一维六方准晶压电材料中唇形裂纹反平面问题的解析解  

ANTI-PLANE ANALYTIC SOLUTIONS OF PROBLEM ABOUT A LIP-SHAPE CRACK IN PIEZOELECTRICITY OF ONE-DIMENSIONAL HEXAGONAL QUASICRYSTALS

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,呼和浩特010022

出　　处：《固体力学学报》2015年第2期179-184,共6页Chinese Journal of Solid Mechanics

基　　金：国家自然基金项目(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)资助

摘　　要：论文在准晶压电材料基本方程的基础上,根据点群的对称性和一维六方准晶的线性压电效应,导出了一维六方准晶压电材料反平面问题的控制方程.利用复变函数的方法,通过引入适当的保角映射,研究了准晶压电材料中唇形裂纹的反平面问题,并利用Cauchy积分理论,得到在电不可通边界条件下的裂纹尖端场强度因子与机械应变能释放率的解析表达式.According to the symmetry of the point groups of one-dimensional hexagonal quasicrystal and its linear piezoelectricity effect, the control equations of anti-plane problem for the one-dimensional hexagonal quasicrystal are derived, which are based on the piezoelectricity fundamental equations of quasic- rystal material. By using the complex variable function method and the technique of conformal mapping, the anti-plane problem of a lip shape crack embedded in piezoelectricity of one-dimensional hexagonal quasicrystals is studied. Then, by means of the Cauchy integral formula, the analytical expressions for the crack tip intensity factor and the mechanical strain energy release rate are presented with the assumption that the crack is electrically impermeable.

关 键 词：一维六方准晶压电材料 唇形裂纹 应力强度因子 保角映射 解析解 

分 类 号：O346.1[理学—固体力学]