An Effective Meshless Approach for Inverse Cauchy Problems in 2D and 3D Electroelastic Piezoelectric Structures  

作　　者：Ziqiang Bai Wenzhen Qu Guanghua Wu 

机构地区：[1]School of Automation,Qingdao University,Qingdao,266071,China [2]School of Mathematics and Statistics,Qingdao University,Qingdao,266071,China [3]Weifang University of Science and Technology,Weifang,262700,China

出　　处：《Computer Modeling in Engineering & Sciences》2024年第3期2955-2972,共18页工程与科学中的计算机建模（英文）

基　　金：the Natural Science Foundation of Shandong Province of China(Grant No.ZR2022YQ06);the Development Plan of Youth Innovation Team in Colleges and Universities of Shandong Province(Grant No.2022KJ140);the Key Laboratory ofRoad Construction Technology and Equipment(Chang’an University,No.300102253502).

摘　　要：In the past decade,notable progress has been achieved in the development of the generalized finite difference method(GFDM).The underlying principle of GFDM involves dividing the domain into multiple sub-domains.Within each sub-domain,explicit formulas for the necessary partial derivatives of the partial differential equations(PDEs)can be obtained through the application of Taylor series expansion and moving-least square approximation methods.Consequently,the method generates a sparse coefficient matrix,exhibiting a banded structure,making it highly advantageous for large-scale engineering computations.In this study,we present the application of the GFDM to numerically solve inverse Cauchy problems in two-and three-dimensional piezoelectric structures.Through our preliminary numerical experiments,we demonstrate that the proposed GFDMapproach shows great promise for accurately simulating coupled electroelastic equations in inverse problems,even with 3%errors added to the input data.

关 键 词：Generalized finite difference method meshless method inverse Cauchy problems piezoelectric problems electroelastic analysis 

分 类 号：O17[理学—数学]