Дослідження температурних напружень у п'єзопластинах з отворами і тріщинами

Установлено, что пренебрежение при исследовании ТЭМУС пьезопластин электрическими и особенно магнитными свойствами материала приводит к существенным погрешностям в значениях основных характеристик ТЭМУС: они отличаются от реальных порой до десятков раз. На значения этих величин велико и влияние значений постоянных материалов: чем больше пироэлектрические и пиромагнитные модули пьезоматериала, тем больше значения основных характеристик. Так, максимальные значения напряжений в пластинке из материала М1, обладающего наибольшими пироэлектрическими и пиромагнитными модулями, в 100 и 10 раз больше, чем напряжения в пластинках соответственно из материалов М2 и М3. При сближении отверстий и трещин друг с другом, а также с прямолинейной границей значения основных характеристик в точках перемычек растут.

Ключевые слова: пьезопластина, связанные механикоэлектромагнитные поля, термоэлектромагнитоупругость, комплексные потенциалы, коэффициенты интенсивности напряжений, индукций и напряженностей.

ANNOTATION

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

The thesis for the Candidate of physical and mathematical sciences degree on specialty 01.02.04 - mechanics of a deformable solid body, Donetsk National University, Donetsk, 2011.

The methods for solving elasticity theory problems for multiconnected anisotropic plates were applied on the thermoelectromagneticelasticity (TEME) problems in thesis. The TEME complex potentials were introduced. The expressions of TEME basic characteristics (stresses and displacements, inductions, tensions and potentials of the field) by means of complex potentials, the boundary conditions deriving for determination of complex potentials.

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 equations, 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, internal heat sources, the uniform heat flow) were solved. In all the problems detailed numerical studies were carried out to establish the influence on the values of the main characteristics thermoelectromagneticelastic state (TEMES) 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 TEMES of piezoplates is leaded to substantial inaccuracy in basic characteristics values of TEMES: sometimes they are differ 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.

Keywords: piezoplate, constrained mechanicelectromagnetic fields, thermoelectromagnetoelasticity, complex potentials, stress, induction and tension intensity factors.

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