Consistent tangent operator for an exact Kirchhoff rod model
From MaRDI portal
Publication:2629050
DOI10.1007/s00161-014-0361-xzbMath1341.74096OpenAlexW2133440874MaRDI QIDQ2629050
Publication date: 19 July 2016
Published in: Continuum Mechanics and Thermodynamics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/s00161-014-0361-x
Related Items
Plane contact problem on indentation of a flat punch into a transversely-isotropic half-plane with functionally graded transversely-isotropic coating ⋮ ``Fast and ``slow pressure waves electrically induced by nonlinear coupling in Biot-type porous medium saturated by a nematic liquid crystal ⋮ Linear pantographic sheets: asymptotic micro-macro models identification ⋮ A total Lagrangian Timoshenko beam formulation for geometrically nonlinear isogeometric analysis of spatial beam structures ⋮ Free vibration analysis of nonlocal nanobeams: a comparison of the one-dimensional nonlocal integral Timoshenko beam theory with the two-dimensional nonlocal integral elasticity theory ⋮ Numerical simulations of classical problems in two-dimensional (non) linear second gradient elasticity ⋮ An updated Lagrangian Bézier finite element formulation for the analysis of slender beams ⋮ A geometrically exact discrete elastic rod model based on improved discrete curvature ⋮ An isogeometric implicit \(G^1\) mixed finite element for Kirchhoff space rods ⋮ Three-dimensional instabilities of pantographic sheets with parabolic lattices: numerical investigations ⋮ Dynamics of taut strings traveled by train of forces ⋮ A review of presentations and discussions of the workshop Computational mechanics of generalized continua and applications to materials with microstructure that was held in Catania 29–31 October 2015 ⋮ On the effect of shear stiffness on the plane deformation of linear second gradient pantographic sheets ⋮ Construction of the effective plastic yield surfaces of vertebral trabecular bone under twisting and bending moments stresses using a 3D microstructural model ⋮ The contribution of Gustav R. Kirchhoff to the dynamics of tapered beams ⋮ Geometrically exact isogeometric Bernoulli-Euler beam based on the Frenet-Serret frame ⋮ Efficiency improvement on the ANCF cable element by using the dot product form of curvature ⋮ Nonlinear dynamics of uniformly loaded Elastica: Experimental and numerical evidence of motion around curled stable equilibrium configurations ⋮ Weakly nonlinear dynamics of taut strings traveled by a single moving force ⋮ Gedanken experiments for the determination of two-dimensional linear second gradient elasticity coefficients ⋮ A beam model for duoskelion structures derived by asymptotic homogenization and its application to axial loading problems ⋮ An Inverse Method to Get Further Analytical Solutions for a Class of Metamaterials Aimed to Validate Numerical Integrations ⋮ Identification of two-dimensional pantographic structure via a linear D4 orthotropic second gradient elastic model ⋮ Large Oscillations Around Curled Equilibrium Configurations of Uniformly Loaded Euler–Bernoulli Beams: Numerical and Experimental Evidences ⋮ A discrete formulation of Kirchhoff rods in large-motion dynamics ⋮ Linear static isogeometric analysis of an arbitrarily curved spatial Bernoulli-Euler beam ⋮ A non-linear symmetric \(\mathrm{G}^1\)-conforming Bézier finite element formulation for the analysis of Kirchhoff beam assemblies ⋮ A review on 2D models for the description of pantographic fabrics ⋮ Hencky-type discrete model for pantographic structures: numerical comparison with second gradient continuum models ⋮ A novel mathematical model for growth of capillaries and nutrient supply with application to prediction of osteophyte onset ⋮ Numerical identification procedure between a micro-Cauchy model and a macro-second gradient model for planar pantographic structures ⋮ A one-dimensional continuum with microstructure for single-wall carbon nanotubes bifurcation analysis ⋮ Analytical Solutions of 2-dimensional Second Gradient Linear Elasticity for Continua with Cubic-D4 Microstructure ⋮ An efficient blended mixed B-spline formulation for removing membrane locking in plane curved Kirchhoff rods ⋮ Locking-free isogeometric collocation formulation for three-dimensional geometrically exact shear-deformable beams with arbitrary initial curvature ⋮ Geometrically exact static isogeometric analysis of an arbitrarily curved spatial Bernoulli-Euler beam ⋮ A targeted review on large deformations of planar elastic beams: extensibility, distributed loads, buckling and post-buckling ⋮ On boundary layers observed in some 1D second-gradient theories
