Senchenko Y. Problems of viscoelasticity for multiconnected isotropic plates

The method of reducing the problem of bending of viscoelastic plates to the task sequence of the classical theory of bending of plates based on the method of small parameter that can be solved by using complex potentials are developed in this work. On the solution of problems of bending of viscoelastic plates with holes and inclusions the numerical-analytical method for solving the plane problem of viscoelasticity is distributed, based on the use the methods of conformal mapping, expansions of functions in Laurent series and Faber polynomials, using discrete least squares method for determining the coefficients of terms of the series, the definition of a viscoelastic state by a complex potential approximation. The solutions for the problem of viscoelasticity for finite and infinite multiconnected plates with a finite number of elliptical holes and inclusions with arbitrary location and their combination, the cyclical problem for a ring or an infinite plate with elliptic holes or inclusions, are given. The exact solutions for the problems of bending of plates with circular hole, a circular plate under uniformly distributed efforts to upper base, a circular annular plate, with an elliptical hole with a circular elastic inclusion, are obtained. The numerical investigations with established regularities of influence on the values of the main characteristics of the deflected mode of the time, the geometrical characteristics and physical and mechanical properties of the plates, are carried out. In particular, it was found that in addition to well-known in the classical theory of bending of thin plates the regularities of influence upon deflected mode by the distance between the holes and inclusions, their number and geometric characteristics, there are also regularities from the viscoelastic properties of material. With time deflected mode of viscoelastic bodies substantially changes, so when studying such bodies one shouldn't limit oneself to classic theory of bending of plates , while neglecting rheological properties of materials; it is necessary to solve the problem of viscoelasticity. The changes deflected mode with time are substantially affected by the distance between inclusions, their quantity. The distance between of holes and inclusions, their quantity increasing leads to the influence of time upon deflected mode plate. The investigations results presented in the thesis have both theoretical and prac-tical importance. The proposed methods can be used for а wide variety of engineering problems solving.