Asymptotic theory of thermoelasticity of multilayer composite plates | Mekhanika | kompozitsionnykh | materialov i konstruktsii
> Volume 20 > №2 / 2014 / Pages: 259-282

Asymptotic theory of thermoelasticity of multilayer composite plates



The thermoelasticity theory of thin multilayer anisotropic composite plates has been developed on the base of equations of the general three-dimensional theory of thermoelasticity with introducing asymptotic expansions in terms of a small parameter being a ratio of a thickness and a typical length of the plate without any hypotheses on a type of distribution of displacements and stresses versus thickness. Recurrent consequences of 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 the certain rules) problem of the plate thermoelasticity theory developed is similar to the Kirchhoff-Love plate theory but differs from this theory by the presence of three-order derivatives of longitudinal displacements of a plate. Terms containing these derivatives are not zero only for plates with nonsymmetrical location of layers through thickness. The method developed allows us to calculate by analytical formulas (having found previously displacements of the middle surface of a plate and its deflection) all the six components of a stress tensor including cross normal stresses and stresses of interlayer shear. Examples of solving problems on bending a multilayer plate by uniform pressure and nonuniform temperature field are presented. Comparison of the analytical solutions for stresses in the plate with finite-element three-dimensional solution computed by complex ANSYS has shown that in order to achieve a solution accuracy compared with the accuracy of the method developed us need using very fine finite-element grids and sufficiently high-capacity hardware