MFS fading regularization method for the identification of boundary conditions from partial elastic displacement field data

ABSTRACT

A method is proposed to solve an inverse problem in two-dimensional linear isotropic elasticity. The inverse problem consists of the determination of both the entire displacement field and the boundary conditions inaccessible to the measurement from the partial knowledge of the displacement field. The algorithm is based on a fading regularization method (FRM) and is numerically implemented using the method of fundamental solutions (MFS). The inverse technique is first validated with synthetic data and is then applied to the interpretation of experimental measurements obtained by digital image correlation (DIC).

KEYWORDS:

• Inverse problems
• regularization method
• method of fundamental solutions
• linear elasticity
• partial full-field measurements

Acknowledgements

The authors would like to thank French Region Centre Val de Loire (in the framework of IMFRA2 APR-2012) and French Region Normandie for supporting this project.

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

1. The reconstructions of the horizontal component of displacement $u_1$ and the horizontal component of the stress vector $T_1$ are not presented because the results are similar to those obtained for the $u_2$ and $T_2$.

Additional information

Funding

This work was supported by French Region Centre Val de Loire [IMFRA2 APR-2012] and French Region Normandie.