Karageorghis, A, Lesnic, D and Marin, L (2016) The method of fundamental solutions for three-dimensional inverse geometric elasticity problems. Computers and Structures, 166. pp. 51-59. ISSN 0045-7949
Abstract
We investigate the numerical reconstruction of smooth star-shaped voids (rigid inclusions and cavities) which are compactly contained in a three-dimensional isotropic linear elastic medium from a single set of Cauchy data (i.e. nondestructive boundary displacement and traction measurements) on the accessible outer boundary. This inverse geometric problem in three-dimensional elasticity is approximated using the method of fundamental solutions (MFS). The parameters describing the boundary of the unknown void, its centre, and the contraction and dilation factors employed for selecting the fictitious surfaces where the MFS sources are to be positioned, are taken as unknowns of the problem. In this way, the original inverse geometric problem is reduced to finding the minimum of a nonlinear least-squares functional that measures the difference between the given and computed data, penalized with respect to both the MFS constants and the derivative of the radial coordinates describing the position of the star-shaped void. The interior source points are anchored and move with the void during the iterative reconstruction procedure. The feasibility of this new method is illustrated in several numerical examples.
Metadata
Item Type: | Article |
---|---|
Authors/Creators: |
|
Copyright, Publisher and Additional Information: | © 2016, Elsevier. This is an author produced version of a paper published in Computers and Structures. Uploaded in accordance with the publisher's self-archiving policy. |
Keywords: | method of fundamental solutions, Cauchy-Navier equations of elasticity, inverse problems |
Dates: |
|
Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Applied Mathematics (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 18 Jan 2016 10:27 |
Last Modified: | 14 Apr 2017 05:22 |
Published Version: | http://dx.doi.org/10.1016/j.compstruc.2016.01.010 |
Status: | Published |
Publisher: | Elsevier |
Identification Number: | 10.1016/j.compstruc.2016.01.010 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:93724 |