一维六方准晶压电材料中Ⅲ型椭圆孔口带不对称裂纹的解析解  

Analytical Solutions of a Mode-Ⅲ Two Asymmetrical Edge Cracks Emanating from an Elliptical Hole of Piezoelectricity of One-Dimensional Hexagonal Quasicrystals

作　　者：周彦斌[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：《内蒙古师范大学学报（自然科学汉文版）》2015年第2期156-161,共6页Journal of Inner Mongolia Normal University(Natural Science Edition)

基　　金：国家自然科学基金资助项目(11262017);教育部科技研究重点项目(212029);内蒙古师范大学科研创新基金项目(CXJJS13042)

摘　　要：用复变函数方法和保角变换研究准晶压电材料中椭圆带不对称裂纹的Ⅲ型问题.根据压电准晶材料的基本方程,利用点群的对称性,导出一维六方准晶压电材料反平面问题的控制方程,并利用Cauchy积分公式,得到在电不可通边界下的裂纹尖端场的强度因子和机械能释放率的解析表达式.This paper adopted variable function method and the technique of conformal mapping to study the anti-plane problem of two asymmetrical edge cracks emanating from an elliptical hole of piezoe-lectricity of onedimensional hexagonal quasicrystals.Based on the fundamental equations of peizoelasticity of quasicrystal materials and the symmetry of onedimensional hexagonal quasicrystals,one-dimensional piezoelectric crystal material control equations of antiplane problem were derived.Using Cauchy integral formula,the analytical expressions of the field intensity factors and the mechanical strain enegy rete were presented with the assumption that the crack were electrically impermeable.

关 键 词：一维六方准晶压电材料 保角映射 应力强度因子 机械能释放率 

分 类 号：O346.1[理学—固体力学]