关于任意边界缺口或裂纹群问题的一类解法(Ⅰ)解析方法

在工程断裂分析中任意边界缺陷如缺口或裂纹群是常见和重要的情况.本文推广穆斯赫利施维利方法作出了任意二维边界缺口或裂纹群问题的一类解法,通过相继应用解析延拓、劳朗级数展开和共形映照.我们最终获得支配问题的一组线性代数方程,然后应用标准的线代数方程组求解程序对问题就作出了解答.值得注意的是.本文方法可用于作出缺陷表面具有任意的光滑载荷分布情况的解答.

On a Class of Methods for Solving Problems of Random Boundary Notches and/or Cracks

In engineering fracture analysis,random boundary imperfections as notches or cracks are common and important.In this paper,we have worked out a class of methods for solving two-dimensional problems of random boundary notches and/or cracks by an extension of Muskhelishvili's method.Through successive applications of analytic conti-nuation,Laurent series expansion and conformal mapping,we finally arrived at a set of linear algebraic equations governing the problem,Then standard com puting program of linear algebraic eq nations may he used to com plete the solution.It is noticed that the prescn method may give solutions for the cases in which there are certain smooth load distrihutmns on the notch surfaces.