On the existence of solutions to quasistatic frictional rational contact problems with limited interpenetration

2022 ◽  
Vol 65 ◽  
pp. 103468
Author(s):  
Jiří Jarušek
Keyword(s):  
Existence Of Solutions ◽  
Contact Problems

scholarly journals EXISTENCE OF SOLUTIONS FOR FRACTIONAL EVOLUTION INCLUSION WITH APPLICATION TO MECHANICAL CONTACT PROBLEMS

Fractals ◽  
2021 ◽  
pp. 2140036
Author(s):  
JINXIA CEN ◽  
YONGJIAN LIU ◽  
VAN THIEN NGUYEN ◽  
SHENGDA ZENG
Keyword(s):  
Existence Of Solutions ◽  
Contact Problems ◽  
Constitutive Law ◽  
Discrete Approximation ◽  
Inclusion Problem ◽  
Elliptic Type ◽  
Evolution Inclusion ◽  
Gronwall’S Inequality ◽  
Priori Estimates ◽  
Backward Euler

The goal of this paper is to study an evolution inclusion problem with fractional derivative in the sense of Caputo, and Clarke’s subgradient. Using the temporally semi-discrete method based on the backward Euler difference scheme, we introduce a discrete approximation system of elliptic type corresponding to the fractional evolution inclusion problem. Then, we employ the surjectivity of multivalued pseudomonotone operators and discrete Gronwall’s inequality to prove the existence of solutions and its priori estimates for the discrete approximation system. Furthermore, through a limiting procedure for solutions of the discrete approximation system, an existence theorem for the fractional evolution inclusion problem is established. Finally, as an illustrative application, a complicated quasistatic viscoelastic contact problem with a generalized Kelvin–Voigt constitutive law with fractional relaxation term and friction effect is considered.

On hyperbolic contact problems

2009 ◽  
Vol 43 (1) ◽  
pp. 25-40
Author(s):  
Igor Bock ◽  
Jiří Jarušek
Keyword(s):  
Variational Inequality ◽  
Differential Operators ◽  
Existence Of Solutions ◽  
Contact Problems ◽  
Large Deflections ◽  
Two Dimensional ◽  
Airy Stress Function ◽  
Penalization Method ◽  
Nonlinear Elliptic ◽  
First Case

Abstract We deal with hyperbolic variational inequalities modeling vibrations of two-dimensional structures with an obstacle. We focus on the plates with moderately large deflections. The nonlinear strain-displacements relations imply nonlinear elliptic parts of differential operators in considered problems.We distinguish two types of problems. In the first case only the deflections are considered with accelerations and the plane displacements are expressed using the Airy stress function. In the case of plane accelerations the full von K´arm´an system consisting of two equations and one variational inequality is considered. The existence of solutions is derived using the penalization method.

DYNAMIC CONTACT PROBLEMS WITH SMALL COULOMB FRICTION FOR VISCOELASTIC BODIES: EXISTENCE OF SOLUTIONS

1999 ◽  
Vol 09 (01) ◽  
pp. 11-34 ◽  
Author(s):  
J. JARUŠEK ◽  
C. ECK
Keyword(s):  
Contact Problem ◽  
Coulomb Friction ◽  
Existence Of Solutions ◽  
Contact Problems ◽  
Dynamic Contact ◽  
Contact Condition ◽  
Regularization Methods ◽  
Dynamic Contact Problem ◽  
The Coefficient Of Friction ◽  
Viscoelastic Bodies

The existence of solutions to the dynamic contact problem with Coulomb friction for viscoelastic bodies is proved with the use of penalization and regularization methods. The contact condition, which describes the nonpenetrability of mass, is formulated in velocities. The coefficient of friction may depend on the solution but is assumed to be bounded by a certain constant.

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