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Convergence behaviour of the enriched scaled boundary finite element method

Bremm, Sophia ; Hell, Sascha ; Becker, Wilfried (2024)
Convergence behaviour of the enriched scaled boundary finite element method.
In: International Journal for Numerical Methods in Engineering, 2019, 120 (7)
doi: 10.26083/tuprints-00016737
Article, Secondary publication, Publisher's Version

Copyright Information: CC BY 4.0 International - Creative Commons, Attribution.

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Item Type: Article
Type of entry: Secondary publication
Title: Convergence behaviour of the enriched scaled boundary finite element method
Language: English
Date: 5 January 2024
Place of Publication: Darmstadt
Year of primary publication: 2019
Place of primary publication: Chichester
Publisher: John Wiley & Sons
Journal or Publication Title: International Journal for Numerical Methods in Engineering
Volume of the journal: 120
Issue Number: 7
DOI: 10.26083/tuprints-00016737
Corresponding Links:
Origin: Secondary publication DeepGreen

In this work, a very efficient numerical solution of three‐dimensional boundary value problems of linear elasticity including stress singularities is discussed, focussing on its convergence behaviour. For the employed scaled boundary finite element method, a discretization is only needed at the boundary, while the solution is considered analytically in a scaling coordinate. This presents a major advantage for two‐dimensional problems, when the scaling center is placed at a stress singularity. Unfortunately, three‐dimensional problems usually do not only include point singularities but also line singularities, which results in singular gradients in the boundary coordinates and thereby diminishes the method's original advantages. To alleviate this drawback, this work discusses an enrichment of the separation of variables representation with analytical asymptotic near fields of the line singularities. In contrast to previous works, besides the near‐field functions with λ=0.5, also those with λ=1.5 were determined and used for enrichment. This leads to a high accuracy and it is shown that this approach is required to recover the convergence properties of smooth boundary value problems without singularities when using quadratic Lagrange shape functions. In order to recover the convergence rates for higher order shape functions, near‐field functions with higher singularity exponent have to be included for enrichment.

Uncontrolled Keywords: convergence, enriched base functions, enriched scaled boundary finite element method (enrSBFEM), scaled boundary finite element method (SBFEM), three‐dimensional elasticity
Status: Publisher's Version
URN: urn:nbn:de:tuda-tuprints-167371
Classification DDC: 500 Science and mathematics > 510 Mathematics
600 Technology, medicine, applied sciences > 620 Engineering and machine engineering
Divisions: 16 Department of Mechanical Engineering > Institute of Structural Mechanics (FSM)
Date Deposited: 05 Jan 2024 14:23
Last Modified: 09 Jan 2024 09:19
SWORD Depositor: Deep Green
URI: https://tuprints.ulb.tu-darmstadt.de/id/eprint/16737
PPN: 514520981
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