THE ASYMPTOTIC THEORY OF THERMOELASTICITY OF MULTILAYER COMPOSITE PLATES

摘要

The theory of thermoelasticity of thin multilayer anisotropic composite plates has been developed on the basis of equations of the general three-dimensional theory of thermoelasticity by introducing asymptotic expansions in terms of a small parameter being a ratio of the thickness to the typical length of the plate, without any hypotheses on the type of distribution of displacements and stresses across the thickness. The recurrent consequences of the so-called local problems have been formulated, and their solutions have been found in the explicit form. It has been shown that the global (averaged according to certain rules) problem of the plate thermoelasticity theory in the developed theory is similar to the Kirchhoff-Love plate theory, but differs from it by the presence of third-order derivatives of longitudinal displacements of the plate. The summands containing these derivatives differ from zero only for the plates with nonsymmetrical location of layers across the thickness. The proposed method allows us to calculate by analytical formulas (having found previous displacements of the middle surface of the plate and its deflection) all six components of the stress tensor, including cross normal stresses and stresses of interlayer shear. Examples of solving the problems on bending a multilayer plate by a uniform pressure and a nonuniform temperature field are presented. The comparison of the analytical solutions for stresses in the plate with a finite-element three-dimensional solution, computed by the ANSYS complex, has shown that in order to achieve a solution accuracy compared with the accuracy of the method developed we should use very fine finite-element grids and sufficiently high-capacity hardware.