压电复合材料中垂直于极化方向具有不对称共线裂纹的圆形孔口问题  

Problem of a Circular Hole with Asymmetry Collinear Cracks Perpendicular to the Polarization Direction in Piezoelectric Composite Materials

作　　者：刘莹[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：《内蒙古大学学报（自然科学版）》2012年第3期244-250,共7页Journal of Inner Mongolia University：Natural Science Edition

基　　金：国家自然科学基金资助项目(10761005);内蒙古自然科学基金资助项目(2009MS0102)

摘　　要：利用复变函数方法,通过构造广义保角映射,研究了压电复合材料中垂直于极化方向具有不对称共线裂纹的圆形孔口问题,给出了电不可渗透边界条件下裂纹尖端的场强度因子和机械应变能释放率的解析解.在极限情形下,该解析解可给出具有对称共线裂纹的圆形孔口,带单裂纹的圆形孔口和Griffith裂纹等构型的相应结果.基于该解析解,通过数值算例讨论了具有不对称共线裂纹圆形孔口的裂纹长度以及半径对机械应变能释放率的影响规律,得到一些重要结论.By constructing a generalized conformal mapping and using the complex variable function method,the problem of a circular hole with asymmetry collinear cracks perpendicular to the polarization direction in piezoelectric composite materials is investigated.The analytical solutions of the field intensity factors and mechanical strain energy release rate are presented with the assumption that the surtace of the crack is electrically impermeable.Under the conditions of limitation,the solutions of a circular hole with symmetrical collinear cracks,a circular hole with one crack and the Griffith crack can be obtained.The influences of the length of cracks and radius on the mechanical strain energy release rate are analyzed by numerical examples and some useful conclusions are got.

关 键 词：压电复合材料 具有不对称共线裂纹的圆形孔口 广义保角映射 机械应变能释放率 

分 类 号：O346.1[理学—固体力学]