Mironenko A. Problems of viscoelasticity and thermal viscoelasticity for multilinked plates with elastic and rigid inclusions

The work proposes the approach to solving problems of viscoelasticity and thermal viscoelasticity for multilinked piece-wise-homogeneous plates, which brings sought problems to a succession of similar problems of elasticity and thermo-elasticity theory resolved with application of complex potentials. Through conformal images, decomposition of functions into Taylor series and with Faber’s polynomials and discrete least-squares method, the problems are resolved by recurrent sequence of linear algebraic equations system to determine the unknown coefficients of the series. The cases of rigid and elastic inclusions have been considered. The series of new problems of viscoelasticity and thermal viscoelasticity for a plate with one, two and final number of inclusions with periodic and double-periodic system of inclusions under the action of mechanical forces and temperature fields have been resolved. For the plate with one rigid elliptic or circular resilient inclu-sion, the exact problem solutions were obtained with inclusion of the Cauchy-type integrals and series. For each of the prob-lems under consideration, there were performed detailed numerical studies of deflected mode’s dependence on time, geo-metrical characteristics of media and elastic properties of materials. There were established new mechanical patterns of in-fluence of time, ways of en each of the problems under environmental impacts, the effect of physico-mechanical parameters of plate materials and their inclusions, their geometrical characteristics, quantity, mutual location relative to each other upon the deflected mode’s main features. In particular, it was found that in addition to known in classical elasticity theory the patterns of influence upon deflected mode by the distance between inclusions and their number and geometric characteris-tics, there are also regularities resulting from the viscoelastic properties of material. With time deflected mode of viscoelas-tic bodies substantially changes, so when studying such bodies one shouldn’t limit oneself to classic theory of elasticity and thermal elasticity, while neglecting rheological properties of materials; it is necessary to solve the problem of viscoelasticity and thermal viscoelasticity. The changes in stress values with time are substantially affected by the distance between inclu-sions, their quantity, and the way of their reinforcement. Inclusions’ approaching to each other and increase of their number enhances time affect upon the deflected mode close to neighboring ones. The results of researches presented in the work are of both theoretic and practical interest. The proposed methods can be used for solving different engineering problems.