Karageorghis, A. and Lesnic, D. orcid.org/0000-0003-3025-2770 (2025) The Method of Fundamental Solutions for Solving Direct and Inverse Signorini Problems in Elasticity. International Journal of Computer Mathematics. ISSN 0020-7160
Abstract
The method of fundamental solutions (MFS) is a meshless boundary collocation method the implementation of which is very simple rendering the numerical solution of challenging boundary value problems such as free boundary and inverse problems. For this reason, in the current study we apply the MFS for the solution of a specific category of two–dimensional free boundary value problems in elasticity, namely, Signorini problems. We demonstrate that the proposed method is ideally suited for solving such problems. In the MFS, the displacement and traction are approximated by linear combinations of fundamental solutions with sources located outside the closure of the solution domain. The unknown coefficients in these expansions as well as the separation points on the Signorini boundary are determined by imposing/collocating the boundary conditions which can be of Dirichlet, Neumann or Signorini type. The MFS reformulation results in a constrained minimization problem which is solved using the MATLAB® optimization toolbox routine fmincon. The proposed technique is applied to problems from the literature previously solved using the boundary element method.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | This is an author produced version of an article published in International Journal of Computer Mathematics made available under the terms of the Creative Commons Attribution License (CC-BY), which permits unrestricted use, distribution and reproduction in any medium, provided the original work is properly cited. |
Keywords: | Signorini problem, method of fundamental solutions, elasticity |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 29 May 2025 15:15 |
Last Modified: | 18 Jun 2025 01:04 |
Status: | Published online |
Publisher: | Taylor & Francis |
Identification Number: | 10.1080/00207160.2025.2508385 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:226715 |