The generalized finite difference method for the inverse Cauchy problem in two-dimensional isotropic linear elasticity

INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES

卷:174

Article

Li, Po-Wei¹  Fu, Zhuo-Jia^1,3  Gu, Yan²  Song, Lina² 

[1] Hohai Univ, Coll Mech & Mat, Nanjing, Jiangsu, Peoples R China

[2] Qingdao Univ, Sch Math & Stat, Qingdao, Shandong, Peoples R China

[3] Dalian Univ Technol, State Key Lab Struct Anal Ind Equipment, Dalian, Peoples R China

关键词: Meshless method;    Generalized finite difference method;    Inverse Cauchy problem;    Linear elasticity;   

DOI  :  10.1016/j.ijsolstr.2019.06.001

来源: Elsevier

【 摘 要 】

In this study, the generalized finite difference method (GFDM) was used to stably and accurately solve two-dimensional (2D) inverse Cauchy problems in linear elasticity by using the Navier equations. In Cauchy problems, overdetermined boundary conditions are imposed on parts of the boundary, whereas there are missing boundary conditions on some parts of the boundary. In Cauchy problems, conventional numerical methods generally generate highly ill-conditioned matrices and thus provide unstable numerical solutions. Moreover, even if a slight noise is added in the boundary conditions, numerical errors are evidently magnified. The GFDM, one of the most promising meshless methods and an extension of the classical finite difference method, can avoid time-consuming tasks of mesh generation and numerical quadrature. The GFDM was applied in this study to stably solve the 2D Cauchy problems in linear elasticity and four numerical examples are provided to illustrate the consistency and accuracy of the presented meshless numerical scheme. Moreover, the stability of the presented scheme for inverse Cauchy problems was proved by adding noise into the boundary conditions. (C) 2019 Elsevier Ltd. All rights reserved.

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