Nonlinear isogeometric spatial Bernoulli beam

Bauer, Anna; Breitenberger, M.; Philipp, Benedikt; Wüchner, Roland; Bletzinger, Kai‐Uwe

doi:10.1016/j.cma.2015.12.027

Cited by 106 publications

(72 citation statements)

References 25 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…Over the last decade, IGA has become a well-established method used in a wide range of problems including structural mechanics [3][4][5][6][7][8][9][10][11][12] with recent developments for spatial Bernoulli beams [13,14], turbulent flow and fluid-structure interaction [15][16][17][18][19][20].…”

Section: Introductionmentioning

confidence: 99%

Isogeometric collocation for three-dimensional geometrically exact shear-deformable beams

Marino

2016

Computer Methods in Applied Mechanics and Engineering

View full text Add to dashboard Cite

Highlights• Isogeometric collocation is extended to geometrically exact beams.• Consistent linearization of the strong form of the governing equations is derived.• Incremental rotations are parametrized through Eulerian rotation vectors.• Numerical tests show efficiency and high accuracy. AbstractWe extend the isogeometric collocation method to the geometrically nonlinear beams. An exact kinematic formulation, able to represent three-dimensional displacements and rotations without any restriction in magnitude, is presented without the introduction of the moving frame concept. A displacement-based formulation is adopted. Full linearization of the strong form of the governing equations is derived consistently with the underlying geometric structure of the configuration manifold. Incremental rotations are parametrized through Eulerian rotation vectors and configuration updates are performed by means of the exponential map. Numerical tests demonstrate that the proposed combination of isogeometric collocation method with the chosen rotations parametrization results in an efficient computational scheme able to model complex problems with high accuracy.

show abstract

Section: Introductionmentioning

confidence: 99%

Isogeometric collocation for three-dimensional geometrically exact shear-deformable beams

Marino

2016

Computer Methods in Applied Mechanics and Engineering

View full text Add to dashboard Cite

show abstract

“…Raknes et al [17] presented the IGA for three-dimensional cable structures undergoing large deformation, with considering bending deformation confined in an osculating plane as well as membrane deformation. Bauer et al [18] suggested an IGA formulation of spatial Kirchhoff beam undergoing large deformation considering torsion. Maurin et al [19] performed the IGA for static and dynamic deformation analyses of planar Kirchhoff beam based on the GEBT considering single patch models.…”

Section: Introductionmentioning

confidence: 99%

Isogeometric configuration design sensitivity analysis of finite deformation curved beam structures using Jaumann strain formulation

Choi

Yoon

Cho

2016

Computer Methods in Applied Mechanics and Engineering

View full text Add to dashboard Cite

“…These approaches are characterized by the fact that translational and rotational degrees of freedom are often considered separately and the beam shape is reconstructed by means of interpolation procedures. A selection of methods can be found in the works by Simo and Vu-Quoc [30], Borri and Bottasso [31], Ibrahimbegović [32], Betsch and Steinmann [33], Meier, Popp and Wall [34,35], Gaćeša and Jelenić [36], Bauer, Breitenberger, Philipp, Wüchner and Bletzinger [37], Yilmaz and Omurtag [38], and Zupan and Zupan [39].…”

Section: The Lie Algebra and The Lie Group Associated With The Rod Dementioning

confidence: 99%

Importance and Effectiveness of Representing the Shapes of Cosserat Rods and Framed Curves as Paths in the Special Euclidean Algebra

Giusteri

Fried

2017

J Elast

View full text Add to dashboard Cite

We discuss how the shape of a special Cosserat rod can be represented as a path in the special Euclidean algebra. By shape we mean all those geometric features that are invariant under isometries of the three-dimensional ambient space. The representation of the shape as a path in the special Euclidean algebra is intrinsic to the description of the mechanical properties of a rod, since it is given directly in terms of the strain fields that stimulate the elastic response of special Cosserat rods. Moreover, such a representation leads naturally to discretization schemes that avoid the need for the expensive reconstruction of the strains from the discretized placement and for interpolation procedures which introduce some arbitrariness in popular numerical schemes. Given the shape of a rod and the positioning of one of its cross sections, the full placement in the ambient space can be uniquely reconstructed and described by means of a base curve endowed with a material frame. By viewing a geometric curve as a rod with degenerate point-like cross sections, we highlight the essential difference between rods and framed curves, and clarify why the family of relatively parallel adapted frames is not suitable for describing the mechanics of rods but is the appropriate tool for dealing with the geometry of curves.

show abstract

Nonlinear isogeometric spatial Bernoulli beam

Cited by 106 publications

References 25 publications

Isogeometric collocation for three-dimensional geometrically exact shear-deformable beams

Isogeometric collocation for three-dimensional geometrically exact shear-deformable beams

Isogeometric configuration design sensitivity analysis of finite deformation curved beam structures using Jaumann strain formulation

Importance and Effectiveness of Representing the Shapes of Cosserat Rods and Framed Curves as Paths in the Special Euclidean Algebra

Contact Info

Product

Resources

About