(untitled) (Advances in Applied Mathematics and Mechanics, 2023)
Accurate and efficient analysis of the coupled electroelastic behavior of piezoelectric structures is a challenging task in the community of computational mechanics. During the past few decades, the method of fundamental solutions (MFS) has emerged as a popular and well-established meshless boundary collocation method for the numerical solution of many engineering applications. The classical MFS formulation, however, leads to dense and non-symmetric coefficient matrices which will be 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-based approximation and the moving least square (MLS) technique are employed. Different to the classical MFS, the LMFS will produce banded and sparse coefficient matrices which makes the method very attractive for large-scale simulations. Preliminary numerical experiments illustrate that the present LMFM is very promising for coupled electroelastic analysis of piezoelectric materials.