Differentical equations, dynamical systems and optimal control

On equilibrium of a two-dimensional viscoelastic body with a thin Timoshenko inclusion

T. S. Popova

M. K. Ammosov North-Eastern Federal University, 48, Kulakovskogo str., Yakutsk, 677000, Russia

Abstract: The equilibrium problem for a two-dimensional viscoelastic body containing a thin elastic inclusion modeled as a Timoshenko beam is considered. Cases without delamination as well as the case when the inclusion delaminates from the body forming a crack are studied. Both variational and differential statements of the corresponding problems containing nonlinear boundary conditions, as well as their solvability is justified. The limiting case, as the stiffness parameter of the inclusion tends to infinity is considered and the problem of the thin rigid inclusion is obtained.

Keywords: variational inequality, Timoshenko inclusion, viscoelastic body, thin elastic inclusion, crack, non-penetration conditions, nonlinear boundary conditions.

UDC: 517.9

MSC: 74D05

Received May 11, 2020, published September 15, 2020

Language: English

DOI: 10.33048/semi.2020.17.102

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