Protsyuk Y. Static thermoelasticity problems for multi-layer thermosensitive bodies of canonical shape

This thesis develops analytical and numerical methods for solving the one-dimensional static problems of thermoelasticity for multi-layer isotropic bodies of canonical shape (plate, cylinder, and sphere). The coordinate and temperature dependence of physical and mechanical properties, complex heat exchange and mechanical loading are taken into account. By making use of the known or developed solutions (exact or approximate ones in case of arbitrary temperature dependences of thermal conductivity) for auxiliary problems, the heat conduction problems are reduced to solving the one or system of two nonlinear algebraic equations disregarding the number of layers. Thermoelasticity problems for cylinders and spheres were solved by making use of the constructed and known Green's function for corresponding elasticity problems. Exact solutions (when only the temperature coefficient of linear expansion depends on the temperature) and approximate closed-form solutions (when other physical and mechanical properties depend on temperature) are obtained for given temperature distribution and four different ways of mechanical loading on the surfaces. The influence of temperature and coordinate dependence of physical and mechanical properties, coefficient of heat transfer, thermal radiation, thickness and grip conditions on temperature distribution and thermoelastic behavior of layered thermosensitive plates, cylinders and spheres was investigated.