Details
| Original language | English |
|---|---|
| Article number | 116368 |
| Journal | Computer Methods in Applied Mechanics and Engineering |
| Volume | 416 |
| Early online date | 7 Sept 2023 |
| Publication status | Published - 1 Nov 2023 |
Abstract
In this paper, a nonlinear finite element formulation for a hyperelastic, modified Timoshenko–Ehrenfest beam with geometrical and material nonlinearities is developed for the first time. A new five-parameter beam element is introduced. The parameters contain displacement, values of difference vector and a through-the-thickness scalar value. Moreover, a new procedure is employed to apply the moment to the beam. The constitutive formulation is derived for Saint Venant–Kirchhoff (SVK) as well as the compressible neo-Hookean (n-H) hyperelastic model. The beam is subjected to different loads such as dead load, point and distributed loads, and follower pressure. To demonstrate the applicability of the formulations, several examples are solved. The results reveal that this formulation can capture the previous results reported in the literature. Furthermore, a comparative study is done between two hyperelastic models. It is demonstrated that in the case of large rotation of the beam, both Saint Venant–Kirchhoff and neo-Hookean models show the same behavior. However, in case of large deformation with large strains of the beam, the Saint Venant–Kirchhoff model behaves stiffer than the neo-Hookean hyperelastic model.
Keywords
- 5-parameter beam element, Beams, Hyperelasticity, Large deformation, Nonlinear finite element method
ASJC Scopus subject areas
- Engineering(all)
- Computational Mechanics
- Engineering(all)
- Mechanics of Materials
- Engineering(all)
- Mechanical Engineering
- Physics and Astronomy(all)
- Computer Science(all)
- Computer Science Applications
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In: Computer Methods in Applied Mechanics and Engineering, Vol. 416, 116368, 01.11.2023.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Large deformation of hyperelastic modified Timoshenko–Ehrenfest beams under different types of loads
AU - Żur, Krzysztof Kamil
AU - Firouzi, Nasser
AU - Rabczuk, Timon
AU - Zhuang, Xiaoying
PY - 2023/11/1
Y1 - 2023/11/1
N2 - In this paper, a nonlinear finite element formulation for a hyperelastic, modified Timoshenko–Ehrenfest beam with geometrical and material nonlinearities is developed for the first time. A new five-parameter beam element is introduced. The parameters contain displacement, values of difference vector and a through-the-thickness scalar value. Moreover, a new procedure is employed to apply the moment to the beam. The constitutive formulation is derived for Saint Venant–Kirchhoff (SVK) as well as the compressible neo-Hookean (n-H) hyperelastic model. The beam is subjected to different loads such as dead load, point and distributed loads, and follower pressure. To demonstrate the applicability of the formulations, several examples are solved. The results reveal that this formulation can capture the previous results reported in the literature. Furthermore, a comparative study is done between two hyperelastic models. It is demonstrated that in the case of large rotation of the beam, both Saint Venant–Kirchhoff and neo-Hookean models show the same behavior. However, in case of large deformation with large strains of the beam, the Saint Venant–Kirchhoff model behaves stiffer than the neo-Hookean hyperelastic model.
AB - In this paper, a nonlinear finite element formulation for a hyperelastic, modified Timoshenko–Ehrenfest beam with geometrical and material nonlinearities is developed for the first time. A new five-parameter beam element is introduced. The parameters contain displacement, values of difference vector and a through-the-thickness scalar value. Moreover, a new procedure is employed to apply the moment to the beam. The constitutive formulation is derived for Saint Venant–Kirchhoff (SVK) as well as the compressible neo-Hookean (n-H) hyperelastic model. The beam is subjected to different loads such as dead load, point and distributed loads, and follower pressure. To demonstrate the applicability of the formulations, several examples are solved. The results reveal that this formulation can capture the previous results reported in the literature. Furthermore, a comparative study is done between two hyperelastic models. It is demonstrated that in the case of large rotation of the beam, both Saint Venant–Kirchhoff and neo-Hookean models show the same behavior. However, in case of large deformation with large strains of the beam, the Saint Venant–Kirchhoff model behaves stiffer than the neo-Hookean hyperelastic model.
KW - 5-parameter beam element
KW - Beams
KW - Hyperelasticity
KW - Large deformation
KW - Nonlinear finite element method
UR - http://www.scopus.com/inward/record.url?scp=85170260424&partnerID=8YFLogxK
U2 - 10.1016/j.cma.2023.116368
DO - 10.1016/j.cma.2023.116368
M3 - Article
AN - SCOPUS:85170260424
VL - 416
JO - Computer Methods in Applied Mechanics and Engineering
JF - Computer Methods in Applied Mechanics and Engineering
SN - 0045-7825
M1 - 116368
ER -