Vibration and Buckling Analysis of Internally Cracked Square Plates by the MLS-Ritz Approach

Based on the classical thin plate theory, this paper proposes new sets of enriched basis functions for in-plane and out-of-plane displacements of square plates that can yield admissible functions for the Ritz method using the moving least-squares (MLS) approach. These admissible functions display the discontinuities of displacement and slope across a crack; give the correct singularity order for the stress resultants at the crack tips; and enhance the Ritz method's ability to recognize the existence of an internal crack in a plate. To confirm the validity of the proposed approach, convergence studies were performed on the buckling loads and vibration frequencies of plates with central horizontal cracks, and the results obtained agree closely with the published ones as well as those generated by the commercial finite element software. To demonstrate the importance of including all the in-plane stress resultant components in the analysis, the effects of different in-plane stress resultant components on the buckling loads and vibration frequencies of simply supported center-cracked square plates under uniaxial uniform loading were investigated. The present approach was further employed to study the effects of cracks' lengths, orientations, and locations on the buckling loads and frequencies of cracked square plates under different boundary conditions and in-plane loading conditions.