Thermoelastic stress analysis of moderately thick inhomogeneous and laminated plates

Abstract

We extend the plane stress theory of Michell (1900, Proc. Lond. Math. Soc.31, 100–124) for a moderately thick homogeneous elastic plate, and that of Kaprielian el al. (1988, Phil Trons. R. Soc. Lond.A324, 565–594) for a laminated plate, to include stretching and bending solutions for an inhomogeneous thermoelastic plate. The inhomogeneities, both in the elastic properties and thermal expansion coefficients, can vary arbitrarily through the thickness of the plate, though for simplicity the analysis is restricted to plates with geometric and material properties symmetric with respect to the mid-plane. The deformation is produced by a temperature field which can also vary arbitrarily through the thickness.The solutions are expressed in terms of the solution of the approximate, two-dimensional, thinplate equations governing an “equivalent” homogeneous plate, and are exact solutions of the full equations of three-dimensional thermoclasticity. By considering laminated plates to be a special case of inhomogeneous plates, we derive an “exact” laminate theory for plates consisting of different, homogeneous and isotropic layers which are perfectly bonded to each neighbouring layer.