An analytical solution of rectangular laminated plates by higher-order theory

On the basis of the Reddy's higher-order theory of composites, this paper introduces a displacement function Φ into it and transforms its three differential equations for symmetric cross-ply composites into only one eight-order differential equation generated by the displacement-function. When a proper Φ is chosen, both solutions are obtained, namely, the Navier-type solution of simply supported rectangular laminated plates and the Levy-type solution with the boundary condition where two opposite edges are simply supported and remains are arbitrary. The numerical examples show that the present results coincide well with the existing results in the references, thus validating that the present solving method is reliable. The higher-order theory of Reddy is simpler in calculation but has higher precision than the first-order shear deformation theory because the former has fewer unknows than the latter and requires no shear coefficients. Project supported by the Science Foundation of Guangdong province