Shevchuk V. Mathematical models and methods of thermomechanics of bodies with coatings.

The thesis focuses on the development of adequate mathematical models and elaboration of effective methods of calculation and investigation of thermal stressed state of bodies with coatings under mechanical and thermal loading. The methodology for solving problems of thermomechanics of bodies with thin coatings is developed, which is based on the simulation of the influence of such coatings by generalized boundary conditions. The corresponding non-classical linear and non-linear boundary value problems are formulated, and a number of new thermoelasticity problems for bodies with multilayer thin coatings under thermal load are solved. The method of solving elasticity and thermoelasticity problems for cylindrical bodies with transversally isotropic nonhomogeneous coatings is developed and applied to the investigation of the damage evolution process in ceramic coatings of arbitrary thickness.