Computationally efficient higher-order shear and normal deformation theory for laminated composite plates

This study presents a compact and accurate higher-order shear and normal deformation theory (HSNDT) for the analysis of laminated composite plates under transverse loading. The formulation employs higher-order through-thickness displacement polynomials to capture displacement and stress fields, incorporating transverse normal stretching following the recommendations of Koiter and Carrera. Transverse shear stresses are recovered through equilibrium-based integration, showing good agreement with benchmark three-dimensional elasticity solutions. The governing equations are derived using the principle of virtual work (PVW), and analytical solutions are obtained via Navier’s method for simply supported plates. Comprehensive numerical studies are performed for various thickness ratios, aspect ratios, and lamination schemes, including symmetric and antisymmetric cross-ply and angle-ply laminates. Results are validated against three-dimensional elasticity solutions and compared with several equivalent single-layer theories, demonstrating better predictive capability of the proposed model. The novelty lies in a higher-order formulation with a fixed number of displacement fields, independent of the number of layers, along with its systematic application to diverse laminate configurations. Graphical comparisons through the thickness further highlight the accuracy at the global levels.