利用三維彈性理論配合MLS-Ritz法分析預載重下具內部裂縫斜菱形功能梯度材料板之穩定及振動

Stability and Vibration Analyses of Preloaded Functionally Graded Material Rhombic Plates with Internal Cracks Using Three-Dimensional Elasticity with MLS-Ritz Method

李品佑

指導教授 ： 黃炯憲

國立交通大學/工學院/土木工程系所/碩士(2018年)

摘要

本研究利用三維彈性理論配合MLS-Ritz 法分析具內部裂縫功能梯度斜菱形板之挫屈載重及預載重下振動頻率。從裂縫尖端處之三維彈性漸進解取適當函數作為移動最小平方差法之增益型基底函數建立x-y 平面允許函數，使允許函數能準確描述內部裂縫尖端處之應力奇異性及跨越裂縫之位移與斜率不連續性。本研究所考慮之功能梯度材料板是由金屬鋁及陶瓷組成，並利用冪級數及體積比例描述材料性質隨厚度方向變化。
本研究先對具內部裂縫功能梯度斜菱形板之挫屈載重及自然振動頻率進行收斂性分析，並和文獻比較，再依此收斂性分析選取適當參數，進一步探討不同板厚、材料性質分佈、裂縫長度和角度、板之斜形角、邊界條件及載重形式對挫屈載重、自然振動頻率及模態之影響。絕大部份數據為文獻首見；可做為依板理論或其他數值方法所得者比對的基準。

關鍵字

挫屈載重 ； 自然振動頻率 ； 三維彈性理論 ； 功能梯度材料 ； 移動最小平方差法

並列摘要

This study examines stability and vibrations of preloaded functionally graded material skewed rhombic plates with internal cracks using three-dimensional elasticity with MLS-Ritz method. Choosing appropriate functions from the three-dimensional asymptotic solutions at a crack tip to form the enriched basis functions of the admissible functions constructed by the moving least square method in x-y plane. The admissible functions correctly account for the singular behaviors of stresses at crack tips and the discontinuities of displacement across a crack. The FGM plates are designed as the
composites of aluminum and ceramic, and the variety of material properties following a simple power law.
The study first shows the convergence of buckling loads and vibrational frequencies of functionally graded material rhombic plates with central vertical internal cracks and compares the convergent results with the published ones. The proposed solutions are further employed to investigate the effects of plate thickness, variations of material properties, skew angles, and crack lengths and angles on the buckling loads and vibrational frequencies of cracked FGM skewed rhombic plates under different inplane loading conditions and boundary conditions. Most of the results are shown for first time in the literature, and they can be used to benchmark data for other solutions based on different plate theories and by different numerical methods.

並列關鍵字

buckling load ； vibrational frequency ； three-dimensional elasticity theory ； functionally graded material ； moving least square method ； Ritz method

參考文獻

Asemi, K. and Shariyat, M. (2013) “Highly accurate nonlinear three-dimensional finite element elasticity approach for biaxial buckling of rectangular anisotropic FGM plates with general orthotropy directions”, Composite Structures, 106, pp. 235-249.

Bodaghi, M. and Saidi, A. R. (2010) “Levy-type solution for buckling analysis of thick

functionally graded rectangular plates based on the higher-order shear deformation

plate theory”, Applied Mathematical Modelling, 34(11), pp. 3659-3673.

Chen, X. L. and Liew, K. M. (2004) “Buckling of rectangular functionally graded material plates subjected to nonlinearly distributed in-plane edge loads”, Smart