摘要
应用复变函数的方法,研究电致伸缩材料内置电极附近的应力奇异性.基于精确的电边界条件,采用Hilbert理论以及复变函数中的Cauchy积分与留数定理,首先分别给出了柔性电极和刚性电极的复势函数解,然后就这两种极限情况,讨论了电极刚度对应力场奇异性的影响.研究结果表明:无论对柔性电极还是刚性电极,Max-well应力的应力场均呈现r-1阶的奇异性,但对于前者总应力奇异性系数为零,而对于后者总应力奇异性系数与基体的材料常数有关.
Based on complex variable method, this work studies the singular structure of stresses at the tips of an electrode embodied in an electrostrictive Material. By using exact electric boundary conditions on the electrode,combined with the solution of Hilbert-problem and the principle of the Cauchy-type integrals, the complex potentials are derived, respectively, for a soft electrode and a rigid electrode. Then, the singular factors of stress fields are presented for these two limiting cases. It is found that in general, for both cases of soft and rigid electrodes,the Maxwell＇s stress fields have the singularity of r^-1-type,but for the former the total stresses have not any singularity, while for the latter the singularity of the total stresses is dependent on the material constants of the matrix.
出处
《固体力学学报》
CAS
CSCD
北大核心
2009年第4期400-404,共5页
Chinese Journal of Solid Mechanics
基金
国家自然科学基金(10672076)资助
关键词
电致伸缩材料
电极
应力奇异性
复变函数法
electrostrictive materials, electrode, stress singularity, complex function method
