摘要
针对不同压电材料中界面裂纹尖端的扇形区域推导出了包含基本方程、裂纹面D-P边界条件和不同压电材料交界面处的边界条件的弱形式。在该弱形式的基础上,利用特征方程展开方法(eigenfunction expansion technique),可以得到一个分析压电材料裂纹尖端处力电耦合场奇异性的特殊的一维有限元列式。该一维有限元列式只需对扇形区域在角度方向上离散,最后的总体方程为一个二次特征根方程。求解该特征根方程就可以得到压电材料裂纹尖端处力电耦合奇异场的特征解。通过数值算例表明该方法可以准确而高效地计算压电材料裂纹尖端处力电耦合奇异场的特征解,进而用该方法研究了双压电材料界面力电耦合场的奇异性。
The weak form of governing equations, impermeable boundary conditions of the crack face and reciprocity conditions at the interface of different piezoelectrics for sectorial biomaterial domains is derived. By using the eigenfunction expansion technique and the weak form, a special one-dimensional finite element formulation is developed to determine singularities of electromechanical fields at the crack tip in piezoelectrics. Discretization in angular coordinate is needed only and the global equation is a second order characteristic matrix equation. The formulation is verified by comparing the computed results with the existing analytical solution. Accurate solutions are produced by very few elements. The singularities of electromechanical fields at the interfaces of bimorph are studied.
出处
《工程力学》
EI
CSCD
北大核心
2006年第1期165-171,共7页
Engineering Mechanics
基金
华南理工大学自然基金项目(200340)
