Nugzar Shavlakadze

Boundary Value Problem for Piecewise-Homogeneous Viscoelastic Plate with Finite Crack

abstract:
A piecewise-homogeneous viscoelastic plate, weakened by a finite crack, which meets the interface at a right angle, is considered. The crack boundary is loaded with normal symmetric forces. Using the analogues of the Kolosov-Mushkelishvili formulas of viscoelasticity theory, the complex potentials are determined and a system of singular integral equations of the first kind with respect to jump of the normal displacement is obtained. The asymptotic behavior of a solution of the resulting system is investigated. In the particular case, using the methods of the theory of analytic functions, the solution to the problem is presented in explicit form. The behavior of normal contact stresses in the neighborhood of singular points is established.

Mathematics Subject Classification: 74D05, 45F15

Key words and phrases: Viscoelasticity theory, the boundary value problems, singular integral equations, Fourier transformation, asymptotic estimates