压电效应下一维六方准晶中正六边形孔边裂纹传播问题  

The Problem of the Propagating Crack from Regular Hexagonal Hole in 1D Hexagonal Quasicrystals under Piezoelectric Effect

作　　者：高慧芳 GAO Huifang(Department of Mathematics and Computer,Shuozhou Normal College,Shuozhou 036000,China)

机构地区：[1]朔州师范高等专科学校数计系,山西朔州036000

出　　处：《安阳师范学院学报》2021年第5期9-13,共5页Journal of Anyang Normal University

摘　　要：为了研究压电效应下一维六方准晶正六边形孔边快速传播裂纹问题,采用动力学理论,推导了一维六方压电准晶在运动坐标系下的反平面弹性问题的控制方程。引入无限大平面内正六边形孔口双裂纹到数学平面的保角映射函数,利用柯西积分公式,研究了在电不渗透的边界条件下一维六方压电准晶中正六边形孔边快速传播裂纹的反平面动态问题,得出了当裂纹匀速传播时,动态应力强度因子和电位移强度因子的解析解。这些结论在工程的动态实践应用分析中具有一定的参考价值。In order to study the problem of fast propagating crack from regular hexagonal hole in one dimensional hexagonal quasicrystals under piezoelectric effect,the governing equation of the antiplane elastic problem of one-dimensional hexagonal piezoelectric quasicrystals in the moving coordinate system was derived by using the kinetic theory and introducing the conformal mapping function of the double crack of a regular hexagonal orifice in an infinite plane to the mathematical plane.Using the cauchy integral formula,the antiplane dynamic problem of rapid spread of hexagonal hole edge crack in one-dimensional hexagonal piezoelectric quasicrystals under the electrically impermeable boundary conditions was studied,the analytical solutions of dynamic stress intensity factor and electric displacement intensity factor ware obtained when the crack was uniformly propagated.These conclusions are certain reference value in the dynamic practical application analysis of engineering.

关 键 词：正六边形孔边裂纹 保角映射函数 动态应力强度因子 电位移强度因子 

分 类 号：O346.1[理学—固体力学]