欢迎光临《计算力学学报》官方网站！ Evaluation of singular physical field near the vertex of piezoelectric material notch

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 作者 单位 邮编 潘伟 合肥工业大学土木与水利工程学院 230009 程长征 合肥工业大学土木与水利工程学院 230009 王飞炀 合肥工业大学土木与水利工程学院 李腾岳 合肥工业大学土木与水利工程学院 牛忠荣 合肥工业大学土木与水利工程学院

切口尖端的奇异应力和奇异电位移,会使压电材料含切口结构发生强度失效或电荷击穿,压电材料切口尖端的奇异物理场分析是一个关键的科学问题。本文采用切口尖端奇性特征分析与有限元法相结合的思路,计算压电材料切口尖端的力学和电学奇异物理场。首先基于奇性渐近展开技巧,推演压电材料切口的奇性特征方程,引入插值矩阵法求解,获得切口尖端奇性渐近展开式的奇性指数、特征角函数及其导数。再根据有限元法的位移和电势计算结果较应力和电位移高一阶精度的特点,利用稀疏有限元网格,计算出切口附近的位移和电势,代入切口尖端物理场渐近展开式,求出幅值系数。根据计算出的幅值系数、奇性指数、特征角函数及其导数,重构出切口尖端附近的奇异应力场和电位移场,继而计算出切口的应力强度因子和电位移强度因子。本文所提半解析方法,基于有限元稀疏网格计算结果,利用较小的计算量,获得较高精度的奇异物理场。该方法无须对有限元法的插值函数进行改造,适合嵌入商业有限元软件,直接用于工程压电材料结构安全分析。

The idea of combining the singularity characteristic analysis with the finite element method is used to calculate the singular physical fields near the vertex of the piezoelectric notch. Firstly, basing on the singular asymptotic expansion technique, the singular characteristic equation of the piezoelectric material notch is established. The interpolating matrix method is then introduced to solve them. The singularity order, eigen angular function and its derivative of the singular asymptotic expansion are obtained. The displacement and electric potential near the notch are calculated by the relatively sparse finite element mesh. These results are introduced into the asymptotic expansion to obtain the amplitude coefficients in the asymptotic expansion. According to the calculated amplitude coefficient, singularity order, characteristic angular function and its derivative, the singular physical field can be reconstructed, and then the stress and electric displacement intensity factors can be calculated. The proposed semi-analytical method is basing on the results from the finite element sparse grid. Thus, a small amount of calculation is needed and a higher-precision singular physical field can be obtained. The proposed method does not need to modify the interpolation function of the finite element method. It is suitable for embedding into the commercial finite element software.
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