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An implicit boundary finite element method with extension to frictional sliding boundary conditions and elasto-plastic analyses

Lu, K; Coombs, WM; Augarde, CE; Hu, L

An implicit boundary finite element method with extension to frictional sliding boundary conditions and elasto-plastic analyses Thumbnail


Authors

K Lu

L Hu



Abstract

Implicit boundary methods, which enrich the interpolation structure with implicit weight functions, are straightforward methods for the enforcement of Dirichlet boundary conditions. In this article, we follow the implicit boundary method that uses approximate step functions (the step boundary method) developed by Kumar et al. and provide modifications that have several advantages. Roller boundary conditions have wide practical applications in engineering, however, the step boundary method for roller boundary conditions with inclinations has yet to be fully formulated through to the final linear system of equations. Thus we provide a complete derivation that leads to simplified sti↵ness matrices compared to the original approach, which can be implemented directly in fictitious domain finite element analysis. The approach is then extended, we believe for the first time, to the nonlinear cases of frictional boundary conditions and elasto-plastic material behaviour. The proposed formulation and procedures are validated on a number of example problems that test di↵erent aspects of the method.

Journal Article Type Article
Acceptance Date Sep 4, 2019
Publication Date Jan 1, 2020
Deposit Date Sep 10, 2019
Publicly Available Date Sep 16, 2020
Journal Computer Methods in Applied Mechanics and Engineering
Print ISSN 0045-7825
Electronic ISSN 1879-2138
Publisher Elsevier
Peer Reviewed Peer Reviewed
Volume 358
Article Number 112620
DOI https://doi.org/10.1016/j.cma.2019.112620
Public URL https://durham-repository.worktribe.com/output/1287555
Publisher URL https://www.journals.elsevier.com/computer-methods-in-applied-mechanics-and-engineering

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