An efficient displacement-based isogeometric formulation for geometrically exact viscoelastic beams

DOI10.1016/j.cma.2023.116413arXiv2307.10106OpenAlexW4386768385MaRDI QIDQ6153867

Giulio Ferri, Diego Ignesti, Enzo Marino

Publication date: 14 February 2024

Published in: Computer Methods in Applied Mechanics and Engineering (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2307.10106

zbMATH Keywords

geometrically nonlinear beamsfinite rotationsisogeometric analysisgeneralized Maxwell modelviscoelastic beamscurved beams

Mathematics Subject Classification ID

Mechanics of deformable solids (74-XX) Optics, electromagnetic theory (78-XX)

Cites Work

• Isogeometric collocation for elastostatics and explicit dynamics
• A discrete geometric approach for simulating the dynamics of thin viscous threads
• Accurate, efficient, and (iso)geometrically flexible collocation methods for phase-field models
• Numerical aspects in the dynamic simulation of geometrically exact rods
• Avoiding shear locking for the Timoshenko beam problem via isogeometric collocation methods
• A nonlinear visco-elastic constitutive model for large rotation finite element formulations
• Multi-body dynamics simulation of geometrically exact Cosserat rods
• A mixed hybrid finite beam element with an interface to arbitrary three-dimensional material models
• A nonlinear hu-washizu variational formulation and related finite-element implementation for spatial beams with arbitrary moderate thick cross-sections
• The interpolation of rotations and its application to finite element models of geometrically exact rods
• Dynamic analysis of beam structures considering geometric and constitutive nonlinearity
• Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement
• Simulation of a viscoelastic flexible multibody system using absolute nodal coordinate and fractional derivative methods
• Static analysis of beam structures under nonlinear geometric and constitutive behavior
• A finite strain beam formulation. The three-dimensional dynamic problem. I
• A three-dimensional finite-strain rod model. II. Computational aspects
• On the choice of finite rotation parameters
• On a geometrically exact curved/twisted beam theory under rigid cross-section assumption
• Non-prismatic Timoshenko-like beam model: numerical solution via isogeometric collocation
• Isogeometric collocation: Neumann boundary conditions and contact
• Isogeometric collocation methods for the Reissner-Mindlin plate problem
• An isogeometric collocation approach for Bernoulli-Euler beams and Kirchhoff plates
• Single-variable formulations and isogeometric discretizations for shear deformable beams
• Plastic instability of beam structures using co-rotational elements.
• On finite element implementation of geometrically nonlinear Reissner's beam theory: Three-dimensional curved beam elements
• Geometrically exact 3D beam theory: Implementation of a strain-invariant finite element for statics and dynamics
• Explicit higher-order accurate isogeometric collocation methods for structural dynamics
• Isogeometric analysis for nonlinear planar Kirchhoff rods: weighted residual formulation and collocation of the strong form
• Fully isogeometric modeling and analysis of nonlinear 3D beams with spatially varying geometric and material parameters
• Explicit isogeometric collocation for the dynamics of three-dimensional beams undergoing finite motions
• Isogeometric shape optimization of nonlinear, curved 3D beams and beam structures
• Isogeometric analysis of 3D beams for arbitrarily large rotations: locking-free and path-independent solution without displacement DOFs inside the patch
• Geometrically exact static isogeometric analysis of an arbitrarily curved spatial Bernoulli-Euler beam
• Isogeometric collocation for implicit dynamics of three-dimensional beams undergoing finite motions
• A discrete, geometrically exact method for simulating nonlinear, elastic and inelastic beams
• A large rotation finite element analysis of 3D beams by incremental rotation vector and exact strain measure with all the desirable features
• Effects of parameterization and knot placement techniques on primal and mixed isogeometric collocation formulations of spatial shear-deformable beams with varying curvature and torsion
• Modeling viscoelastic behavior in flexible multibody systems
• Mixed stress-displacement isogeometric collocation for nearly incompressible elasticity and elastoplasticity
• Geometrically nonlinear multi-patch isogeometric analysis of spatial Euler-Bernoulli beam structures
• An isogeometric finite element formulation for geometrically exact Timoshenko beams with extensible directors
• Geometrically exact elastoplastic rods: determination of yield surface in terms of stress resultants
• Isogeometric collocation for three-dimensional geometrically exact shear-deformable beams
• The variational collocation method
• Isogeometric collocation methods for Cosserat rods and rod structures
• Locking-free isogeometric collocation formulation for three-dimensional geometrically exact shear-deformable beams with arbitrary initial curvature
• Isogeometric collocation for the Reissner-Mindlin shell problem
• Isogeometric collocation for Kirchhoff-Love plates and shells
• Locking-free isogeometric collocation methods for spatial Timoshenko rods
• Isogeometric collocation: cost comparison with Galerkin methods and extension to adaptive hierarchical NURBS discretizations
• Poisson modes and general nonlinear constitutive models in the large displacement analysis of beams
• Isogeometric collocation for large deformation elasticity and frictional contact problems
• A consistent co-rotational formulation for nonlinear, three-dimensional, beam-elements
• Mixed isogeometric collocation for geometrically exact 3D beams with elasto-visco-plastic material behavior and softening effects
• An improved isogeometric collocation formulation for spatial multi-patch shear-deformable beams with arbitrary initial curvature
• An isogeometric finite element formulation for frictionless contact of Cosserat rods with unconstrained directors
• Geometrically exact isogeometric Bernoulli-Euler beam based on the Frenet-Serret frame
• ISOGEOMETRIC COLLOCATION METHODS
• On a non-linear formulation for curved Timoshenko beam elements considering large displacement/rotation increments
• A beam finite element non-linear theory with finite rotations
• Objectivity of strain measures in the geometrically exact three-dimensional beam theory and its finite-element implementation
• Isogeometric Analysis
• Using finite strain 3D‐material models in beam and shell elements
• An objective finite element approximation of the kinematics of geometrically exact rods and its use in the formulation of an energy-momentum conserving scheme in dynamics
• Frame-indifferent beam finite elements based upon the geometrically exact beam theory
• On the differentiation of the Rodrigues formula and its significance for the vector‐like parameterization of Reissner–Simo beam theory
• Computational aspects of vector‐like parametrization of three‐dimensional finite rotations
• An updated Lagrangian Bézier finite element formulation for the analysis of slender beams
• Collocation Methods and Beyond in Non-linear Mechanics
• Two-scale off-and online approaches to geometrically exact elastoplastic rods
• Simulation of viscoelastic Cosserat rods based on the geometrically exact dynamics of special Euclidean strands
• Isogeometric mixed collocation of nearly-incompressible electromechanics in finite deformations for cardiac muscle simulations
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