Three‐Dimensional Solutions for Thermal Buckling of Multilayered Anisotropic Plates

Abstract

Analytic three‐dimensional elasticity solutions are presented for the thermal buckling problem of multilayered anisotropic plates. The plates are assumed to have rectangular geometry and an antisymmetric lamination with respect to the middle plane. The temperature is assumed to be independent of the surface coordinates, but it has an arbitrary symmetric variation through the thickness of the plate. No external loads are present, but the motion of the plate is partially restrained in its plane. A mixed formulation is used, with the fundamental unknowns consisting of the six stress components and the three displacement components of the plate. The prebuckling deformations are taken into account. Each of the plate variables is decomposed into symmetric and antisymmetric components in the thickness direction, and is expressed in terms of a double Fourier series in the Cartesian surface coordinates. Extensive numerical results are presented showing the effects of the prebuckling deformation on the critical temperature, as well as the effects of variation in the lamination and geometric parameters of composite plates on the importance of the transverse stress and strain components.