Weighted reproducing kernel collocation method based on error analysis for solving inverse elasticity problems

For inverse problems equipped with incomplete boundary conditions, a simple solution strategy to obtain approximations remains a challenge in the fields of engineering and science. Based on our previous study, the weighted reproducing kernel collocation method (W-RKCM) shows optimal convergence in s...

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Bibliographic Details
Published in:Acta mechanica 2019-10, Vol.230 (10), p.3477-3497
Main Authors: Yang, Judy P., Hsin, Wen-Chims
Format: Article
Language:English
Subjects:
Boundary conditions
Classical and Continuum Physics
Collocation methods
Control
Convergence
Dynamical Systems
Elasticity
Engineering
Engineering Fluid Dynamics
Engineering Thermodynamics
Error analysis
Heat and Mass Transfer
Inverse problems
Kernels
Original Paper
Shape functions
Solid Mechanics
Theoretical and Applied Mechanics
Vibration
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Summary:For inverse problems equipped with incomplete boundary conditions, a simple solution strategy to obtain approximations remains a challenge in the fields of engineering and science. Based on our previous study, the weighted reproducing kernel collocation method (W-RKCM) shows optimal convergence in solving inverse Cauchy problems. As such, this work further introduces the W-RKCM to solve inverse problems in elasticity. From mathematical error estimate and numerical convergence study, it is shown that the weighted least-squares formulation can properly balance the errors in the domain and on the boundary. By comparing the approximations obtained by W-RKCM with those obtained by the direct collocation method, the reproducing kernel shape function can retain the locality without using a large support size, and the corresponding approximations exhibit extremely high solution accuracy. The stability of the W-RKCM is demonstrated by adding noise on the boundary conditions. This work shows the efficacy of the proposed W-RKCM in solving inverse elasticity problems as no additional technique is involved to reach the desired solution accuracy in comparison with the existing methods in the literature.
ISSN:0001-5970
1619-6937
DOI:10.1007/s00707-019-02473-0