where v i (xj) and v 3 (xj) are the unknown functions of tangential and normal displacements, respectively, on arbitrary surfaces 9 (k) and a (4) z = 8ct in the layers let, attl~va -" ctl~,a are the elements of the compliance and stiffness matrices of Hooke's law allowing for the Duhamel--Neumann hypothesis e~ -act-(t),~.(t) -" aet)el~,a ~ in the x a axes, ot~ ) are the coefficients of thermal expansion of the material of the layer k in the directions xct, and T (4) is the temperature at a point. Hereafter the partial derivatives are denoted-by the subscripts after the comma. The summation is performed over the repeating subscripts, where i, j, m = I, 2, ot = 1, 3, Z = 1, 4. The sum of the integrals with respect to z of a discontinuous function at the interfaces is denoted by a single integral of this function [1,2]. The superscript in parentheses denotes the number of the layer.In modeling, it is appropriate to postulate "reasonable" hypotheses on the distribution of the transverse shear r and compression o~ ) stresses across the thickness of the plate. In these hypotheses, the approximations over the transverse coordinate z are Ukrainian State Academy of Water Management, Rovno, the Ukraine.
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