第三型裂縫受動態荷重之分析

Abstract

本文主要在探討於均勻(Homogeneous)的一無限線彈性(Linear Elastic)內之多個共線裂縫，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)模擬裂縫，建立裂縫面上應力分布的積分方程式。求解方法是先將相關積分方程式做拉普拉斯積分轉換，再使用高斯─柴比雪夫(Gauss-Chebyshev)積分法，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，再使用拉普拉斯逆變換(Laplace inverse Transform)，計算裂縫之應力強度因子。 本文計算了單一裂縫、對稱或非對稱雙裂縫及對稱三裂縫的應力強度因子。由單裂縫的結果與理論解之比較顯示本法具有極高的準確性。

The problem of a homogeneous linear elastic body containing multiple collinear cracks under anti-plane dynamic load is considered in this work. The cracks are simulated by distributions of dislocations and an integral equation relating tractions on the crack planes and the dislocation densities is derived. The integral equation in the Laplace transform domain is solved by Gaussian-Chebyshev integration quadrature. The stress intensity factor associated with each crack tip is calculated by a numerical inverse Laplace scheme. Specifically the cases studied include: a single crack, a pair of cracks of identical or different lengths and three equally spaced cracks of identical length. Comparison of the numerical result for the single crack i with the analytic solution shows that the present method is highly accurate.