Hygrothermoelastic analysis of anisotropic inhomogeneous and laminated plates

Abstract

We extend the theory proposed by Kaprielianet al. (to be published, 1990) for stress analysis of a moderately thick, inhomogeneous and anisotropic elastic plate to include hygrothermal effects. The inhomogeneities, both in the elastic properties and expansion coefficients, can vary arbitrarily through the thickness of the plate. The applied temperature and/or moisture fields can also vary arbitrarily through the thickness. However, for convenience the inhomogeneities are assumed to be symmetric about the mid-surface of the plate, and for much of the paper we consider only thermal or moisture effects, the combined effect requiring only superposition of solution. As in Kaprielianet al. (1990) and previous related papers by its authors, the solutions obtained are for the full equations of three-dimensional linear elasticity, but are expressed in terms of the solution of the approximate, two-dimensional, thin-plate equations governing an ‘equivalent’ homogeneous plate. By considering laminated plates as a special case of inhomogeneous plates, we also derive an ‘accurat’ laminate theory for plates consisting of different homogeneous and anisotropic layers which are perfectly bonded to each neighbouring layer.