STRESS AND DEFORMATION IN MODERATELY ANISOTROPIC INHOMOGENEOUS ELASTIC PLATES

A three-dimensional theory is developed for determining the stress and deformation of a moderately anisotropic plate. In terms of an aspect ratio epsilon and an extension to shear modulus ratio delta a moderately anisotropic plate has epsilon/delta = O(1) and delta much less than 1. The plate is uniform in thickness and is composed of a transversely isotropic material which is inhomogeneous in the through-thickness direction. A laminated material is treated by assuming piecewise constant through-thickness properties. The theory is based on the transfer matrix method which makes no initial assumptions about the form of the stress or displacement components. The solution throughout the thickness may then be transferred to the solution on a reference plane. Application of lateral surface boundary conditions leads to two-dimensional differential equations governing the reference plane values, which are solved using an expansion in the material parameter delta. The special case of a cross-ply symmetric laminate is analysed as an illustrative example.