Finite-element formulation of geometrically exact three-dimensional beam theories based on interpolation of strain measures
Dejan Zupan,Miran Saje +1 more
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TLDR
In this paper, a new finite element formulation of the geometrically exact finite-strain beam theory is presented, in which the governing equations of the beam element are derived in a non-linear configuration space.About:
This article is published in Computer Methods in Applied Mechanics and Engineering.The article was published on 2003-12-05 and is currently open access. It has received 116 citations till now. The article focuses on the topics: Finite element method & Configuration space.read more
Citations
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An objective 3D large deformation finite element formulation for geometrically exact curved Kirchhoff rods
TL;DR: In this paper, the authors developed a finite element formulation for beams according to the Kirchhoff theory of thin rods, which includes the deformation states of axial tension, torsion and bending.
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Geometrically Exact Finite Element Formulations for Curved Slender Beams: Kirchhoff-Love Theory vs. Simo-Reissner Theory
TL;DR: It will be shown that the geometrically exact Kirchhoff–Love beam elements proposed in this work are the first ones of this type that fulfill all essential requirements and provide considerable numerical advantages such as lower spatial discretization error levels, improved performance of time integration schemes as well as linear and nonlinear solvers and smooth geometry representation as compared to shear-deformable Simo–Reissner formulations when applied to highly slender beams.
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Geometrically Exact Finite Element Formulations for Slender Beams: Kirchhoff–Love Theory Versus Simo–Reissner Theory
TL;DR: In this paper, a detailed review of existing formulations of Kirchhoff-love and Simo-Reissner type for highly slender beams is presented, where two different rotation interpolation schemes with strong or weak Kirchoff constraint enforcement, as well as two different choices of nodal triad parametrizations in terms of rotation or tangent vectors are proposed.
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Strain-based geometrically nonlinear beam formulation for modeling very flexible aircraft
Weihua Su,Carlos E. S. Cesnik +1 more
TL;DR: In this paper, a strain-based geometrically nonlinear beam formulation for structural and aero-elastic modeling and analysis of slender wings of very flexible aircraft is introduced, with beam extensional strain, twist, and bending curvatures defined as the independent degrees of freedom.
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Asymptotic post-buckling FEM analysis using corotational formulation
TL;DR: In this article, a corotational description of the strain energy is proposed for finite element asymptotic post-buckling analysis, where each element is referred to a local frame which moves with the element, so filtering its rigid motion.
References
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A proposed standard set of problems to test finite element accuracy
TL;DR: A proposed standard set of test problems is described and applied to representative quadrilateral plate and solid brick finite elements, some of which have become de facto standards for comparing the accuracy of finite elements.
Journal ArticleDOI
A three-dimensional finite-strain rod model. Part II: Computational aspects
Juan C. Simo,Loc Vu-Quoc +1 more
TL;DR: In this article, a variational formulation and computational aspects of a three-dimensional finite-strain rod model, considered in Part I, are presented, which bypasses the singularity typically associated with the use of Euler angles.
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A three-dimensional finite-strain rod model. Part II: Computational aspects
Juan C. Simo,Loc Vu-Quoc +1 more