Benchmark solution for buckling of thick rectangular transversely isotropic plates under biaxial load

This paper presents an analytical solution for elastic buckling problems of thick rectangular transversely isotropic simply supported plates subjected to uniaxial or biaxial uniformly distributed in-plane load, one of which could also be tensile. Governing equations are simplified to two partial differential equations using displacement potential functions (DPF) which are solved using the separation of variables method with exact satisfaction of boundary conditions. The presented solution is applicable to any plate with no restriction on its thickness ratio and also to any composite plates which have the same in-plane mechanical properties in all directions of the plate. Obtained results for critical buckling loads are compared with other analytical results for thin and moderately thick, and with numerical results for thick plates which show excellent agreement between them. Then, the effects of loading conditions aspect and thickness ratios for four transversely isotropic materials and also the engineering constants on the buckling of plates are discovered. The results show that the presented method is applicable and reliable for various kinds of material properties, thickness ratios, and loading conditions. Results also show that in comparison with a uniaxially loaded plate, adding a compressive load in second direction decreases the critical buckling load and the plate buckles in lower modes, while for adding a tensile load it is vice versa. Among materials engineering constants, in-plane modulus of elasticity and transverse shear module have the most effects on the critical buckling load of plates. (C) 2017 Elsevier Ltd. All rights reserved.