本研究主要在探討非共線多裂縫位於均質的無限線彈性體內,受到反平面動態荷重之應力強度因子。 本文係利用差排模擬裂縫,建構出裂縫面上應力分布的積分方程式,再將積分方程式進行拉普拉斯積分轉換,之後再使用高斯-柴比雪夫積分法將方程式離散,進而得到拉普拉斯轉換域下之數值解形式。接著利用雅克比多項式做拉普拉斯逆轉換,得到時域下裂縫之應力強度因子。 本文計算了非共線等長無錯位雙裂縫或三裂縫、非共線等長錯位雙裂縫、非共線不等長無錯位雙裂縫與非共線不等長錯位雙裂縫的應力強度因子。由非共線等長無錯位雙裂縫的結果與文獻結果比較得知,本方法有極高的準確性。
The stress intensity factor of non-collinear cracks in a homogeneous linear elastic body under anti-plane dynamic load is constructed in this study. Distribution of dislocations is used to simulate the cracks and derive the integral equation which relating tractions on the crack planes. The integral equation in the Laplace transform domain is solved by Gaussian-Chebyshev integration quadrature. Then, Jacobi-Polynomials is used in a numerical inverse Laplace scheme to calculate the stress intensity factor in the time domain. Specifically the cases studied include: two or three non-collinear cracks of identical length without malposition, a pair of non-collinear cracks of identical or different lengths with malposition and a pair of non-collinear cracks of different lengths without malposition. Comparison of the numerical result for two non-collinear cracks of identical length without malposition with literature shows that the present method is highly accurate.