Buckling of composite laminated plates via a refined higher-order theory

The buckling stresses and mode shapes of rectangular laminated composite plates are investigated employing a global higher-order theory. The displacement field is expanded along the thickness direction in a complete polynomial series with arbitrary degree whereas the series coefficients, function of the in-plane coordinates, are expressed, according to Ritz method, as a superposition of admissible functions. Expressing the energy functionals in terms of the generalized coordinate, the expressions of the elastic and geometric stiffness matrices are obtained. The problem is suitably nondimensionalized so as to single out the independent parameters affecting the buckling behaviour. The convergence properties of the adopted discretization scheme are investigated first considering simply supported orthotropic three-layer symmetric composite plates under a transverse distributed load. It is shown that higher-order terms in the thickness direction are needed for convergence. Variations of the lowest buckling loads with the width-to-thickness ratio and with the ratio between the in-plane elastic moduli are also investigated to ascertain the sensitivity of the buckling behavior with respect to these parameters. The semi-analytical solutions are compared with those obtained using a finite element code (NASTRAN) for the three- and four-layer plates and a good agreement is found.