摘要
运用复变函数法,通过保角变换公式,研究了一维六方压电准晶狭长体中快速传播与静态的Griffith裂纹问题。给出了电非渗透型与电渗透型两种情况下动态的应力与电位移强度因子的解析解。当运动速度趋于零时,解析解将退化成为静止状态下的解。通过算例,分析了静止状态下裂纹长度、狭长体高度对应力强度因子的影响规律。结果表明:当狭长体高度不变时,各应力强度因子随裂纹长度的变大而递增,而后趋于某个稳定值;当裂纹长度固定时,各应力强度因子随狭长体高度的增大而增大,最后趋于某一常数;当狭长体高度趋于无穷大时,所得应力强度因子的解析解可退化为无穷大平面内Griffith裂纹解。
The plane problem of one-dimensional hexagonal piezoelectric quasicrystal strip with a rapid propagation Griffith crack is investigated based on a conformal transformation mapping and using complex variable function method. The analytic solutions of the dynamic stress intensity factors with electrically impermeable and permeable conditions are obtained. When the movement velocity tends to zeros,the analytic solutions of the dynamic stress intensity factors can be degenerated to stationary solution. Some numerical experiments are performed to analyze the influences of the crack length and the eight of the strip on the field intensity factors. The results show that the stress intensity factor will increase with the crack length as the height of the strip is constant,and will then tend to a stable value. When the crack length is fixed,the stress intensity factor will increase with the height of the strip and will then tend to a constant.When the height of the strip tends to infinity,the result is reduced to the well-known result.
作者
郭怀民
麻桂英
赵国忠
GUO Huaimin;MA Guiying;ZHAO Guozhong(College of Mathematic Science,Baotou Teachers College,Baotou 014030,China)
出处
《黑龙江大学自然科学学报》
CAS
2018年第3期342-349,共8页
Journal of Natural Science of Heilongjiang University
基金
国家自然科学基金资助项目(11261035)
内蒙古自然科学基金资助项目(2015MS0108)
内蒙古自治区高等学校青年科技英才支持计划资助(NJYT-15-A07)
内蒙古自治区高等学校科学研究重点项目(NJZZ12198)
包头师范学院阴山学者培养计划
内蒙古自治区高等学校科学研究项目(NJZY16235)
关键词
一维压电准晶
Griffith裂纹
复变函数法
应力强度因子
one-dimensional hexagonal piezoelectric quasicrystal
Griffith crack
complex function meth-od
stress intensity factor
