压电材料平面裂纹尖端场的杂交应力有限元分析  

ANALYSES OF CRACK-TIP FIELDS OF PLANE PIEZOELECTRIC MATERIALS BY THE HYBRID STRESS FINITE ELEMENT METHOD

作　　者：周勇[1] 王鑫伟[1] 

机构地区：[1]南京航空航天大学航空宇航学院,南京210016

出　　处：《力学学报》2004年第3期354-358,共5页Chinese Journal of Theoretical and Applied Mechanics

基　　金：国家自然科学基金(10072026;50135030);国家教委博士点基金(20020287003)资助项目.~~

摘　　要：基于复势理论和杂交变分原理建立了一种适用于力电耦合分析的杂交应力有限元模型.给出了建立刚度矩阵的主要公式和推导过程,单元内的位移场和应力场采用满足平衡方程的复变函数级数解,假设的复变函数级数解事先精确满足裂纹的无应力和电位移法向分量为零的条件,单元外边界的位移场假设按抛物线变化,单元的刚度矩阵采用Gauss积分的方法得出.通过对力电耦合裂尖场的数值计算验证了程序的正确性和单元的有效性,同时也用所得结果校验了理论解.A hybrid stress finite element based on the complex potential theory and hybrid variational principle is proposed for mechanical-electrical coupling analyses. The formulations are given in detail in this paper. The complex series solutions satisfying the equilibrium equations and compatibility equations are chosen as the displacement and stress fields in the element domain. Assume that the series solutions satisfy exactly the traction free and the zero normal electrical displacement boundary conditions along the crack surface in advance. While the displacements along the element outer boundaries vary parabolically. The element stiffness matrix is then obtained by using the Gauss quadrature method. Numerical examples verify the accuracy of the program and the efficiency of the proposed element. Meanwhile, the theoretical results are verified by the finite element results.

关 键 词：压电材料 裂纹 杂交有限元 数值计算 复变函数 

分 类 号：TM22[一般工业技术—材料科学与工程] TB301[电气工程—电工理论与新技术]