Journal article
Strong-form approach to elasticity: Hybrid finite difference-meshless collocation method (FDMCM)
Applied Mathematical Modelling, Vol.57, pp.316-338
2018
Abstract
We propose a numerical method that combines the finite difference (FD) and strong form (collocation) meshless method (MM) for solving linear elasticity equations. We call this new method FDMCM. The FDMCM scheme uses a uniform Cartesian grid embedded in complex geometries and applies both methods to calculate spatial derivatives. The spatial domain is represented by a set of nodes categorized as (i) boundary and near boundary nodes, and (ii) interior nodes. For boundary and near boundary nodes, where the finite difference stencil cannot be defined, the Discretization Corrected Particle Strength Exchange (DC PSE) scheme is used for derivative evaluation, while for interior nodes standard second order finite differences are used. FDMCM method combines the advantages of both FD and DC PSE methods. It supports a fast and simple generation of grids and provides convergence rates comparable to weak formulations. We demonstrate the appropriateness and robustness of the proposed scheme through various benchmark problems in 2D and 3D. Numerical results show good accuracy and h-convergence properties. The ease of computational grid generation makes the method particularly suited for problems where geometries are very complicated and known only imperfectly from images, frequently occurring in e.g. geomechanics and patient-specific biomechanics, where the proposed FDMCM method, after its extension to non-linear regime, appears to be a promising alternative to the traditional weak form-based numerical schemes used in the field.
Details
- Title
- Strong-form approach to elasticity: Hybrid finite difference-meshless collocation method (FDMCM)
- Authors/Creators
- G.C. Bourantas (Author/Creator) - The University of Western AustraliaK.A. Mountris (Author/Creator) - InsermV.C. Loukopoulos (Author/Creator) - University of PatrasL. Lavier (Author/Creator) - The University of Texas at AustinG.R. Joldes (Author/Creator) - Murdoch UniversityA. Wittek (Author/Creator) - The University of Western AustraliaK. Miller (Author/Creator) - The University of Western Australia
- Publication Details
- Applied Mathematical Modelling, Vol.57, pp.316-338
- Publisher
- Elsevier BV
- Identifiers
- 991005542633307891
- Copyright
- © 2017 Elsevier Inc.
- Murdoch Affiliation
- School of Engineering and Information Technology
- Language
- English
- Resource Type
- Journal article
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- Collaboration types
- Domestic collaboration
- International collaboration
- Citation topics
- 7 Engineering & Materials Science
- 7.63 Mechanics
- 7.63.1370 Meshless Method
- Web Of Science research areas
- Engineering, Multidisciplinary
- Mathematics, Interdisciplinary Applications
- Mechanics
- ESI research areas
- Engineering