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Title: A Fourier-series-based virtual fields method for the identification of 2-D stiffness distributions
Authors: Nguyen, Truong Tho
Huntley, Jonathan M.
Ashcroft, Ian A.
Ruiz, Pablo D.
Pierron, Fabrice
Keywords: Virtual fields method
Inverse method
Stiffness identification
Fourier series
Issue Date: 2014
Publisher: © John Wiley & Sons, Ltd.
Citation: NGUYEN, T.T. ... et al, 2014. A Fourier-series-based virtual fields method for the identification of 2-D stiffness distributions. International Journal for Numerical Methods in Engineering, 98 (12), pp.917-936.
Abstract: The virtual fields method (VFM) is a powerful technique for the calculation of spatial distributions of material properties from experimentally determined displacement fields. A Fourier-series-based extension to the VFM (the F-VFM) is presented here, in which the unknown stiffness distribution is parameterised in the spatial frequency domain rather than in the spatial domain as used in the classical VFM.We present in this paper the theory of the F-VFM for the case of elastic isotropic thin structures with known boundary conditions. An efficient numerical algorithm based on the two-dimensional Fast Fourier Transform (FFT) is presented, which reduces the computation time by three to four orders of magnitude compared with a direct implementation of the F-VFM for typical experimental dataset sizes. Artefacts specific to the F-VFM (ring- ing at the highest spatial frequency near to modulus discontinuities) can be largely removed through the use of appropriate filtering strategies. Reconstruction of stiffness distributions with the F-VFM has been vali- dated on three stiffness distribution scenarios under varying levels of noise in the input displacement fields. Robust reconstructions are achieved even when the displacement noise is higher than in typical experimental fields
Description: This is the peer reviewed version of the article, which has been published in final form at http://dx.doi.org/10.1002/nme.4665. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving.
Version: Accepted for publication
DOI: 10.1002/nme.4665
URI: https://dspace.lboro.ac.uk/2134/16772
Publisher Link: http://dx.doi.org/10.1002/nme.4665
ISSN: 1097-0207
Appears in Collections:Published Articles (Mechanical, Electrical and Manufacturing Engineering)

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