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Objectivity of strain measures in the geometrically exact three-dimensional beam theory and its finite-element implementation
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Outgoing claims: the papers this work cites, builds on, or argues with.
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Methodus inveniendi lineas curvas maximi minimive proprietate gaudentes, sive, Solutio problematis isoperimetrici latissimo sensu accepti
What points at this work
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Geometrically exact 3D arbitrarily curved rod theory for dynamic analysis: Application to predicting the motion of hard-magnetic soft robotic arm
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Numerical aspects in the dynamic simulation of geometrically exact rods
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Finite-element formulation of geometrically exact three-dimensional beam theories based on interpolation of strain measures
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Static analysis of beam structures under nonlinear geometric and constitutive behavior
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Dynamic analysis of beam structures considering geometric and constitutive nonlinearity
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Consistent quaternion interpolation for objective finite element approximation of geometrically exact beam
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A solid-like FEM for geometrically non-linear 3D frames
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Invariant Hermitian finite elements for thin Kirchhoff rods. I: The linear plane case
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Invariant Hermitian finite elements for thin Kirchhoff rods. II: The linear three-dimensional case
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Geometrically exact beam finite element formulated on the special Euclidean group
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An objective 3D large deformation finite element formulation for geometrically exact curved Kirchhoff rods
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Nonlinear performance of continuum mechanics based beam elements focusing on large twisting behaviors
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A locking-free finite element formulation and reduced models for geometrically exact Kirchhoff rods
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A finite element approach for the line-to-line contact interaction of thin beams with arbitrary orientation
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Isogeometric configuration design sensitivity analysis of finite deformation curved beam structures using Jaumann strain formulation
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Velocity-based approach in non-linear dynamics of three-dimensional beams with enforced kinematic compatibility
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A unified approach for beam-to-beam contact
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Locking-free isogeometric collocation formulation for three-dimensional geometrically exact shear-deformable beams with arbitrary initial curvature
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On the global interpolation of motion
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Linear static isogeometric analysis of an arbitrarily curved spatial Bernoulli–Euler beam
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Explicit isogeometric collocation for the dynamics of three-dimensional beams undergoing finite motions
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Isogeometric configuration design sensitivity analysis of geometrically exact shear-deformable beam structures
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Isogeometric collocation for implicit dynamics of three-dimensional beams undergoing finite motions
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A discrete, geometrically exact method for simulating nonlinear, elastic and inelastic beams
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A large rotation finite element analysis of 3D beams by incremental rotation vector and exact strain measure with all the desirable features
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Numerical modeling of inextensible elastic ribbons with curvature-based elements
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Geometrically exact thin-walled beam including warping formulated on the special Euclidean group SE(3)
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Isogeometric analysis of 3D beams for arbitrarily large rotations: Locking-free and path-independent solution without displacement DOFs inside the patch
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An isogeometric finite element formulation for geometrically exact Timoshenko beams with extensible directors
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Geometrically exact static isogeometric analysis of an arbitrarily curved spatial Bernoulli–Euler beam
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A geometrically exact discrete elastic rod model based on improved discrete curvature
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On invariance of spatial isogeometric Timoshenko–Ehrenfest beam formulations for static analysis
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A novel four-field mixed FE approximation for Kirchhoff rods using Cartan’s moving frames
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Geometrically exact isogeometric Bernoulli–Euler beam based on the Frenet–Serret frame
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A geometrically nonlinear Cosserat shell model for orientable and non-orientable surfaces: Discretization with geometric finite elements
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An efficient displacement-based isogeometric formulation for geometrically exact viscoelastic beams
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An objective FE-formulation for Cosserat rods based on the spherical Bézier interpolation
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Relative-kinematic formulation of geometrically exact beam dynamics based on Lie group variational integrators
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Shear-flexible geometrically exact beam element based on finite differences
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A new finite element interpolation of the Cosserat directors for nonlinear three-dimensional Kirchhoff rods
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A finite element-based simulation of microstructure evolution through a 3D finite strain Cosserat phase-field model
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Geometrically exact beam finite element with generalized B-spline interpolation on the special Euclidean group S E ( 3 )
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Fluid-structure interaction between dimensionally-reduced nonlinear dragged solids and incompressible flows
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A large deformation finite element analysis of SE(3)-based beams using dual algebra
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Mixed formulation and structure-preserving discretization of Cosserat rod dynamics in a port-Hamiltonian framework
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A structure-preserving discretisation of SO(3)-rotation fields for finite Cosserat micropolar elasticity
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A reduced angular-coordinate equilibrium formulation with exact embedding of prescribed angular data for inextensible Kirchhoff rods
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Beam-inside-beam contact: Mechanical simulations of slender medical instruments inside the human body
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Rotational invariants in finite element formulation of three-dimensional beam theories
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A transfer matrix model of large deformations of curved rods
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A geometrically exact nonlinear finite element for composite closed section thin-walled beams
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Consistent structural linearisation in flexible-body dynamics with large rigid-body motion
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A finite element for nonlinear three-dimensional Kirchhoff rods
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Analyzing material softening and strain localisation through embedded strong discontinuity approach within velocity-based beam formulation
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On invariant and locking-free formulations for planar arbitrarily curved beams with Timoshenko-Ehrenfest beam model and peridynamic differential operator
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An efficient 3D corotational beam formulation using hybrid spatial discretization for nonlinear dynamics of flexible multibody system
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A relative configuration vector method for solving geometrically exact beam problems
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Geometrically explicit cosserat-rod modeling with piecewise linear strain for complex rod systems
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Continuous inter-laminar stresses for regular and inverse geometrically non linear dynamic and static analyses of laminated plates and shells
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Geometrically nonlinear analysis of layered beams using symbolic approach
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A mortar-based coupling method for fiber-reinforced composites with application to tire mechanics
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A form-finding method based on the geometrically exact rod model for bending-active structures
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3D small strain large deflection beam shape sensing including poisson effect
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A two-director Cosserat rod model using unconstrained quaternions
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Dimensionally reduced, nonlinear dragged solids: Theory and finite elements for rigid and shell-like bodies
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Assumed-metric spherically interpolated quadrilateral shell element
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Explicit symplectic momentum-conserving time-stepping scheme for the dynamics of geometrically exact rods
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