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Analysis of piezoelectric plates with a hole using nature boundary integral equation and domain decomposition

机译：利用自然边界积分方程和区域分解法分析带孔压电板

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In this paper, the plane problems of piezoelectricity are studied by using nature boundary integral equation and domain decomposition. A general displacement solution in terms of three potential functions is adopted to solve exterior boundary value problems of piezoelectricity, and three mapping relations corresponding to three potential functions are proposed for domain decomposition. By symbolic matrix inversion and derivation calculus, each potential function is governed by harmonic second-order partial differential equation in transformed domain with prescribed boundary condition. Therefore, three classic harmonic problems equivalent to the original plane piezoelectricity are established. Two cases of boundary conditions are considered, in which the displacement and electric potential are prescribed or the traction and electric displacement are given on the boundary. All problems considered are equivalent to three independent harmonic problems, which are solved by using nature boundary integration method proposed by Feng and Yu. A piezoelectric plate with a circular hole is analyzed as numerical examples. The results show that the proposed method is valid for the piezoelectric plates with holes. The proposed method has potential applications to analyze multi-field coupling problems.
机译：本文利用自然边界积分方程和域分解研究了压电的平面问题。采用了基于三个势函数的一般位移解来解决压电的外边界值问题，并提出了与三个势函数相对应的三个映射关系进行域分解。通过符号矩阵求逆和微分演算，每个势函数由具有规定边界条件的变换域中的谐波二阶偏微分方程控制。因此，建立了三个与原始平面压电等效的经典谐波问题。考虑两种边界条件，其中规定了位移和电势或在边界上给出了牵引力和电位移。所考虑的所有问题都等同于三个独立的谐波问题，这是通过使用Feng和Yu提出的自然边界积分方法解决的。分析具有圆孔的压电板作为数值示例。结果表明，该方法对带孔压电板是有效的。所提出的方法在分析多场耦合问题方面具有潜在的应用价值。

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