含孔洞正交性材料板應力集中之研究

Abstract

本文利用柯西積分方程式結合異向性彈性力學所得到的雙積分方程式，分析了五種正交性材料板內或邊界上不同類型橢圓孔洞的最大應力值。分析前先以含單一孔洞之無限板中受均勻張力的解析解確認本文數值分析方法的準確性。並將五種孔洞類型與文獻有關等向性材料數值解與本文數值解的比較以進一步驗證方法的正確性。本文另考慮以立方晶體矽為例，探討當橢圓孔洞短軸除以長軸比例越小以及兩個或兩個以上的孔洞之間彼此間距越小時均有最大應力值增加的情形，且最大應力值均較等向性材料略小。最後探討當由彈性常數所組成的材料常數A值越小時最大應力值越大；而最大應力值並不隨著材料常數B的改變而有明顯變化。本文建立一套輸入材料常數、孔洞大小、與間距即可求得最大應力值的方法。

With dual boundary integral equation, combined from Cauchy's formalism and anisotropic elastic mechanics, this thesis is aimed to analyze the maximum stress concentration on the inner plate or boundary by five different types of elliptic holes in an orthotropic plate. First, the analytic solution of the infinite plate with single elliptic hole under uniform tensile stress is used to confirm the accuracy of the numerical method. Second, five different types of elliptic holes are compared with literature numerical solution for isotropic material to further confirm the accuracy of the method. And then, this thesis takes Silicon, a cubic materials, for example, when the ratio of minor axes to major axes and the distance between two or more than two elliptic holes are smaller, the maximum stress value will be larger, and it would be slightly smaller than that for isotropic material. Last, when the material constant A formed by elastic constant is smaller, the maximum stress value would be larger, but the value would not change obviously with material constant B. This thesis constructs a method for computing the maximum stress concentration value by inputting the elastic constant, the size of holes, and distance between each holes.