无限大板功能梯度材料裂纹尖端的应力场分析  

Analysis of Stress Field at Crack Tip of Functionally-graded Material in Infinite Plate

作　　者：郭璐 张雪霞[1,2] 赵文彬 GUO Lu;ZHANG Xue-xia;ZHAO Wen-bin(School of Applied Science,Taiyuan University of Science and Technology,Taiyuan 030024,China;Department of mathematics,Jinzhong University,Shanxi Jinzhong 030619,China)

机构地区：[1]太原科技大学应用科学学院,太原030024 [2]晋中学院数学系,山西晋中030619

出　　处：《太原科技大学学报》2022年第3期254-257,263,共5页Journal of Taiyuan University of Science and Technology

基　　金：国家青年科学基金(11402139);山西省自然科学基金(201601D102003)。

摘　　要：文章研究了无限大功能梯度材料(FGM)的反平面静态裂纹问题,针对反平面静态裂纹问题,建立了任意偶数次的负指数幂函数模型。基于任意偶数次的负指数幂函数模型以及FGM裂纹问题静态理论,经过一系列的数学处理,将问题转化为求解一组奇异积分方程组。利用copson方法求解得到了裂纹尖端的应力强度因子。在分析计算结果的基础上,综合讨论了梯度参数和不均匀系数对应力强度因子的影响。The anti-plane static crack problem of infinite functionally-graded materials(FGM)is studied.An arbitrary even order negative exponential power function model is established for the anti-plane static crack problem.Based on the negative exponential power function model of any even order and the static theory of FGM crack problem,after a series of mathematical treatment,the problem is transformed into solving a set of singular integral equations.The stress intensity factors at the crack tip are obtained by copson method.Based on the analysis of the calculation results,the effects of gradient parameters and inhomogeneous coefficient on the SIF are discussed.

关 键 词：功能梯度材料 应力强度因子 积分变换 对偶积分方程 

分 类 号：O29[理学—应用数学] TB11[理学—数学]