Vibrations and stability of a loaded side-cracked rectangular plate via the MLS-Ritz method

This study deals with vibration and stability analyses of a rectangular plate with a side crack based on classical thin plate theory using the famous Ritz method with admissible functions that are constructed by the moving least square (MLS) method with enriched basis functions. The enriched basis functions consist of regular polynomial functions along with crack functions that appropriately describe the stress singularities at the crack tip and show the discontinuities of displacement or slope crossing the crack. Comprehensive convergence studies on the stress intensity factor, buckling loads and vibration frequencies of a cracked rectangular plate under uniform loading at its two opposite edges are carried out and demonstrate the accuracy and efficiency of the presented approach by comparing the present results with previously published ones. Finally, the present approach is applied to investigate the effects of location, length and orientation of side cracks on the buckling loads, vibration frequencies and mode shapes of cracked rectangular plates. The in-plane boundary conditions are normal traction prescribed along two opposite edges and free along the other edges. Two out-of-plane boundary condition combinations are considered. One is simply supported along all the edges, and the other is simply supported along the two loaded edges and free along the other edges.