A higher-order approach to the mechanical behaviour of shear-deformable composite laminated plates

A general two-dimensional higher-order theory describing the mechanical behavior of multi-layered composite plates with arbitrary lamination scheme is proposed. The displacement field is expanded in the thickness direction in a complete polynomial series with arbitrary degree and the unknown series coefficients are expressed, according to the Ritz-Galerkin method, as a superposition of admissible functions. The elastic and geometric stiffness matrices and the mass matrix are obtained from the potential and kinetic energy functionals. The equations governing the elastic static deformation, the buckling and vibration behaviour are derived. The onset of the Eulerian instability, caused by an in-plane uni-axial compressive force, is ascertained determining the load multiplier leading to vanishing of one of the the eigenvalues of the plate stiffness. The instability is also assessed as a divergence bifurcation for the linear vibration problem. For accuracy assessment of the theory, a 16-layer generally oriented laminate with a technically relevant lamination scheme is investigated for the case of elastic static deflection under a tranverse pressure load. The associated deformation and stress results are compared with those obtained by FE calculation. The buckling behavior and associated phenomena are further investigated for several cross- and angle-ply generally oriented laminates. An in-depth investigation is presented on the phenomena of modification of the fundamental buckling mode shape from a symmetric into a skew-symmetric configuration due to variation of the ply orientation angles. Conclusions are drawn towards selection of optimal orientation schemes for moderately thick laminates with respect to the critical buckling load.