压电复合材料中翼形裂纹反平面问题的解析解  

Analytical Solutions of a mode-Ⅲ wing-shape Crack in Piezoelectric Composite Materials

作　　者：钟海英[1] 刘官厅[1] 

机构地区：[1]内蒙古师范大学数学科学学院,内蒙古呼和浩特010022

出　　处：《数学的实践与认识》2015年第5期219-225,共7页Mathematics in Practice and Theory

基　　金：国家自然科学基金(11262017;11262012);教育部科技研究重点项目(212029);内蒙古师范大学"十百千人才工程"研究项目(RCPY-2-2012-K-035);研究生科研创新基金项目(CXJJS13042)

摘　　要：利用保角映射和cauchy积分理论研究了压电复合材料中翼形裂纹的反平面问题,分别得到了电不可通和电可通两种边界条件下裂纹尖端场强度因子和机械应变能释放率的解析表达式.结果表明K随β的变化而变化,当β=0时,退化为无限大压电体中Ⅲ型Griffith裂纹.Based on the technique of conformal mapping and the complex variable func- tion method, the anti-plane problem of a wing-shape in a piezoelectric composite material was studied. By using Cauchy integral formula and the Residue theorem, the analytical expressions of the field intensity factors and the mechanical strain energy release rate were presented with the assumption that the surfaces of the crack were electrically impermeable and electrically permeable. The results showed that K was with changes of β, whenβ= 0, the type Degenerate to III Griffith crack in an infinite piezoelectric.

关 键 词：压电复合材料 翼形裂纹 复变函数方法 场强度因子 机械应变能释放率 

分 类 号：TB33[一般工业技术—材料科学与工程] O346.1[理学—固体力学]