Loughborough University
Leicestershire, UK
LE11 3TU
+44 (0)1509 263171
Loughborough University

Loughborough University Institutional Repository

Please use this identifier to cite or link to this item: https://dspace.lboro.ac.uk/2134/12658

Title: The fourier virtual fields method for the identification of material property distributions
Authors: Nguyen, Truong Tho
Keywords: Inverse problems
Stiffness distribution identification
Virtual fields method
Fourier series
Fast algorithm
Fourier transform
Genetic algorithm
Issue Date: 2013
Publisher: © Truong Tho Nguyen
Abstract: The requirement of a fast and accurate modulus identification technique has arisen in many fields of research, such as solid mechanics, structural health monitoring, medical diagnosis, etc. An inverse technique based on an appropriate interpretation of the principle of virtual work, namely the Virtual Fields Method (VFM), has been proposed in the literature, which is able to return elastic modulus values after a single matrix inversion. An extension of the virtual fields method to the spatial frequency domain in order to determine modulus distributions of materials based on a sine/cosine parameterisation of the unknown modulus is developed in this thesis, and will be called the Fourier-series-based Virtual Fields Method (F-VFM). The technique accepts in-plane (two-dimensional) or volumetric (three-dimensional) deformation measurement data as its input. An efficient numerical algorithm of the F-VFM based on the fast Fourier transform is presented, which can return thousands of unknown Fourier coefficients within a minute thus reducing the computation time by several orders of magnitude compared to a direct implementation of the F-VFM for typical dataset sizes. The F-VFM technique is also adapted to cope with a common situation in experimental mechanics where the knowledge of the boundary conditions is limited. The three versions of the F-VFM in this situation are respectively the experimental traction , windowed traction and Fourier-series traction approaches. The technique is then validated with numerical data from different stiffness patterns. The performance is compared to that of an iterative updating technique based on a genetic algorithm for one of these patterns, and computational effort is demonstrated to be at least five orders of magnitude less for the new F-VFM than for this updating method. The sensitivity of the performance of the F-VFM to noise is also investigated. Finally, the technique is applied to experimental data in both 2-D and 3-D cases with promising results.
Description: A Doctoral Thesis. Submitted in partial fulfilment of the requirements for the award of Doctor of Philosophy of Loughborough University.
URI: https://dspace.lboro.ac.uk/2134/12658
Appears in Collections:PhD Theses (Mechanical, Electrical and Manufacturing Engineering)

Files associated with this item:

File Description SizeFormat
Form-2013-Nguyen.pdf4.58 MBAdobe PDFView/Open
Thesis-2013-Nguyen.pdf11.25 MBAdobe PDFView/Open


SFX Query

Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.