Simulation of antiplane piezoelectricity problems with multiple inclusions using the generalized finite difference method

In this paper, antiplane piezoelectricity problems with multiple inclusions are studied by the generalized finite difference method (GFDM). Developed from the Taylor series and the Moving Least Squares, the GFDM expresses the derivatives of variables as the combination of values of surrounding nodes where the sparse matrix will be obtained considering the boundary conditions and interface conditions. Stress concentration and electric field concentration are analyzed in three numerical examples, which contain circular and elliptical piezoelectric inclusions in various sizes, locations, and material parameters. The applicability and validity of the proposed method are verified through the comparison with reference results.

Automated summary

In this paper, the generalized finite difference method (GFDM) is used to study antiplane piezoelectricity problems with multiple inclusions. The applicability and validity of the proposed method are verified through the analysis of numerical examples.