任意傾斜多裂縫受反平面動態載重之暫態分析

Abstract

本文主要在探討於均勻(Homogeneous)的一無限線彈性(Linear Elastic)內之任意傾斜多裂縫，受反平面(Anti-plane)動態荷重之應力強度因子(Stress Intensity Factor)。 本文利用差排(Dislocation)分布模擬裂縫，建立裂縫平面上應力分布和差排密度的積分方程式。先將積分方程式做拉普拉斯積分轉換(Laplace Integration Transform)，再使用高斯─柴比雪夫積分法(Gaussian-Chebyshev Integration Quadrature) 求解，將方程式進行離散，進而得到拉普拉斯轉換域之數值解形式。最後透過拉普拉斯逆變換(Laplace inverse Transform)，計算每個裂縫尖端之應力強度因子。 本文計算了平行雙裂縫受傾斜平面應力波作用、單裂縫和平行雙裂縫受傾斜平面應力波作用之比較、任意傾斜裂縫受由法向量入射的水平剪力波的應力強度因子。由平行雙裂縫受傾斜平面應力波作用與傾斜且平行雙裂縫受由法向量入射的水平剪力波兩者的結果相互比較得知，本方法有極高的準確性。

The problem of a homogeneous linear elastic body containing arbitrary oriented cracks under anti-plane dynamic load is considered in this work. Distribution of dislocations is used to simulate the cracks and derive the integral equation which relates to tractions on the crack planes. The integral equation in the Laplace transform domain is solved by Gaussian-Chebyshev integration quadrature. For each crack tip we calculate the stress intensity factor using a numerical inverse Laplace scheme. Specifically the cases studied include: two parallel cracks under an oriented plane stress wave; comparing a single crack with two cracks under an oriented plane stress wave; and multiple arbitrarily oriented cracks under the normal incidence of a plane horizontal shear stress wave. Comparison of the numerical results for two cracks under an oriented plane stress wave with multiple arbitrarily oriented cracks under the normal incidence of a plane horizontal shear stress wave shows that the present method is highly accurate.