利用三維彈性理論配合MLS-Ritz法分析預載重下具邊緣裂縫矩形功能梯度材料板之穩定及振動

本研究主要是以三維彈性理論為基礎，分析受單向軸壓力和張力載重下，不同材料性質分佈：邊界條件、載重形式、厚度、裂縫長度、裂縫角度及位置對邊緣裂縫FGM 矩形板挫屈載重和振動頻率的影響。本研究所考慮之FGM 板是由金屬鋁及陶瓷組成，並使用體積比例描述材料性質隨著厚度方向變化。以移動最小平方差法建構Ritz 法之允許函數，並於基底函數中導入裂縫函數來準確描述裂縫尖端之應力奇異特性及位移與斜率的跨裂縫不連續。將所提出之允許函數進行收斂分析，並與文獻比較。繪出挫屈模態與自然振動頻率模態中平面等高線圖與立體圖。

關鍵字

挫屈載重；自然振動頻率；功能梯度材料；移動最小平方差法；三維彈性理論

並列摘要

The main purpose of the study is to apply the Ritz method based on the three-dimensional elasticity theory to determine the buckling loads and vibrational frequencies of preloaded functionally graded material rectangular plates with side cracks. The admissible functions of the Ritz method are consist of regular polynomials in the thickness direction (z direction) and the functions in x-y plane constructed by the moving least square method with a set of enriched basis functions, which show the stress singularities at the front of a crack and the displacement discontinuity across the crack.The functionally graded material under consideration is made of aluminum and ceramic,and the variations of material properties in the thickness direction follow a simple power law.The convergence studies of buckling loads and vibrational frequencies of cantilevered FGM rectangular plates with vertical side cracks are conducted to demonstrate the efficiency and accuracy of the proposed approach. Then, the proposed approach is further employed to investigate the effects of boundary conditions, loading conditions, variations of material properties, plate thickness, and crack lengths, angles,and locations on the buckling loads and vibration frequencies of side-cracked FGM rectangular plates. The results are tabulated and the vibration and buckling mode shapes are also shown. Most of the results are reported for the first time and can be used as standard to judge the accuracy of other numerical methods and various plate theories.

並列關鍵字

buckling load ； vibrational frequencies ； functionally graded material ； moving least square method ； threedimensional elasticity theory ； Ritz method

參考文獻

Alinia, M. M., Hosseinzadeh, S. A. A., & Habashi, H. R. (2007). Influence of central cracks on buckling and post-buckling behaviour of shear panels. Thin-Walled Structures, 45(4), pp. 422-431.

Google Scholar

Alinia, M. M., Hosseinzadeh, S. A. A., & Habashi, H. R. (2007). Numerical modelling for buckling analysis of cracked shear panels. Thin-Walled Structures, 45(12), pp.