Anti-plane analysis of semi-infinite crack in piezoelectric strip  

作　　者：郭俊宏 刘萍 卢子兴 秦太验 

机构地区：[1]Institute of Solid Mechanics,Beijing University of Aeronautics and Astronautics [2]College of sciences,China Agricultural University

出　　处：《Applied Mathematics and Mechanics(English Edition)》2011年第1期75-82,共8页应用数学和力学（英文版）

基　　金：Project supported by the National Natural Science Foundation of China(Nos.10932001 and 11072015);the Scientific Research Key Program of Beijing Municipal Commission of Education (No.KZ201010005003);the Ph.D.Innovation Foundation of Beijing University of Aeronautics and Astronautics(No.300351)

摘　　要：Using the complex variable function method and the technique of the conformal mapping, the fracture problem of a semi-infinite crack in a piezoelectric strip is studied under the anti-plane shear stress and the in-plane electric load. The analytic solutions of the field intensity factors and the mechanical strain energy release rate are presented under the assumption that the surface of the crack is electrically impermeable. When the height of the strip tends to infinity, the analytic solutions of an infinitely large piezoelectric solid with a semi-infinite crack are obtained. Moreover, the present results can be reduced to the well-known solutions for a purely elastic material in the absence of the electric loading. In addition, numerical examples are given to show the influences of the loaded crack length, the height of the strip, and the applied mechanical/electric loads on the mechanical strain energy release rate.Using the complex variable function method and the technique of the conformal mapping, the fracture problem of a semi-infinite crack in a piezoelectric strip is studied under the anti-plane shear stress and the in-plane electric load. The analytic solutions of the field intensity factors and the mechanical strain energy release rate are presented under the assumption that the surface of the crack is electrically impermeable. When the height of the strip tends to infinity, the analytic solutions of an infinitely large piezoelectric solid with a semi-infinite crack are obtained. Moreover, the present results can be reduced to the well-known solutions for a purely elastic material in the absence of the electric loading. In addition, numerical examples are given to show the influences of the loaded crack length, the height of the strip, and the applied mechanical/electric loads on the mechanical strain energy release rate.

关 键 词：piezoelectric strip semi-infinite crack complex variable function method field intensity factor mechanical strain energy release rate 

分 类 号：O346.1[理学—固体力学]