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Cut Finite Element Methods for Linear Elasticity Problems
Jönköping University, School of Engineering, JTH, Product Development.ORCID iD: 0000-0001-7352-1550
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics. (UMIT)ORCID iD: 0000-0001-7838-1307
2018 (English)In: Geometrically Unfitted Finite Element Methods and Applications: Proceedings of the UCL Workshop 2016 / [ed] Stéphane P. A. Bordas; Erik Burman; Mats G. Larson; Maxim A. Olshanskii, Springer, 2018, p. 25-63Chapter in book (Refereed)
Abstract [en]

We formulate a cut finite element method for linear elasticity based on higher order elements on a fixed background mesh. Key to the method is a stabilization term which provides control of the jumps in the derivatives of the finite element functions across faces in the vicinity of the boundary. We then develop the basic theoretical results including error estimates and estimates of the condition number of the mass and stiffness matrices. We apply the method to the standard displacement problem, the frequency response problem, and the eigenvalue problem. We present several numerical examples including studies of thin bending dominated structures relevant for engineering applications. Finally, we develop a cut finite element method for fibre reinforced materials where the fibres are modeled as a superposition of a truss and a Euler-Bernoulli beam. The beam model leads to a fourth order problem which we discretize using the restriction of the bulk finite element space to the fibre together with a continuous/discontinuous finite element formulation. Here the bulk material stabilizes the problem and it is not necessary to add additional stabilization terms.

Place, publisher, year, edition, pages
Springer, 2018. p. 25-63
Series
Lecture Notes in Computational Science and Engineering, ISSN 1439-7358, E-ISSN 2197-7100 ; 121
National Category
Computational Mathematics
Identifiers
URN: urn:nbn:se:umu:diva-145934DOI: 10.1007/978-3-319-71431-8ISBN: 978-3-319-71430-1 (print)ISBN: 978-3-319-71431-8 (electronic)OAI: oai:DiVA.org:umu-145934DiVA, id: diva2:1192427
Available from: 2018-03-22 Created: 2018-03-22 Last updated: 2018-06-09

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Hansbo, PeterLarson, Mats G.Larsson, Karl

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CiteExportLink to record
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  • apa
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