Isogeometric analysis for nonlinear planar Kirchhoff rods: weighted residual formulation and collocation of the strong form
type: Item
instance of: scholarly article
title: Isogeometric analysis for nonlinear planar Kirchhoff rods: weighted residual formulation and collocation of the strong form
zbMATH Open document ID: 1440.74186
author: F. Greco
author: Sander Dedoncker
author: Florian Paul Robert Maurin
author: Wim Desmet
published in: Computer Methods in Applied Mechanics and Engineering
publication date: 2020-04-08T00:00:00Z
full work available at URL: https://lirias.kuleuven.be/handle/123456789/624902
Mathematics Subject Classification ID: 74K10
Mathematics Subject Classification ID: 74S05
Mathematics Subject Classification ID: 65D07
Mathematics Subject Classification ID: 65N30
zbMATH DE Number: 7188315
zbMATH Keywords: isogeometric analysis
zbMATH Keywords: planar Kirchhoff rod
zbMATH Keywords: weighted residual form
zbMATH Keywords: collocation
zbMATH Keywords: nonlinear deformation
zbMATH Keywords: convergence order
describes a project that uses: NURBS
describes a project that uses: GeoPDEs
MaRDI profile type: Publication
OpenAlex ID: W2806567946
Wikidata QID: Q117221223
cites work: Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement
cites work: Isogeometric Analysis
cites work: ISOGEOMETRIC COLLOCATION METHODS
cites work: Isogeometric collocation: cost comparison with Galerkin methods and extension to adaptive hierarchical NURBS discretizations
cites work: Isogeometric collocation for elastostatics and explicit dynamics
cites work: Accurate, efficient, and (iso)geometrically flexible collocation methods for phase-field models
cites work: Isogeometric collocation for phase-field fracture models
cites work: Isogeometric collocation: Neumann boundary conditions and contact
cites work: Isogeometric collocation for large deformation elasticity and frictional contact problems
cites work: An isogeometric collocation method for frictionless contact of Cosserat rods
cites work: Avoiding shear locking for the Timoshenko beam problem via isogeometric collocation methods
cites work: Locking-free isogeometric collocation methods for spatial Timoshenko rods
cites work: Single-variable formulations and isogeometric discretizations for shear deformable beams
cites work: Isogeometric collocation methods for Cosserat rods and rod structures
cites work: Non-prismatic Timoshenko-like beam model: numerical solution via isogeometric collocation
cites work: Isogeometric collocation methods for the Reissner-Mindlin plate problem
cites work: Isogeometric collocation for the Reissner-Mindlin shell problem
cites work: An isogeometric collocation approach for Bernoulli-Euler beams and Kirchhoff plates
cites work: Isogeometric collocation using analysis-suitable T-splines of arbitrary degree
cites work: Isogeometric collocation for Kirchhoff-Love plates and shells
cites work: An isogeometric collocation method using superconvergent points
cites work: Optimal-order isogeometric collocation at Galerkin superconvergent points
cites work: A collocated isogeometric finite element method based on Gauss-Lobatto Lagrange extraction of splines
cites work: A fully ``locking-free'' isogeometric approach for plane linear elasticity problems: a stream function formulation
cites work: Isogeometric analysis of the Cahn-Hilliard phase-field model
cites work: Isogeometric analysis and error estimates for high order partial differential equations in fluid dynamics
cites work: Isogeometric shell analysis with Kirchhoff-Love elements
cites work: Isogeometric rotation-free bending-stabilized cables: statics, dynamics, bending strips and coupling with shells
cites work: Isogeometric rotation-free analysis of planar extensible-elastica for static and dynamic applications
cites work: B-spline interpolation of Kirchhoff-Love space rods
cites work: An implicit \(G^1\) multi patch B-spline interpolation for Kirchhoff-Love space rod
cites work: An isogeometric implicit \(G^1\) mixed finite element for Kirchhoff space rods
cites work: On One‐Dimensional Large‐Displacement Finite‐Strain Beam Theory
cites work: Q3514988
cites work: A continuum mechanics based derivation of Reissner's large-displacement finite-strain beam theory: the case of plane deformations of originally straight Bernoulli-Euler beams
cites work: Behaviour of the extensible elastical solution
cites work: Exact solutions for the buckling and postbuckling of shear-deformable beams
cites work: Large deformation and stability of an extensible elastica with an unknown length
cites work: Static snapping load of a hinged extensible elastica
cites work: How to improve efficiency and robustness of the Newton method in geometrically non-linear structural problem discretized via displacement-based finite elements
cites work: On one-dimensional finite-strain beam theory: the plane problem
cites work: Weak form quadrature element analysis of planar slender beams based on geometrically exact beam theory
cites work: A collocatedC0finite element method: Reduced quadrature perspective, cost comparison with standard finite elements, and explicit structural dynamics
cites work: Reduced integration at superconvergent points in isogeometric analysis
cites work: The variational collocation method
cites work: B-spline goal-oriented error estimators for geometrically nonlinear rods
cites work: An isogeometric formulation of the Koiter's theory for buckling and initial post-buckling analysis of composite shells
cites work: \textsc{GeoPDEs}: a research tool for isogeometric analysis of PDEs
DOI: 10.1016/J.CMA.2018.05.025
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