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- Title
Boundary contact problems with regard to friction of couple-stress viscoelasticity for inhomogeneous anisotropic bodies (quasi-static cases).
- Authors
Gachechiladze, Roland; Gachechiladze, Avtandil
- Abstract
In this paper, quasi-statical boundary contact problems of couple-stress viscoelasticity for inhomogeneous anisotropic bodies with regard to friction are investigated. We prove the uniqueness theorem of weak solutions using the corresponding Green's formulas and positive definiteness of the potential energy. To analyze the existence of solutions, we equivalently reduce the problem under consideration to a spatial variational inequality. We consider a special parameter-dependent regularization of this variational inequality which is equivalent to the relevant regularized variational equation depending on a real parameter, and study its solvability by the Galerkin approximate method. Some a priori estimates for solutions of the regularized variational equation are established and with the help of an appropriate limiting procedure, the existence theorem for the original contact problem with friction is proved.
- Subjects
VARIATIONAL inequalities (Mathematics); FRICTION; GALERKIN methods; EXISTENCE theorems; POTENTIAL energy; COULOMB friction; VISCOELASTICITY
- Publication
Georgian Mathematical Journal, 2023, Vol 30, Issue 6, p855
- ISSN
1072-947X
- Publication type
Article
- DOI
10.1515/gmj-2023-2047