Xia, Hao; Gu, Yan Generalized finite difference method for electroelastic analysis of three-dimensional piezoelectric structures. (English) Zbl 1462.74165 Appl. Math. Lett. 117, Article ID 107084, 8 p. (2021). Summary: This short communication makes the first attempt to apply the generalized finite difference method (GFDM), a newly-developed meshless collocation method, for the numerical solutions of three-dimensional (3D) piezoelectric problems. In the present method, the entire computational domain is divided into a set of overlapping subdomains in which the local Taylor series expansion and moving-least square approximation are applied to construct the local systems of linear equations. By satisfying the coupled mechanical and electrical governing equations, a sparse and banded stiffness matrix can be established which makes the method very attractive for large-scale engineering simulations. Preliminary numerical experiments are presented to demonstrate the applicability and accuracy of the present method, where the results obtained are compared with the analytical solutions with very good agreement. Cited in 29 Documents MSC: 74S20 Finite difference methods applied to problems in solid mechanics 74F15 Electromagnetic effects in solid mechanics Keywords:meshless collocation method; Taylor series expansion; moving-least square approximation; sparse stiffness matrix PDFBibTeX XMLCite \textit{H. Xia} and \textit{Y. Gu}, Appl. Math. Lett. 117, Article ID 107084, 8 p. (2021; Zbl 1462.74165) Full Text: DOI References: [1] Chen, S. S.; Li, Q. H.; Liu, Y. H.; Xue, Z. Q., A meshless local natural neighbour interpolation method for analysis of two-dimensional piezoelectric structures, Eng. Anal. Bound. Elem., 37, 2, 273-279 (2013) · Zbl 1351.74079 [2] Liu, Y.; Fan, H., Analysis of thin piezoelectric solids by the boundary element method, Comput. Methods Appl. Mech. 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