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dc.description.sponsorshipGefördert durch den Publikationsfonds der Universität Kassel
dc.subjectLogarithmic finite element methodeng
dc.subjectGeometrically exact beameng
dc.subjectFinite rotationseng
dc.subjectLarge deformationseng
dc.subjectLie group theoryeng
dc.subjectBernoulli kinematicseng
dc.titleIntroducing the Logarithmic finite element method: a geometrically exact planar Bernoulli beam elementeng
dcterms.abstractWe 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.eng
dcterms.accessRightsopen access
dcterms.bibliographicCitationIn: Advanced Modeling and Simulation in Engineering Sciences. - Berlin u.a. : Springer. - (2016)3:27
dcterms.creatorSchröppel, Christian
dcterms.creatorWackerfuß, Jens

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