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 -