Numerical Solution Of The Singular Integral Equation Of The Anisotropic Medium With Inclined Cracks

This thesis is consisted of three parts totally.The first part summarizes the investigation situation of some aspects related to this thesis and the main content discussed in this paper.In the second part, the problem of anisotropic elastic plate with arbitrarily inclined cracks is investigated by the complex variable method. This problem is reduced to solve the boundary value problem for analytic functions. By constructing a Kolosov function and a Sherman transformation, the boundary value problem is transformed into singular integral equation. This singular integral equation is solved numerically by employing Lobotto-Chebyshev quadrature formulas. The approximate analytical expressions of stress intensity factors are obtained. At the end an instance of an infinite plate with a single inclined crack is discussed. It shows this numerical solution coincides with the analytical solution.In the third part, the periodic problem of arbitrarily inclined cracks in the infinite anisotropic plate is studied, using the similar method in the second part. We obtain the numerical solution of singular integral equation with Hilbert kernel and the approximate expression of stress intensity factor at the end of the cracks. A numerical example is given in the basic periodic strip which containing a single inclined crack, and analysis the factors that affect the SIFs.