Lwner理论对动态断裂问题的应用初探

Preliminary Exploration on the Application of Lwner's Theory in Developmental Fracture

对于固体中裂纹扩张的动态过程,如考虑惯性及弹性波的影响,则应力场的求解是一个相当困难的问题,有关研究进展缓慢。本文在不计惯性及弹性波影响的情形下,借助共形映射的Lwner理论,对由边界向内的裂纹扩展过程中应力场的连续变化解,提出一种近似处理的方法。当考虑裂纹扩展速度影响时,在现有的Radok—范天佑方法中也尝试着引入Lwner理论,使该方法得以改进。....

For the developmental problems of crack propagating in solid,if the effections of elastic waves and inertia are not negelected,then the determination about stress fields is very difficult.Over a long period of time,the researchs concerning this problems make slow progress.In this paper,neglecting the effections of elastic waves and inertia,we advance an approximate methods with the aid of Lwner’s theory belonging to conformal maps.This methods probably provide a certain continuous solution of stess fields with the condition that the crack propagate inside from boundary.Considering the effections of propagating velocity,we can improve the classical Radok-Fan methods by combine the Radok-Fan methods with Lwner＇s theory.