Antonov Y. Thermoelasticity problems for anisotropic plates with holes and cracks

The considered in the thesis problem of plates geometrical and their materials thermophysical charac-teristics, thermal loads types influence on the thermoe-lastic state detection is the current fundamental and practical problem of the deformable solids mechanics. The theory of heat conductivity and thermoelasticity boundary problems solution methods and their applica-tions for the anisotropic plates with holes and cracks thermoelectroelastic state investigation are developed. The methods are based on the analysis of plates materi-als heat-conductivity coefficients, using of generalized complex potentials for the stationary heat-conductivity, thermoelasticity and their properties, the logarithmic singularities and derivatives singularities in the cracks ends, the conformal mapping, the expansion in Loran series and Faber polynoms, their variables determina-tion by the least squares method. Through the functions the disturbed temperature field, the thermostressed state and the stress intensity factors (SIF) are defined. The plane problem general solution for the anisotropic plates with randomly placed holes and cracks under the contour temperatures (heat flows), the infinite linear heat flow and the concentrated heat source loads is constructed. The developed methods high performance, stability and accuracy of the obtained results are estab-lished. The new multiconnected plates problems set of practical importance is solved. There is the analytical solution for the anisotropic plate with the elliptical hole (crack), when contour is thermoisolated or temperature is applied, under infinite linear heat flow load obtained. In particular, heat conductivity and thermoelasticity problems solutions for the multiconnected disk or the infinite plate are obtained. The various thermal load types are examined (infinite linear heat flow, concen-trated heat source and etc.). For all cases detailed nu-merical investigations of temperature, stresses, internal energy and SIF for cracks ends distributions are carried out. Some new thermomechanical laws are figured out. Presented in the thesis research results have both theo-retical and practical interests. The proposed methods can be used for the various engineering problems solu-tion.