【作者】 李圆； 赵明皞； 范翠英； 徐广涛；

【Author】 Li Yuan;Zhao Minghao;Fan Cuiying;Xu Guangtao;School of Mechanics and Engineering Science,Zhengzhou University;School of Mechanical Engineering,Zhengzhou University;

【机构】 郑州大学力学与工程科学学院； 郑州大学机械工程学院；

【摘要】 不连续位移边界积分方程方法是分析裂纹问题的一种有效方法,已经被广泛应用于研究弹性、压电、电磁等智能材料的断裂问题。本文将这种方法推广到含有任意形状平片三维压电半导体材料,得到了利用广义不连续位移表示的强度因子的表达式。具体工作如下:(1)引入了裂纹面上不连续载流子密度这一概念,完善了广义不连续位移体系;(2)考虑了压电材料与压电半导体的联系,利用压电介质和拉普拉斯方程的格林函数,得到了含有体积分的广义不连续位移表示的超奇异边界积分方程组;(3)分析了广义不连续位移在裂纹尖端的奇异性并求解得到广义不连续位移表示的广义应力强度因子表达式;(4)给出了有限元法求解的圆盘裂纹的一个算例,验证了求得的强度因子表达式。更多还原

【Abstract】 The displacement discontinuity boundary integral equation method is extended to analyze the singularity of near-border fields of a planar crack of arbitrary shape in the isotropic plane of a three-dimensional transversely isotropic piezoelectric semiconductor.The hyper-singular boundary integral equations are derived in terms of the displacement,electric potential and carrier density discontinuities across the crack faces,in which body integrals of the carrier density are introduced.Based on the finite-part integrals,singularity exponents and asymptotic expressions of the crack border fields are obtained.The stress,electric displacement and electric current intensity factors are given in terms of the displacement,electric potential and carrier density discontinuities.Finite element results of a penny-shaped crack based on the piezoelectric-conductor iterative method(PCIM) are used to verify the derivations of the intensity factors.更多还原