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

• 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
• ISSN: 0001-5970; 1619-6937
• DOI: 10.1007/s00707-019-02473-0

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.