利用MLS-Ritz法分析具部份貫穿內部裂縫3D功能梯度材料矩形板之挫屈及振動

Application of MLS-Ritz Method to Study Buckling And Free Vibration of 3D FGM Rectangular Plates with Internal Part-Through Surface Crack

葉宜欣(Yi-Sin Yeh)

指導教授 ： 黃炯憲

國立交通大學/工學院/土木工程系所/碩士(2020年)

摘要

板在製造過程中，因工程實務而產生裂縫，使板之初始應力重新分配，導致其動態行為及穩定性與完整板不同。本研究依三維彈性理論配合MLS-Ritz法求解具內部局部開裂裂縫功能梯度材料板之挫屈載重及自然振動頻率。從三維彈性漸近解中取適當函數建立 平面允許函數，使允許函數本身及一階導數具跨越裂縫不連續現象，並準確描述內部貫穿裂縫尖端處之應力奇異性，再加上虛擬人工彈簧模擬裂縫局部閉合之行為。本研究中所探討之功能梯度板是由金屬鋁(Al)和陶瓷(Al2O3)組成，且板之材料性質沿厚度方向(z)以冪次方改變。
本研究對具中央局部開裂裂縫FGM方形板之挫屈載重和自然振動頻率進行收斂性分析。依收斂性分析結果選取適當求解參數，進一步探討不同邊界條件、板厚、板長寬比、裂縫角度、裂縫位置、裂縫長度、裂縫開裂深度及功能梯度材料參數對挫屈載重、自然頻率及模態圖之影響。

關鍵字

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

並列摘要

Cracks can be caused by loading and improper manufacturing process. A crack yields the redistributions of the internal stresses in a loaded plate, reduces the plate stiffness and significantly changes the dynamic characteristics and stability of the plate. This study applies MLS-Ritz method with three-dimensional elasticity theory to examine buckling loads and vibration frequencies of functionally graded material (FGM) rectangular plates with internal part-through surface cracks. The three-dimensional admissible functions consist of polynomials in the thickness (z) direction and shape functions in x-y plane established by the moving least squares technique with the enriched basis functions, which include appropriate functions taken from the three-dimensional asymptotic solutions for stress singularities at a crack front. The admissible functions correctly account for the discontinuities of displacement across a crack and the stress singularities at crack fronts. Such admissible functions appropriately describe a cut-through crack. Virtual artificial springs are installed on the surfaces, where are supposed to be closed in a part-through surface crack, and the resulting spring potential energy is included in the total energy in the Ritz method.
The proposed solutions is validated through the comprehensive convergence studies of buckling loads and vibration frequencies of FGM square plates with and without central vertical internal part-through surface crack. The FGM plates considered in this study is composed of aluminum and ceramic, and the material properties of the plate change along the thickness direction with a simple power law. The proposed approach is further employed to investigate the effects of boundary conditions, plate thickness and aspect ratios, crack configurations and variations of material property on the buckling loads and vibration frequencies of cracked FGM rectangular plates.

並列關鍵字

buckling load ； vibration frequency ； moving least square method ； functionally graded material ； three-dimensional elasticity ； part-through surface crack ； Ritz method

參考文獻

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