Dobryak O. The thermal stresses researches in piezoplates with holes and cracks

The methods for solving elasticity theory problems for multiconnected anisotropic plates were applied on the thermoelec-tromagneticelasticity problems in thesis. The thermoelectromagneticelasticity complex potentials were introduced. The ex-pressions of thermoelectromagneticelasticity basic characteristics (stresses and displacements, inductions, tensions and po-tentials of the field) by means of complex potentials, the boundary conditions deriving for determination of complex poten-tials. An exact analytical solutions of some problems for simply connected domains were received by series and Cauchy type integrals methods. For the finite and infinite multiply domains and for the half-plane with using the conformal mapping, the expansions of functions in series a general representations of the complex potentials containing the unknown coefficients of the series terms, determination of which by least squares method was reduced to solving systems of linear algebraic equa-tions, were obtained. The many particular problems solutions (for ring, disk with crack, square or rectangular plate with hole, infinite plate with holes and cracks) for the various cases of the temperature field (temperature values on the contours, inter-nal heat sources, the uniform heat flow) were solved. In all the problems detailed numerical studies were carried out to estab-lish the influence on the values of the main characteristics thermoelectromagneticelastic state of accounting degree of mechanicalelectromagnetic fields connectedness, the material constants, geometrical properties of holes and cracks, their number, combination and relative position, mode of temperature influence. With the help of numerical studies the solutions convergence and results reliability, the series new thermomechanical laws were established. It was established, that neglect of electric and especially magnetic material properties in research of thermoelectromagneticelastic state of piezoplates is leaded to substantial inaccuracy in basic characteristics values of thermoelectromagneticelastic state: sometimes they are dif-fer from the real to tens of times. The influence of materials constants are also great on these values: the greater pyroelectric and pyromagnetic modules of piezomaterial, the greater the value of the basic characteristics. The maximum values of stresses in plate of the material M1 having the highest pyroelectric and pyromagnetic modules 100 and 10 times more, when the stresses in plates of the materials M2 and M3. Closer the holes and cracks with each other and with the straight boundary lead to growing the values of basic characteristics in the points of the bridges.