复合材料反平面切口端部奇性研究  

Singularity at Tip of a Composite Notch Under Anti-plane Loading

作　　者：程长征[1] 葛仁余[1] 薛伟伟[1] 牛忠荣[1] 

机构地区：[1]合肥工业大学土木与水利工程学院,安徽合肥230009

出　　处：《计算物理》2013年第5期700-705,共6页Chinese Journal of Computational Physics

基　　金：国家自然科学基金(11102056;11372094);安徽省自然科学基金(11040606Q38)资助项目

摘　　要：基于复合材料切口尖端位移场的渐近展开,将切口的反平面平衡控制方程转化为关于切口奇性指数的特征微分方程,采用一种变换将其化为线性特征微分方程组,引入插值矩阵法计算相应边界条件下方程组的特征值以获取切口尖端的应力奇性指数.研究单相材料切口、双相材料切口及止于异质界面切口的奇异性,算例表明该方法可以一次性计算出多阶奇性指数.对所取得的非奇异指数尽管切口不表现出奇性状态,但却是描述切口尖端完整应力场必不可少的参量.Based on asymptotic extension of displacement field at a composite notch tip, equilibrium equation for a notch subjected to anti-plane loading is transformed into a characteristic differential equation respects to notch singularity orders. A transformation is applied to convert the equation into a set of characteristic linear ordinary differential equations. Interpolate matrix method is introduced to solve the equations for getting notch singularity orders. A single material notch, a bi-material notch and a notch terminated at bi- material interface are studied successively. Examples indicate that the method provides all stress singularity orders synchronously. Though singular stress state is not shown with regard to non-singular orders, non-singular stress orders are indispensable parameters as evaluating complete stress field at notch tip region.

关 键 词：复合材料 反平面切口 奇性分析 渐近展开 

分 类 号：O343.6[理学—固体力学]