雙材料板內奇異應力場之計算

Computation of Singular Stress Fields in Bimaterial V-notched Plates

羅翊栩(Yi-Hsu Lo)

指導教授 ： 吳光鐘

國立臺灣大學/工學院/應用力學研究所/碩士(2013年)

https://doi.org/10.6342/NTU.2013.00160

摘要

由線彈性力學理論可知在V型缺口尖端之應力常存在奇異性。本文探討異向性雙材料缺口板受到外加張應力作用所產生之奇異應力場，並計算異向性雙材料介面缺口之尖端應力強度因子。
本研究結合對偶邊界積分方程及缺口尖端應力場，發展一數值計算方法。計算時將兩材料之邊界及介面離散為若干個邊界元素，並把其各分為靠近缺口尖端的兩元素以及其他一般元素。一般元素上之位移梯度及曳引力係假設為常數，而含尖端的兩元素上位移梯度及曳引力則以漸進場形式表示。將一般元素中點設為邊界積分方程式的配置點，再加上與路徑無關積分即可建立聯立方程式，求解未知位移梯度、曳引力及應力強度因子。
本文以均質及雙材料缺口板受外加張應力作用下文獻已存之相關算例，驗證所提方法之正確性。本文並討論雙材料缺口板中缺口連接長度與應力強度因子之關係，結果發現當兩材料缺口連接長度越短時，所得之應力強度因子會越大。本文另討論雙材料缺口板中缺口開角與應力強度因子之關係，結果顯示缺口開角與應力強度因子的關聯性不大。

關鍵字

均質 ； 雙材料 ； 應力強度因子 ； 奇異應力 ； Ｖ型缺口 ； 邊界積分方程式 ； 線彈性力學 ； 史磋法

並列摘要

Based on linear elasticity, it is well known that the stresses is singular at the tip of a v-notched plate. The purpose of this thesis is to discuss the stress fields of an anisotropic bimaterial v-notched plate associated with tensile stress, and compute the stress intensity factors and the singular stress at the notch tip.
In this thesis, the dual boundary integral equations and the near-tip stress field are combined to develop a numerical computation method. The boundary and the interface of the two materials are discretized into a number of elements, including regular elements and tip elements. The displacement gradient and the traction are assumed to be constant on the regular elements, and the displacement gradient and the traction are assumed to be given by the near-tip fields. A set of simultaneous equations is established by choosing the midpoints of each regular elements as collocation points in conjunction with the path-independent integrals to solve the unknown displacement gradients, the unknown tractions, and the stress intensity factors.
The accuracy of the proposed method is checked by comparing the results with those in the literature for several examples. The method is used to investigate the relation of the connecting length and the stress intensity factors. The results shows that the shorter the connecting length, the larger the stress intensity factor is. The relation of the notch angle and the stress intensity factor is discussed as well. It appears that the notch angle has little to do with the stress intensity factors.

並列關鍵字

homogeneous ； bimaterial ； stress intensity factor ； singular stress ； v-notched ； boundary integral equation ； linear elastic

參考文獻

[27] 林宜璇 (2010)。邊界積分法於鍍膜半空間之應用；國立台灣大學應用力學研究所碩士論文。

[28] 王裕升 (2012)。裂縫受集中力作用之分析；國立台灣大學應用力學研究所碩士論文。

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