Weighted reproducing kernel collocation method based on error analysis for solving inverse elasticity problems
- 21 Downloads
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.
The support of this work by the Ministry of Science and Technology of the Republic of China (Taiwan) under the Grant MOST 107-2221-E-009-141-MY3 is gratefully acknowledged.
- 6.Marin, L., Elliott, L., Ingham, D.B., Lesnic, D.: Boundary element based solution for the Cauchy problem in linear elasticity by the Tikhonov regularization method. In: Harris, P.J. (ed.) Third UK Conference on Boundary Integral Methods, pp. 149–158. University of Brighton Press, Brighton, UK (2001)Google Scholar