A discrete formulation of Kirchhoff rods in large-motion dynamics
From MaRDI portal
Publication:5133793
DOI10.1177/1081286519900902zbMath1482.74105OpenAlexW3002772741WikidataQ118359301 ScholiaQ118359301MaRDI QIDQ5133793
Publication date: 11 November 2020
Published in: Mathematics and Mechanics of Solids (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1177/1081286519900902
large displacementPoisson effectLagrange multipliers methoddiscrete Hencky bar modelKirchhoff nonlinear rod modelsingularity-free parametrization
Rods (beams, columns, shafts, arches, rings, etc.) (74K10) Numerical and other methods in solid mechanics (74S99)
Related Items (24)
A 3D extension of pantographic geometries to obtain metamaterial with semi-auxetic properties ⋮ Out-of-plane deformation reduction via inelastic hinges in fibrous metamaterials and simplified damage approach ⋮ In-plane dynamic buckling of duoskelion beam-like structures: discrete modeling and numerical results ⋮ Rules governing swarm robot in continuum mechanics ⋮ Modeling of three-dimensional beam nonlinear vibrations generalizing Hencky’s ideas ⋮ Investigating infill density and pattern effects in additive manufacturing by characterizing metamaterials along the strain-gradient theory ⋮ Third-gradient continua: nonstandard equilibrium equations and selection of work conjugate variables ⋮ An updated Lagrangian Bézier finite element formulation for the analysis of slender beams ⋮ The effect of local random defects on the response of pantographic sheets ⋮ Matrix-embedded metamaterials: Applications for the architectural heritage ⋮ Experimental and numerical investigation of the deformation behaviour of cables and thin beam-like structures under multi-axial loading ⋮ Generalized Reissner-type variational principles in the micropolar theories of multilayer thin bodies with one small size ⋮ On some variational principles in micropolar theories of single-layer thin bodies ⋮ A novel four-field mixed FE approximation for Kirchhoff rods using Cartan's moving frames ⋮ Bayesian design optimization of biomimetic soft actuators ⋮ A non-linear symmetric \(\mathrm{G}^1\)-conforming Bézier finite element formulation for the analysis of Kirchhoff beam assemblies ⋮ An implicit \(\operatorname{G}^1\)-conforming bi-cubic interpolation for the analysis of smooth and folded Kirchhoff-Love shell assemblies ⋮ Identification of a geometrically nonlinear micromorphic continuum via granular micromechanics ⋮ Stepwise analysis of pantographic beams subjected to impulsive loads ⋮ On boundary layers observed in some 1D second-gradient theories ⋮ From the swarm robotics to material deformations ⋮ Finite element formulations for constrained spatial nonlinear beam theories ⋮ A numerical investigation on impulse-induced nonlinear longitudinal waves in pantographic beams ⋮ Numerical evidence for the approximation of dissipative systems by gyroscopically coupled oscillator chains
Cites Work
- Unnamed Item
- On the whole spectrum of Timoshenko beams. II: Further applications
- An implicit \(G^1\) multi patch B-spline interpolation for Kirchhoff-Love space rod
- B-spline interpolation of Kirchhoff-Love space rods
- An energy-based method to determine material constants in nonlinear rheology with applications
- Hencky-type discrete model for pantographic structures: numerical comparison with second gradient continuum models
- On the constitutive equations of viscoelastic micropolar plates and shells of differential type
- A finite strain beam formulation. The three-dimensional dynamic problem. I
- A three-dimensional finite-strain rod model. II. Computational aspects
- On the dynamics in space of rods undergoing large motions - A geometrically exact approach
- On the dynamics of rods in the theory of Kirchhoff and Clebsch
- Variational theory for spatial rods
- Statics of shallow inclined elastic cables under general vertical loads: a perturbation approach
- Energy transfer between modes in a nonlinear beam equation
- Variational formulations and isogeometric analysis for the dynamics of anisotropic gradient-elastic Euler-Bernoulli and shear-deformable beams
- Discrete is it enough? The revival of Piola-Hencky keynotes to analyze three-dimensional \textit{Elastica}
- A revival of electric analogs for vibrating mechanical systems aimed to their efficient control by PZT actuators
- Locking-free variational formulations and isogeometric analysis for the Timoshenko beam models of strain gradient and classical elasticity
- On the wave dispersion in microstructured solids
- An efficient blended mixed B-spline formulation for removing membrane locking in plane curved Kirchhoff rods
- Pantographic beam: a complete second gradient 1D-continuum in plane
- Effects of damping on the stability of the compressed Nicolai beam
- Geometric continuum mechanics and induced beam theories
- On a thermodynamic theory of rods with two temperature fields
- Isogeometric analysis of nonlinear Euler-Bernoulli beam vibrations
- Piezo-electromechanical (PEM) structures: Passive vibration control using distributed piezoelectric transducers
- Consistent tangent operator for an exact Kirchhoff rod model
- An isogeometric implicit \(G^1\) mixed finite element for Kirchhoff space rods
- Constitutive models for strongly curved beams in the frame of isogeometric analysis
- Cosserat-Type Rods
- Director-based beam finite elements relying on the geometrically exact beam theory formulated in skew coordinates
- Hencky Bar-Chain Model for Buckling and Vibration of Beams with Elastic End Restraints
- Truss Modular Beams with Deformation Energy Depending on Higher Displacement Gradients
- Finite element of slender beams in finite transformations: a geometrically exact approach
- Flexible multibody dynamics based on a non-linear Euler-Bernoulli kinematics
- Equilibria of a clamped Euler beam (Elastica) with distributed load: Large deformations
- Vacancies for controlling the behavior of microstructured three-dimensional mechanical metamaterials
- On the dependence of standard and gradient elastic material constants on a field of defects
- Variational asymptotic homogenization of beam-like square lattice structures
- Mechanical metamaterials: a state of the art
- A targeted review on large deformations of planar elastic beams: extensibility, distributed loads, buckling and post-buckling
- Variational formulations, model comparisons and numerical methods for Euler–Bernoulli micro- and nano-beam models
- Isogeometric analysis of plane-curved beams
- Nonlinear hysteretic damping effects on the post-critical behaviour of the visco-elastic Beck’s beam
- Piezoelectric Passive Distributed Controllers for Beam Flexural Vibrations
- At the origins and in the vanguard of peridynamics, non-local and higher-gradient continuum mechanics: An underestimated and still topical contribution of Gabrio Piola
- Nonlinear dynamics of uniformly loaded Elastica: Experimental and numerical evidence of motion around curled stable equilibrium configurations
This page was built for publication: A discrete formulation of Kirchhoff rods in large-motion dynamics