Recently, there is a theory called Mechanics of Structure Genome which enables others to handle buckling analysis of laminated composite plates similarly as buckling analysis of metal plates. Only difference is the constitutive relations specific for composites, for which you can try SwiftComp, a general-purpose constitutive modeling software based on a revolutionary multiscale theory called Mechanics of Structure Genome. You can still use tradiational plate/shell elements in FEA for buckling, vibration or other structural analysis similarly as metallic structures, but SwiftComp's prediction is accurate as if you are carry out detailed 3D FEA. The code can be launched in the cloud at https://cdmhub.org/resources/scstandard. 

https://cdmhub.org/resources/scstandard.