

Section: γmentioning

confidence: 99%

“…The first proof of existence of solutions to a general class of incremental coercive friction problems was due to Duvaut and Lion in 1972, [10] and [11]. However, they only established the existence of solutions to friction problems with prescribed normal pressure on the contact surface.…”

Section: Introductionmentioning

confidence: 99%

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Existence theorems for noncoercive incremental contact problems with Coulomb friction

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Rietz

Analysis and Simulation of Contact Problems

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Smoothing Newton method for solving two- and three-dimensional frictional contact problems

Leung

Chen

Wanji

1998

Int. J. Numer. Meth. Engng.

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Two-and three-dimensional frictional contact problems are uniformly formulated as a system of nondifferentiable equations based on variational inequality theory. Through constructing a simple continuously differentiable approximation function to the non-differentiable one, the smoothing Newton method is directly implemented as an exact method. Both the global convergence and the local quadratic convergent rate of the method are guaranteed. None of the additional variables and linear approximations on Coulomb friction law is introduced and hence the formulation exactly describes the frictional contact phenomenon in both two-and three-dimensional cases. Numerical experiments suggest that the method is very efficient and promising.

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Inequalities in Mechanics and Physics

Cited by 1,603 publications

References 0 publications

On the stability of Mindlin–Timoshenko plates

On the stability of Mindlin–Timoshenko plates

Existence theorems for noncoercive incremental contact problems with Coulomb friction

Smoothing Newton method for solving two- and three-dimensional frictional contact problems

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