Cites Work
- Unnamed Item
- Unnamed Item
- Buckling of an elastic hemispherical shell with an obstacle
- Thermomechanics of shells undergoing phase transition
- An implicit \(G^1\) multi patch B-spline interpolation for Kirchhoff-Love space rod
- A hierarchic family of isogeometric shell finite elements
- B-spline interpolation of Kirchhoff-Love space rods
- On a stress resultant geometrically exact shell model. I: Formulation and optimal parametrization
- Modeling the onset of shear boundary layers in fibrous composite reinforcements by second-gradient theory
- Local symmetry group in the general theory of elastic shells
- On the geometrically exact formulation of structural mechanics and its applications to dynamics, control and optimization
- Multimode vibration control using several piezoelectric transducers shunted with a multiterminal network
- 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
- The Hamiltonian structure of nonlinear elasticity: The material and convective representations of solids, rods, and plates
- Continuum modelling of piezoelectromechanical truss beams: An application to vibration damping
- On finite deformations of space-curved beams
- Formulations of finite elasticity with independent rotations
- The (symmetric) Hessian for geometrically nonlinear models in solid mechanics: Intrinsic definition and geometric interpretation
- On the perturbation analysis of interactive buckling in nearly symmetric structures
- A drill rotation formulation for geometrically exact shells
- Dynamic problems for metamaterials: review of existing models and ideas for further research
- The nonlinear theory of elastic shells with phase transitions
- On a model of layered piezoelectric beams including transverse stress effect
- An excursion into large rotations
- A revival of electric analogs for vibrating mechanical systems aimed to their efficient control by PZT actuators
- Stress resultant geometrically nonlinear shell theory with drilling rotations. I: A consistent formulation
- Stress resultant geometrically nonlinear shell theory with drilling rotations. II: Computational aspects
- A kinematically exact space finite strain beam model -- finite element formulation by generalized virtual work principle
- How contact interactions may depend on the shape of Cauchy cuts in \(N\)th gradient continua: approach ``à la d'Alembert
- Geometrically exact 3D beam theory: Implementation of a strain-invariant finite element for statics and dynamics
- Statically and kinematically exact nonlinear theory of rods and its numerical verification
- Modal coupling in one-dimensional electro-mechanical structured continua
- Piezo-electromechanical (PEM) structures: Passive vibration control using distributed piezoelectric transducers
- Director-based beam finite elements relying on the geometrically exact beam theory formulated in skew coordinates
- ON THE DYNAMICS OF A BEAM PARTIALLY SUPPORTED BY AN ELASTIC FOUNDATION: AN EXACT SOLUTION-SET
- Extended non-linear relations of elastic shells undergoing phase transitions
- Multiple interaction and localization phenomena in the postbuckling of compressed thin-walled members
- Objectivity of strain measures in the geometrically exact three-dimensional beam theory and its finite-element implementation
- Truss Modular Beams with Deformation Energy Depending on Higher Displacement Gradients
- Frame-indifferent beam finite elements based upon the geometrically exact beam theory
- Circuit analog of a beam and its application to multimodal vibration damping, using piezoelectric transducers
- Lagrangian Aspects of the Kirchhoff Elastic Rod
- Piezoelectric Passive Distributed Controllers for Beam Flexural Vibrations
- Nonlinear problems of elasticity
- Mode localization in dynamics and buckling of linear imperfect continuous structures