Three-dimensional buckling analyses of cracked functionally graded material plates via the MLS-Ritz method

This study presents a novel three-dimensional elasticity-based numerical solution for buckling analysis of a functionally grated material (FGM) plate with a side crack or an internal crack, which is first shown in literature. The distributions of material properties are assumed to follow a power law through plate thickness. The buckling loads of cracked plates are found by the Ritz method with admissible functions constructed by the moving least-squares (MLS) technique. The admissible functions are formed by multiplying a set of regular polynomials in the z coordinate with shape functions in x-y coordinates, established by MLS along with a set of basis functions consisting of regular polynomials and proposed crack functions. The proposed crack functions yields the correct singularity order for stresses at a crack front and shows the displacement and slope discontinuities across the crack, which enhances the ability of the Ritz method to handle problems with cracks. In order to validate the proposed solutions, convergence studies for buckling loads of cracked homogeneous plates are performed and a comparison is presented between the present results, previously published ones, and those obtained from commercial finite element software. The proposed approach is further applied to analyze the buckling of Al/Al₂O₃ FGM rectangular plates with side cracks and skewed rhombic plates with central internal cracks while considering the effects of material distributions, plate thickness, skew angles, crack lengths, inclination angles and positions, boundary conditions, and loading conditions on the buckling loads of these plates.