有限高狭长压电体中半无限反平面裂纹分析  

Anti-Plane Analysis of a Semi-Infinite Crack in a Piezoelectric Strip

作　　者：郭俊宏[1] 刘萍[1] 卢子兴[1] 秦太验[2] 

机构地区：[1]北京航空航天大学固体力学所,北京100191 [2]中国农业大学理学院,北京100083

出　　处：《应用数学和力学》2011年第1期72-78,共7页Applied Mathematics and Mechanics

基　　金：国家自然科学基金资助项目(10932001;11072015);北京市教育委员会共建项目建设计划资助项目(KZ201010005003);高等学校博士学科点专项科研基金资助项目(20101102110016);北京航空航天大学博士创新基金(300351)的资助

摘　　要：利用保角变换和复变函数方法,研究了裂纹面上受反平面剪应力和面内电载荷共同作用下的有限高狭长压电体中半无限裂纹的断裂问题,给出了电不可通边界条件下裂纹尖端场强度因子和机械应变能释放率的解析解.当狭长体高度趋于无限大时,可得到无限大压电体中半无限裂纹的解析解.若不考虑电场作用,所得解可退化为纯弹性材料的已知结果.此外,通过数值算例,分析了裂纹面上受载长度、狭长体高度以及机电载荷对机械应变能释放率的影响规律.Using the complex variable function method and the technique of conformal mapping,the fracture problem of a semi-infinite crack in a piezoelectric strip was studied under the anti-plane shear stress and in-plane electric load. The analytical solutions of the field intensity factors and the mechanical strain energy release rate were presented with the assumption that the surface of the crack was electrically impermeable. When the height of the strip tends to infinity,the analytical solutions of an infinitely large piezoelectric solid with a semi-infinite crack were obtained. Moreover,the present results can be reduced to the well-known solutions for a purely elastic material in the absence of electric loading. In addition,numerical examples were conducted to analyze the influences of loaded crack length,the height of the strip and applied mechanical/electric loads on the mechanical strain energy release rate.

关 键 词：狭长压电体 半无限裂纹 复变函数方法 场强度因子 机械应变能释放率 

分 类 号：O346.1[理学—固体力学]