A new exact semi-analytical solution for buckling analysis of laminated plates under biaxial compression

In the present work, an innovative approach is developed and employed to investigate the buckling load of composite laminated plates using polar representation of the fourth-order flexural stiffness tensor. Based on the Rayleigh-Ritz method for calculating the buckling load of orthotropic uncoupled laminates, a new approach is proposed for calculating the critical buckling load as a function of fiber orientation and the number of layers. A new formula is also represented for measuring the possible numbers of buckling modes based on the length-to-width ratio of the plate. Moreover, the new methods make it easy to handle buckling problems, optimization and design of laminated plates subjected to in-plane loads. The efficiency and precision of this method are proved by numerical examples. The anisotropic parts of the buckling load are calculated, and their polar variations are investigated.