压电与导体双材料界面端的奇异性研究

SINGULARITIES IN THE WEDGE OF PIEZOELECTRIC MEDIA AND CONDUCTOR

提出了一种求解平面应变条件下横观各向同性压电与导体双材料界面端的应力及电位移奇异性的特征值法。基于横观各向同性压电材料的基本方程和一阶近似假设,利用分离变量形式的位移函数和电势函数,导出了关于应力和电位移奇异性指数的奇异性特征方程。求解由无网格法离散的特征方程,即可得到应力和电位移的各阶奇异性指数,同时还可得到相应的应力和电位移角函数。数值计算结果与文献中给出的结果非常吻合,表明该方法具有很高的精度和效率。

An eigenvalue method was proposed to study the singular stress field and the singular electric displacement field of a piezoelectric/conductor wedge under a plane strain state.Based on the fundamental equations of transversely isotropic piezoelectric materials and a first-order approximation assumption,the discrete characteristic equation was derived by using displacement functions and electric potential functions with separated variables and the meshless method.The eigenvalue is relative to the order of stress singularity and electric displacement singularity,and the associated eigenvector is with respect to the stress angular variations and electric displacement angular variations.The numerical results of both singularity orders and angular variations obtained by the proposed method agree with those presented in the reference literatures very well.The accuracy and efficiency of the proposed eigenvalue method were also verified.