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
Article, Bibliographie
This is the latest version of this item.
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.
| Item Type: | Article |
|---|---|
| Erschienen: | 2023 |
| Creators: | Eisenträger, Sascha ; Kapuria, Santosh ; Jain, Mayank ; Zhang, Junqi |
| Type of entry: | Bibliographie |
| Title: | On the numerical properties of high‐order spectral (Euler‐Bernoulli) beam elements |
| Language: | English |
| Date: | 2023 |
| Place of Publication: | Weinheim |
| Publisher: | Wiley-VCH |
| Journal or Publication Title: | ZAMM ‐ Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik |
| Volume of the journal: | 103 |
| Issue Number: | 9 |
| Collation: | 45 Seiten |
| DOI: | 10.1002/zamm.202200422 |
| Corresponding Links: | |
| 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. |
| Identification Number: | Artikel-ID: e202200422 |
| Classification DDC: | 500 Science and mathematics > 510 Mathematics 600 Technology, medicine, applied sciences > 624 Civil engineering and environmental protection engineering |
| Divisions: | 13 Department of Civil and Environmental Engineering Sciences 13 Department of Civil and Environmental Engineering Sciences > Mechanics 13 Department of Civil and Environmental Engineering Sciences > Mechanics > Numerical Mechanics |
| Date Deposited: | 02 Aug 2024 13:16 |
| Last Modified: | 02 Aug 2024 13:16 |
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| Suche nach Titel in: | TUfind oder in Google |
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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) [Currently Displayed]
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