Abstract
We investigate the finite element method and the Tikhonov regularization for smoothing noisy displacement field obtained from the digital image correlation (DIC). Among various finite elements, the C2 continuous Hermite finite element has been proven to be an effective high-order element which ensures both continuity and smoothness of the final strain field. However, the standard Hermite element is required to be rectangular, which cannot tackle the region of interest of arbitrary shape. To overcome this constraint, we propose the improved Hermite finite element smoothing method (IHFESM) to extend the generality of Hermite finite element that is able to measure the arbitrary region of interest. The IHFESM is implemented by eliminating the contribution to the global regularization matrix from the invalid region. The proposed method could be employed to smooth the noisy displacement field obtained by DIC, and reconstruct the reliable strain field by differentiation. The effectiveness of IHFESM is verified by two tension experiments of plates with three and four holes.
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