Electroelastic Analysis of Two-Dimensional Piezoelectric Structures by the Localized Method of Fundamental Solutions (Advances in Applied Mathematics and Mechanics, 2023)
Accurate and efficient analysis of the coupled electroelastic behavior ofpiezoelectric structures is a challenging task in the community of computational mechanics. During the past few decades, the method of fundamental solutions (MFS) hasemerged as a popular and well-established meshless boundary collocation method forthe numerical solution of many engineering applications. The classical MFS formulation, however, leads to dense and non-symmetric coefficient matrices which willbe computationally expensive for large-scale engineering simulations. In this paper,a localized version of the MFS (LMFS) is devised for electroelastic analysis of two-dimensional (2D) piezoelectric structures. In the LMFS, the entire computational domain is divided into a set of overlapping small sub-domains where the MFS-basedapproximation and the moving least square (MLS) technique are employed. Differentto the classical MFS, the LMFS will produce banded and sparse coefficient matriceswhich makes the method very attractive for large-scale simulations. Preliminary numerical experiments illustrate that the present LMFM is very promising for coupledelectroelastic analysis of piezoelectric materials.