基于复变函数的含孔边裂纹结构弹性断裂力学问题研究

Research on Elastic Fracture Mechanics of Perforated Edge Crack Structures Based on Complex Variable Function

针对当前含孔边裂纹结构弹性断裂力学研究方法存在的研究结果与实际结果吻合性差、研究结果用户满意度低的问题,提出基于复变函数的含孔边裂纹结构弹性断裂力学问题研究方法。基于裂纹受力条件以及受力状况,将含孔边裂纹划分成两类:Ⅰ型裂纹和Ⅱ型裂纹。发现Ⅰ型裂纹的上下表面是相对张开的,Ⅱ型裂纹的上下表面沿横轴相对滑开。根据含孔边裂纹分析情况,利用复变函数法对含孔边裂纹结构弹性断裂力学问题予以解决,通过构建保角映射函数,并将无限放大的含孔边裂纹外部区域映射至单位圆内部或者是上半面,以此解决裂纹结构平面弹性相关问题,得到裂纹应力强度因子,实现含孔边裂纹结构弹性断裂力学研究。实验结果表明,基于复变函数的含孔边裂纹结构弹性断裂力学研究方法分析结果与实际情况吻合度最高为99%,研究结果用户满意度相较当前方法更高。所提方法整体性能优越,可为该领域研究提供一定的借鉴。

Aiming at the problem that the existing research results of elastic fracture mechanics with cracked edge structures are inconsistent with the actual results and the low user satisfaction of the research results,a method based on complex variable function for elastic fracture mechanics of perforated edge cracks is proposed.Based on the stress conditions of the crack and the stress conditions,the cracks with hole edges are divided into two types:I-type crack and type II crack.The upper and lower surfaces of the type I crack were found to be relatively open,and the upper and lower surfaces of the type II crack were relatively slid along the horizontal axis.According to the analysis of cracks in the edge of the hole,the complex fracture function method is used to solve the problem of elastic fracture mechanics of the cracked structure with holes.By constructing the conformal mapping function,the infinitely enlarged outer region of the hole containing crack is mapped to the inside of the unit circle or It is the upper half,in order to solve the problem of the plane elasticity of the crack structure,obtain the crack stress intensity factor,and realize the elastic fracture mechanics of the cracked structure with holes.The experimental results show that the analysis results of the elastic fracture mechanics method based on the complex variable function are the highest with the actual situation,and the user satisfaction is higher than the current method.The overall performance of the proposed method is superior,which can provide some reference for the research in this field.