Applications of MLS-Ritz Method to Stability and Vibrations of Preloaded Side-Cracked or V-notched Rectangular Plates

• Main Authors: Zeng, Hua-Chun, 曾華醇
• Other Authors: Huang, Chiung-Shiann
• Format: Others
• Language: zh-TW
• Published: 2015
• Online Access: http://ndltd.ncl.edu.tw/handle/20292035542361555690

碩士 === 國立交通大學 === 土木工程系所 === 104 === This study deals with vibration and stability analyses of a rectangular plate with a side crack or a v-notch based on classical plate theory using the famous Ritz method with the 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 and crack functions that appropriately describe the stress singularities at the tip of a crack or a v-notch 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 or a v-notched rectangular plate under linear 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 the published ones. Finally, the present approach is applied to investigate the effects of location, length and orientation of side cracks or v-notches on the buckling loads, vibration frequencies and mode shapes of cracked rectangular plates. The boundary conditions for in-plane are normal traction prescribed along two opposite edges and free along the other edges. Four boundary condition combinations are considered for out-of-plane, and they are SSSS, CSCS, CFCF, SFSF, where S, C, and F donate simply-supported, clamped, and free boundary conditions, respectively.