Aufsatz
Artikel (Publikationen im Open Access gefördert durch die UB)
Introducing the Logarithmic finite element method: a geometrically exact planar Bernoulli beam element
Zusammenfassung
We propose a novel finite element formulation that significantly reduces the number of degrees of freedom necessary to obtain reasonably accurate approximations of the low-frequency component of the deformation in boundary-value problems. In contrast to the standard Ritz–Galerkin approach, the shape functions are defined on a Lie algebra—the logarithmic space—of the deformation function. We construct a deformation function based on an interpolation of transformations at the nodes of the finite element. In the case of the geometrically exact planar Bernoulli beam element presented in this work, these transformation functions at the nodes are given as rotations. However, due to an intrinsic coupling between rotational and translational components of the deformation function, the formulation provides for a good approximation of the deflection of the beam, as well as of the resultant forces and moments. As both the translational and the rotational components of the deformation function are defined on the logarithmic space, we propose to refer to the novel approach as the “Logarithmic finite element method”, or “LogFE” method.
Zitierform
In: Advanced Modeling and Simulation in Engineering Sciences. - Berlin u.a. : Springer. - (2016)3:27Förderhinweis
Gefördert durch den Publikationsfonds der Universität KasselSammlung(en)
Publikationen (Fachgebiet Baustatik)Artikel (Publikationen im Open Access gefördert durch die UB)
Zitieren
@article{urn:nbn:de:hebis:34-2016110951337,
author={Schröppel, Christian and Wackerfuß, Jens},
title={Introducing the Logarithmic finite element method: a geometrically exact planar Bernoulli beam element},
year={2016}
}
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2016-11-09T11:01:33Z 2016-11-09T11:01:33Z 2016-09-15 2213-7467 urn:nbn:de:hebis:34-2016110951337 http://hdl.handle.net/123456789/2016110951337 Gefördert durch den Publikationsfonds der Universität Kassel eng Urheberrechtlich geschützt https://rightsstatements.org/page/InC/1.0/ Logarithmic finite element method Geometrically exact beam Finite rotations Large deformations Lie group theory Bernoulli kinematics 620 Introducing the Logarithmic finite element method: a geometrically exact planar Bernoulli beam element Aufsatz We propose a novel finite element formulation that significantly reduces the number of degrees of freedom necessary to obtain reasonably accurate approximations of the low-frequency component of the deformation in boundary-value problems. In contrast to the standard Ritz–Galerkin approach, the shape functions are defined on a Lie algebra—the logarithmic space—of the deformation function. We construct a deformation function based on an interpolation of transformations at the nodes of the finite element. In the case of the geometrically exact planar Bernoulli beam element presented in this work, these transformation functions at the nodes are given as rotations. However, due to an intrinsic coupling between rotational and translational components of the deformation function, the formulation provides for a good approximation of the deflection of the beam, as well as of the resultant forces and moments. As both the translational and the rotational components of the deformation function are defined on the logarithmic space, we propose to refer to the novel approach as the “Logarithmic finite element method”, or “LogFE” method. open access In: Advanced Modeling and Simulation in Engineering Sciences. - Berlin u.a. : Springer. - (2016)3:27 Schröppel, Christian Wackerfuß, Jens doi:10.1186/s40323-016-0074-8
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