Navier's solution for laminated plate buckling with prebuckling in-plane deformation

This paper presents closed-form buckling solutions for simply supported cross-ply rectangular symmetric laminates with allowance for the effects of prebuckling in-plane deformation and higher-order strain terms (curvature terms), using the Navier solution method. In the formulation, the transverse shear effect is incorporated through the first order shear deformation theory and the incremental total potential energy approach is adopted. Buckling of laminates subject to different combinations of tension and compression along plate edges is investigated. The significant effects of prebuckling in-plane deformation and curvature terms on buckling loads are studied, with various loading conditions, thickness ratios, aspect ratios, degrees of material orthotropy and numbers of layers. Some exact buckling solutions for simplified cases with and without the inclusion of prebuckling in-plane deformation and curvature terms are obtained and compared with results available elsewhere in literature. The investigation concludes that the effect of prebuckling in-plane deformation is of the same order of magnitude as the shear effect with certain kinds of loading conditions and aspect ratios