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

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.