The MFS for the Cauchy problem in two-dimensional steady-state linear thermoelasticity

INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES

卷:50

Article

Marin, Liviu^1,2  Karageorghis, Andreas³ 

[1] Romanian Acad, Inst Solid Mech, Bucharest 010141, Romania

[2] Univ Bucharest, Fac Math & Comp Sci, Ctr Continuum Mech, Bucharest 010014, Romania

[3] Univ Cyprus, Dept Math & Stat, CY-1678 Nicosia, Cyprus

关键词: Linear thermoelasticity;    Inverse problem;    Cauchy problem;    Method of fundamental solutions (MFS);    Method of particular solutions (MPS);    Regularization;    L-curve method;   

DOI  :  10.1016/j.ijsolstr.2013.06.006

来源: Elsevier

【 摘 要 】

We study the reconstruction of the missing thermal and mechanical fields on an inaccessible part of the boundary for two-dimensional linear isotropic thermoelastic materials from over-prescribed noisy.(Cauchy) data on the remaining accessible boundary. This problem is solved with the method of fundamental solutions (MFS) together with the method of particular solutions (MPS) via the MFS-based particular solution for two-dimensional problems in uncoupled thermoelasticity developed in Mann and Karageorghis (2012a, 2013). The stabilisation/regularization of this inverse problem is achieved by using the Tikhonov regularization method (Tikhonov and Arsenin, 1986), whilst the optimal value of the regularization parameter is selected by employing Hansen's L-curve method (Hansen, 1998). (C) 2013 Elsevier Ltd. All rights reserved.

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