Mechanical behavior analysis of functionally graded porous plates resting on elastic foundations using a simple quasi-3D hyperbolic shear deformation theory-based effective meshfree method

This paper presents a novel numerical approach for the mechanical behavior analysis of graded porous plates supported by elastic foundations, which employs an advanced element-free Galerkin method based on moving Kriging interpolation in conjunction with a new simple quasi-3-dimensional hyperbolic shear deformation theory. The present plate theory accounts for both transverse shear and normal deformations via a hyperbolic distribution of in-plane displacements, which naturally fulfills the stress-free boundary conditions on the upper and lower surfaces of the plate without the use of a shear correction factor. The pragmatic feature of the present plate theory is that the displacement field is approximated by only four insted of five or more variables used in the corresponding quasi-3-dimensional shear deformation theories, leading to a reduction in the number of unknowns and governing equations, making it simple to utilize. By comparing the obtained results to those provided by reference plate theories, the accuracy of the proposed approach is confirmed. Comprehensive studies have been performed to investigate the effects of the gradient index, porous coefficient, types of porosity distribution, geometric parameters, and foundation stiffness on the normalized deflection, non-dimensional fundamental frequency, and buckling load for three kinds of porous functionally graded sandwich plates.