Eisenträger, Sascha ; Kapuria, Santosh ; Jain, Mayank ; Zhang, Junqi (2023)
On the numerical properties of high‐order spectral (Euler‐Bernoulli) beam elements.
In: ZAMM ‐ Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, 103 (9)
doi: 10.1002/zamm.202200422
Artikel, Bibliographie
Dies ist die neueste Version dieses Eintrags.
Kurzbeschreibung (Abstract)
In this paper, the numerical properties of a recently developed high‐order Spectral Euler‐Bernoulli Beam Element (SBE) featuring a C¹‐continuous approximation of the displacement field are assessed. The C¹‐continuous shape functions are based on two main ingredients, which are an Hermitian interpolation scheme and the use of Gauß‐Lobatto‐Legendre (GLL) points. Employing GLL‐points does not only avoid Runge oscillations, but also yields a diagonal mass matrix when exploiting the nodal quadrature technique as a mass lumping scheme. Especially in high‐frequency transient analyses, where often explicit time integration schemes are utilized, having a diagonal mass matrix is an attractive property of the proposed element formulation. This is, however, achieved at the cost of an under‐integration of the mass matrix. Therefore, a special focus of this paper is placed on the evaluation of the numerical properties, such as the conditioning of the element matrices and the attainable rates of convergence (ROCs). To this end, the numerical behavior of the SBEs is comprehensively analyzed by means of selected benchmark examples. In a nutshell, the obtained results demonstrate that the element yields good accuracy in combination with an increased efficiency for structural dynamics exploiting the diagonal structure of the mass matrix.
| Typ des Eintrags: | Artikel |
|---|---|
| Erschienen: | 2023 |
| Autor(en): | Eisenträger, Sascha ; Kapuria, Santosh ; Jain, Mayank ; Zhang, Junqi |
| Art des Eintrags: | Bibliographie |
| Titel: | On the numerical properties of high‐order spectral (Euler‐Bernoulli) beam elements |
| Sprache: | Englisch |
| Publikationsjahr: | 2023 |
| Ort: | Weinheim |
| Verlag: | Wiley-VCH |
| Titel der Zeitschrift, Zeitung oder Schriftenreihe: | ZAMM ‐ Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik |
| Jahrgang/Volume einer Zeitschrift: | 103 |
| (Heft-)Nummer: | 9 |
| Kollation: | 45 Seiten |
| DOI: | 10.1002/zamm.202200422 |
| Zugehörige Links: | |
| Kurzbeschreibung (Abstract): | In this paper, the numerical properties of a recently developed high‐order Spectral Euler‐Bernoulli Beam Element (SBE) featuring a C¹‐continuous approximation of the displacement field are assessed. The C¹‐continuous shape functions are based on two main ingredients, which are an Hermitian interpolation scheme and the use of Gauß‐Lobatto‐Legendre (GLL) points. Employing GLL‐points does not only avoid Runge oscillations, but also yields a diagonal mass matrix when exploiting the nodal quadrature technique as a mass lumping scheme. Especially in high‐frequency transient analyses, where often explicit time integration schemes are utilized, having a diagonal mass matrix is an attractive property of the proposed element formulation. This is, however, achieved at the cost of an under‐integration of the mass matrix. Therefore, a special focus of this paper is placed on the evaluation of the numerical properties, such as the conditioning of the element matrices and the attainable rates of convergence (ROCs). To this end, the numerical behavior of the SBEs is comprehensively analyzed by means of selected benchmark examples. In a nutshell, the obtained results demonstrate that the element yields good accuracy in combination with an increased efficiency for structural dynamics exploiting the diagonal structure of the mass matrix. |
| ID-Nummer: | Artikel-ID: e202200422 |
| Sachgruppe der Dewey Dezimalklassifikatin (DDC): | 500 Naturwissenschaften und Mathematik > 510 Mathematik 600 Technik, Medizin, angewandte Wissenschaften > 624 Ingenieurbau und Umwelttechnik |
| Fachbereich(e)/-gebiet(e): | 13 Fachbereich Bau- und Umweltingenieurwissenschaften 13 Fachbereich Bau- und Umweltingenieurwissenschaften > Fachgebiete der Mechanik 13 Fachbereich Bau- und Umweltingenieurwissenschaften > Fachgebiete der Mechanik > Fachgebiet Numerische Mechanik |
| Hinterlegungsdatum: | 02 Aug 2024 13:16 |
| Letzte Änderung: | 02 Aug 2024 13:16 |
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Verfügbare Versionen dieses Eintrags
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On the numerical properties of high‐order spectral (Euler‐Bernoulli) beam elements. (deposited 09 Feb 2024 14:10)
- On the numerical properties of high‐order spectral (Euler‐Bernoulli) beam elements. (deposited 02 Aug 2024 13:16) [Gegenwärtig angezeigt]
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