Buckling analysis of the porous sandwich functionally graded plates resting on Pasternak foundations by Navier solution combined with a new refined quasi-3D hyperbolic shear deformation theory

This article presents a numerical method for analyzing the compressive buckling of porous power-law functionally graded (PPFG) plates placed on Pasternak foundations, which is based on a novel refined quasi-3-dimensional hyperbolic shear deformation theory (RQHSDT) combined with the Navier solution technique. The RQHSDT employs a novel hyperbolic distribution of in-plane displacements through the plate thickness to account for non-linear variations in transverse shear stresses, satisfies the traction free boundary conditions on the top and bottom surfaces, and accounts for shear deformation and thickness stretching effects of the plates without the use of any shear correction factors. Unlike classical shear and normal deformation theories, the RQHSDT has only four variables in its displacement field, as opposed to five or more variables in other quasi-3D shear deformation theories, which reduces the number of unknown variables and governing equations in plate analyses and simplifies calculations. The governing equations of the buckling problem are derived using the virtual work principle. In problem solving, the Navier solution technique is used to obtain the exact solutions for the rectangular PPFG plates with simply supported edges subjected to in-plane loading. The accuracy of the proposed approach is confirmed by comparing the obtained results to those of previously published quasi-3D shear deformation theories. Using comprehensive parametric studies, the effects of gradient index, porosity fraction index, porosity distribution type, geometric parameters, two-direction compression ratio, and stiffness of foundation parameters on buckling of PPFG plates are investigated.