裂縫受集中力作用之分析

Abstract

本研究主要在探討均質的線彈性體內多裂縫系統受到集中力作用之應力強度因子。本文係利用差排模擬裂縫，建構出裂縫面上應力分佈之積分方程式，並使用高斯-謝比雪夫積分法得到方程式之數值解形式；進而由積分方程式之數值解建立聯立方程式，解得差排密度源函數之節點值，由此計算出裂縫尖端之應力強度因子。 本文首先討論了無限空間中受集中力作用之共線等長雙裂縫與半無限空間中受集中力作用之單一邊裂縫兩個算例與文獻做比較，得知本文解法具有高度準確性；接著計算無限空間中受集中力作用之非共線多裂縫系統以及半無限空間中受集中力作用之共線多裂縫系統。本文建立了一套求解集中力作用於多裂縫系統之應力強度因子的分析方法。

The stress intensity factor of multiple cracks system in a homogeneous linear elastic body under concentrated load is discussed in this study. Distribution of dislocations are used to simulate the cracks and construct the integral equation which relating tractions on crack planes. The integral equation can be calculated numerically using Gaussian- Chebyshev integration quadrature and derive simultaneous equations. Solving the simultaneous equation can obtain the nodes of dislocation intensity function and then calculate the stress intensity factor at the crack tips. This thesis studied two collinear cracks of identical length under concentrated loading in infinite body and one edge crack under concentrated loading in semi- infinite body at first, to compare the numerical result with literature showing that the present method is highly accurate. Then calculate non-collinear multiple cracks system under concentrated loading in infinite body and collinear multi-edge cracks under concentrated loading in semi-infinite body. This thesis construct a method solving stress intensity factor for multiple cracks under concentrated loading.