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
Artikel, Zweitveröffentlichung, Verlagsversion
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Kurzbeschreibung (Abstract)
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.
| Typ des Eintrags: | Artikel |
|---|---|
| Erschienen: | 2024 |
| Autor(en): | Bremm, Sophia ; Hell, Sascha ; Becker, Wilfried |
| Art des Eintrags: | Zweitveröffentlichung |
| Titel: | Convergence behaviour of the enriched scaled boundary finite element method |
| Sprache: | Englisch |
| Publikationsjahr: | 5 Januar 2024 |
| Ort: | Darmstadt |
| Publikationsdatum der Erstveröffentlichung: | 2019 |
| Ort der Erstveröffentlichung: | Chichester |
| Verlag: | John Wiley & Sons |
| Titel der Zeitschrift, Zeitung oder Schriftenreihe: | International Journal for Numerical Methods in Engineering |
| Jahrgang/Volume einer Zeitschrift: | 120 |
| (Heft-)Nummer: | 7 |
| DOI: | 10.26083/tuprints-00016737 |
| URL / URN: | https://tuprints.ulb.tu-darmstadt.de/16737 |
| Zugehörige Links: | |
| Herkunft: | Zweitveröffentlichung DeepGreen |
| Kurzbeschreibung (Abstract): | 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. |
| Freie Schlagworte: | convergence, enriched base functions, enriched scaled boundary finite element method (enrSBFEM), scaled boundary finite element method (SBFEM), three‐dimensional elasticity |
| Status: | Verlagsversion |
| URN: | urn:nbn:de:tuda-tuprints-167371 |
| Sachgruppe der Dewey Dezimalklassifikatin (DDC): | 500 Naturwissenschaften und Mathematik > 510 Mathematik 600 Technik, Medizin, angewandte Wissenschaften > 620 Ingenieurwissenschaften und Maschinenbau |
| Fachbereich(e)/-gebiet(e): | 16 Fachbereich Maschinenbau 16 Fachbereich Maschinenbau > Fachgebiet für Strukturmechanik (FSM) |
| Hinterlegungsdatum: | 05 Jan 2024 14:23 |
| Letzte Änderung: | 08 Jan 2024 07:55 |
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| Suche nach Titel in: | TUfind oder in Google |
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- Convergence behaviour of the enriched scaled boundary finite element method. (deposited 05 Jan 2024 14:23) [Gegenwärtig angezeigt]
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