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Weak impositions of Dirichlet boundary conditions in solid mechanics : a critique of current approaches and extension to partially prescribed boundaries.

Lu, K. and Augarde, C.E. and Coombs, W.M. and Hu, Z. (2019) 'Weak impositions of Dirichlet boundary conditions in solid mechanics : a critique of current approaches and extension to partially prescribed boundaries.', Computer methods in applied mechanics and engineering., 348 . pp. 632-659.

Abstract

In this article we first review various approaches developed to date for the weak imposition of Dirichlet boundary conditions in fictitious domain analysis for elasticity problems. The Hellinger-Reissner (H-R) principle, the linked Lagrange multiplier (LLM) method, the implicit boundary method and the fat boundary method are discussed along with the well-known Lagrange multiplier, penalty and Nitsche’s methods. We state these approaches in a common form starting with energy functionals and weak forms, and discretise using the fictitious domain finite element method. Previous formulations of these methods were in general developed for full prescription along the Dirichlet boundary, which generally implies no local effect of boundary inclination. However, partially prescribed conditions (such as the structural roller boundary condition) with inclination have wide practical applications in engineering. Here we provide techniques of imposing such boundary conditions in these methods in detail. For those methods that contain algorithmic parameters, such as the penalty and Nitsche’s methods, extra computation or empirical estimation is necessary to decide values of the parameters, and hence we discuss parametric and convergence behaviours through numerical examples to provide guidance on the choice of parameters.

Item Type:Article
Full text:(AM) Accepted Manuscript
Available under License - Creative Commons Attribution Non-commercial No Derivatives.
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Status:Peer-reviewed
Publisher Web site:https://doi.org/10.1016/j.cma.2019.01.035
Publisher statement:© 2019 This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/
Date accepted:25 January 2019
Date deposited:25 January 2019
Date of first online publication:05 February 2019
Date first made open access:05 February 2020

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