Importance and effectiveness of representing the shapes of Cosserat rods and framed curves as paths in the special Euclidean algebra

DOI10.1007/s10659-017-9656-zzbMath1393.74090arXiv1611.07155OpenAlexW2750242756WikidataQ59607252 ScholiaQ59607252MaRDI QIDQ1653418

Giulio G. Giusteri, Eliot Fried

Publication date: 3 August 2018

Published in: Journal of Elasticity (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1611.07155

zbMATH Keywords

Euclidean algebraCosserat rodframed curveshape discretization

Mathematics Subject Classification ID

Rods (beams, columns, shafts, arches, rings, etc.) (74K10) Curves in Euclidean and related spaces (53A04)

Related Items

Deformation of framed curves with boundary conditions, Issues concerning isometric deformations of planar regions to curved surfaces, Unified static equilibrium modeling and analysis of elastic rods with large deformations for complex constraints, Simulation of viscoelastic Cosserat rods based on the geometrically exact dynamics of special Euclidean strands, On a nonlinear rod exhibiting only axial and bending deformations: mathematical modeling and numerical implementation, Discrete Cosserat rod kinematics constructed on the basis of the difference geometry of framed curves -- Part I. Discrete Cosserat curves on a staggered grid, The rotating rigid body model based on a non-twisting frame

Uses Software

• CoRdE

Cites Work

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• A discrete geometric approach for simulating the dynamics of thin viscous threads
• Interpolation of rotation and motion
• Multi-body dynamics simulation of geometrically exact Cosserat rods
• Geometrically exact beam finite element formulated on the special Euclidean group \(SE(3)\)
• A distance on curves modulo rigid transformations
• Notwendige und hinreichende Bedingungen dafür, daß eine Raumkurve geschlossen ist
• Kirchhoff elastic rods in three-dimensional space forms
• A comparison of finite elements for nonlinear beams: the absolute nodal coordinate and geometrically exact formulations
• A three-dimensional finite-strain rod model. II. Computational aspects
• The Hamiltonian structure of nonlinear elasticity: The material and convective representations of solids, rods, and plates
• Kirchhoff's theory of rods
• On the formulation of contact problems of shells and plates
• Finite-element formulation of geometrically exact three-dimensional beam theories based on interpolation of strain measures.
• The nonlinear dynamics of filaments
• An objective 3D large deformation finite element formulation for geometrically exact curved Kirchhoff rods
• Moving frames and the characterization of curves that lie on a surface
• Framed curves in the Euclidean space
• A locking-free finite element formulation and reduced models for geometrically exact Kirchhoff rods
• Global injectivity and topological constraints for spatial nonlinearly elastic rods
• On finite element implementation of geometrically nonlinear Reissner's beam theory: Three-dimensional curved beam elements
• Sides of the Möbius strip
• Characterisation of cylindrical curves
• Velocity-based approach in non-linear dynamics of three-dimensional beams with enforced kinematic compatibility
• Solution of the Kirchhoff-Plateau problem
• The linearized three-dimensional beam theory of naturally curved and twisted beams: The strain vector formulation
• Nonlinear isogeometric spatial Bernoulli beam
• Dynamics of flexible beams: Finite-element formulation based on interpolation of strain measures
• Three-dimensional nonlinear dynamics of slender structures: Cosserat rod element approach
• A group-theoretic approach to the geometry of elastic rings
• A discrete mechanics approach to the Cosserat rod theory-Part 1: static equilibria
• A Concise Parametrization of Affine Transformation
• Geodesic finite elements for Cosserat rods
• A Differential-Geometric Criterion for a Space Curve to be Closed
• There is More than One Way to Frame a Curve
• An intrinsic beam model based on a helicoidal approximation—Part I: Formulation
• The Critical Role of the Base Curve for the Qualitative Behavior of Shearable Rods
• Frame-indifferent beam finite elements based upon the geometrically exact beam theory
• Matrix G-strands
• Lagrangian Aspects of the Kirchhoff Elastic Rod
• Relative geodesics in the special Euclidean group
• Geometric Numerical Integration
• A soliton on a vortex filament
• On the differential geometry of closed space curves
• Linear integral equations
• Nonlinear problems of elasticity
• Hidden symmetry of global solutions in twisted elastic rings