A Fourier-series-based virtual fields method for the identification of 2-D stiffness distributions

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 pa...

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Main Authors:	Tho Nguyen, Jonathan Huntley, Ian A. Ashcroft, Pablo Ruiz, Fabrice Pierron
Format:	Default Article
Published:	2014
Subjects:	Mechanical engineering not elsewhere classified Virtual fields method Inverse method Stiffness identification Fourier series Mechanical Engineering not elsewhere classified
Online Access:	https://hdl.handle.net/2134/16772
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id	rr-article-9570866
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spelling	rr-article-95708662014-04-29T00:00:00Z A Fourier-series-based virtual fields method for the identification of 2-D stiffness distributions Tho Nguyen (1254036) Jonathan Huntley (1248681) Ian A. Ashcroft (7125329) Pablo Ruiz (1247799) Fabrice Pierron (7208855) Mechanical engineering not elsewhere classified Virtual fields method Inverse method Stiffness identification Fourier series Mechanical Engineering not elsewhere classified 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 2014-04-29T00:00:00Z Text Journal contribution 2134/16772 https://figshare.com/articles/journal_contribution/A_Fourier-series-based_virtual_fields_method_for_the_identification_of_2-D_stiffness_distributions/9570866 CC BY-NC-ND 4.0
institution	Loughborough University
collection	Figshare
topic	Mechanical engineering not elsewhere classified Virtual fields method Inverse method Stiffness identification Fourier series Mechanical Engineering not elsewhere classified
spellingShingle	Mechanical engineering not elsewhere classified Virtual fields method Inverse method Stiffness identification Fourier series Mechanical Engineering not elsewhere classified Tho Nguyen Jonathan Huntley Ian A. Ashcroft Pablo Ruiz Fabrice Pierron A Fourier-series-based virtual fields method for the identification of 2-D stiffness distributions
description	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
format	Default Article
author	Tho Nguyen Jonathan Huntley Ian A. Ashcroft Pablo Ruiz Fabrice Pierron
author_facet	Tho Nguyen Jonathan Huntley Ian A. Ashcroft Pablo Ruiz Fabrice Pierron
author_sort	Tho Nguyen (1254036)
title	A Fourier-series-based virtual fields method for the identification of 2-D stiffness distributions
title_short	A Fourier-series-based virtual fields method for the identification of 2-D stiffness distributions
title_full	A Fourier-series-based virtual fields method for the identification of 2-D stiffness distributions
title_fullStr	A Fourier-series-based virtual fields method for the identification of 2-D stiffness distributions
title_full_unstemmed	A Fourier-series-based virtual fields method for the identification of 2-D stiffness distributions
title_sort	fourier-series-based virtual fields method for the identification of 2-d stiffness distributions
publishDate	2014
url	https://hdl.handle.net/2134/16772
_version_	1797559244414779392

A Fourier-series-based virtual fields method for the identification of 2-D stiffness distributions

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