摘要
基于切口根部物理场的幂级数渐近展开假设,从三维应力平衡方程和麦克斯韦方程组出发,导出关于双压电材料楔形界面切口端部奇性指数的特征微分方程组,并将切口的力电学边界条件表达为奇性指数和特征角函数的组合,从而将双压电材料楔形界面切口端部奇性指数的计算转化为相应边界条件下常微分方程组特征值的求解,运用插值矩阵法求解界面端部若干阶应力奇性指数和相应特征函数.计算结果与已有结果对比表明本文方法的有效性和具有较高的计算精度.
With asymptotic assumption for physical field near notch tip, characteristic differential equations for electroelastic singularities of wedges that contain bounded piezo/piezo materials are built from three-dimensional equilibrium equations and Maxell equations. Mechanical and electric boundary conditions are expressed by combination of singularity orders and characteristic angle functions. Thus, evaluation of singularity orders is transformed into solving ordinary differential equations （ODEs） under designated boundary conditions. Interpolating matrix method is introduced to solve derivative ODEs. More electroelastic singularity orders and associated eigenfunctions in wedges that comprise two bounded transverse isotropic piezoelectrics materials are obtained. It shows that the method is efficient and has high accuracy compared with existent solutions.
出处
《计算物理》
CSCD
北大核心
2016年第1期57-65,共9页
Chinese Journal of Computational Physics
基金
国家自然科学基金(11372094)
安徽省教育厅(TSKJ2014B16和TSKJ2014B13)资助项目
关键词
奇异性
压电材料
渐近展开
特征函数
插值矩阵法
singularity
piezoelectric material
asymptotic expansion
characteristic angle functions
interpolating matrix method
