Pertenko O. Problems of viscoelasticity and thermоviscoelasticity for multiconnected anisotropic plates

The work proposes the method for solving problems of viscoelasticity and ther-moviscoelasticity for multiconnected anisotropic plates, which consists in the reduc-tion of the problem to a sequence of similar problems in the theory of elasticity and thermo-elasticity solved by using complex potentials. With the help of conformal im-ages, expansions functions of Laurent series, Faber polynomials and the generalized finite elements method problems are reduced to solving systems of linear algebraic equations to determine the unknown coefficients of the series. The method for deter-mining stress strain behavior at any time using the function approximation. Solved a number of new problems of viscoelasticity and thermoviscoelasticity for a plate with holes, rigid and elastic inclusions under the action of mechanical forces and tempera-ture fields. The detailed numerical studies of stress strain behavior depending on the time, of the geometric characteristics of the media and the elastic properties of mate-rials are conducted. Identified new mechanical patterns of influence of time, impact time forcing method, the physico-mechanical properties of materials and the inclu-sion of plates, their geometrical characteristics, number, relative position with respect to each other on the values of the main characteristics of stress strain behavior. In particular, it was found that over time the stress strain behavior viscoelastic bodies varies considerably and therefore the study of such bodies stress strain behavior can not be limited to a solution of the classical theory of elasticity and thermo-elasticity and it is necessary to solve the problem of viscoelasticity and thermoviscoelasticity.