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On the numerical properties of high‐order spectral (Euler‐Bernoulli) beam elements

Eisenträger, Sascha ; Kapuria, Santosh ; Jain, Mayank ; Zhang, Junqi (2024)
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, 2023, 103 (9)
doi: 10.26083/tuprints-00024665
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Item Type: Article
Type of entry: Secondary publication
Title: On the numerical properties of high‐order spectral (Euler‐Bernoulli) beam elements
Language: English
Date: 9 February 2024
Place of Publication: Darmstadt
Year of primary publication: 2023
Place of primary 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: 10.26083/tuprints-00024665
Corresponding Links:
Origin: Secondary publication DeepGreen
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
Status: Publisher's Version
URN: urn:nbn:de:tuda-tuprints-246650
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 > Mechanics > Numerical Mechanics
Date Deposited: 09 Feb 2024 14:10
Last Modified: 09 Feb 2024 14:10
SWORD Depositor: Deep Green
URI: https://tuprints.ulb.tu-darmstadt.de/id/eprint/24665
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