【作者】 张建勇；

【导师】 李星；

【作者基本信息】 宁夏大学 ， 应用数学， 2004， 硕士

【摘要】 本文共分为三个部分。 第一部分概述了相关方面的研究现状以及本文的主要内容。 第二部分讨论了正交无限各向异性板中任意斜裂纹问题，应用平面弹性复变方法，将该问题转化为求解一组解析函数边值问题，通过构造Kolosov函数和Shemann变换，进一步将求解边值问题转化为求解Cauchy奇异积分方程的解，应用数值求积公式，求得奇异积分方程的数值解，并得到了应力强度因子的近似表达式。最后给出了板中含单条裂纹的算例，并与精确结果进行比较，吻合的很好。 第三部分讨论了无限各向异性板中含有周期斜裂纹的问题，运用了与第二部分类似的方法，但是所得方程是Hilbert核奇异积分方程。最后得到该奇异积分方程的数值解和应力强度因子的近似表达式。文中给出了在一个基本周期带中含有一条裂纹的数值算例，并分析了影响应力强度因子的因素。更多还原

【Abstract】 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.更多还原