Analytical asymptotic solutions for rectangular laminated composite plates

An analytical solution for rectangular laminated composite plates was obtained via a formal asymptotic method. From three-dimensional static equilibrium equations, the microscopic one-dimensional and macroscopic two-dimensional equations were systematically derived by scaling of the thickness coordinate with respect to the characteristic length of the plate. The one-dimensional through-the-thickness analysis was performed by applying a standard finite element method. The derived two-dimensional plate equations, which take the form of recursive equations, were solved under sinusoidal loading with simply-supported boundary conditions. To demonstrate the validity and accuracy of the present method, various types of composite plates were studied, such as cross-ply, anti-symmetric angle-ply and sandwich plates. The results obtained were compared to those of the classical laminated plate theory, the first-order shear deformation theory and the three-dimensional elasticity. In the present analysis, the characteristic length of each composite was dependent upon the layup configurations, which affected the convergence rate of the method. The results shown herein are promising that it can serve as an efficient tool for the analysis and design of laminated composite plates.