Scaling laws for buckling of polar orthotropic annular plates subjected to compressive and torsional loading

This paper derives the similitude invariants and scaling laws for buckling of polar orthotropic annular plates subjected to radial compressive load and torsional load. The similitude transformation is applied to the governing differential equation directly resulting in a scaling law for buckling load of annular plates and the similarity conditions between a model and a prototype. The scaling law is verified by a series of numerical tests using the solutions from the Ritz method as the theoretical solutions. For complete similitude cases, the buckling loads obtained from the scaling laws are identical to those of the theoretical solution. Since the derived scaling law is independent of the boundary conditions, it is valid for any pairs of model and prototype on the condition that they have identical boundary condition. Therefore, buckling behaviors of the prototype with complicated boundary conditions, of which a theoretical solution is not available, can be predicted from the experimental result on the model. Partial similitude model or scaling law for a pair of model and prototype without complete similarity is also investigated. The partial similarity model is not recommended for polar orthotropic materials, however it demonstrated good estimations for isotropic materials.