On nonlinear geometric transformations of finite elements
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Publication:6589350
DOI10.1002/NME.7506MaRDI QIDQ6589350
Claudio M. Perez, Filip C. Filippou
Publication date: 19 August 2024
Published in: International Journal for Numerical Methods in Engineering (Search for Journal in Brave)
rotationboundary value problemlarge deformationpath independenceCosserat rodmanifold parameterizationdirector constraintstrain objectivity
Rods (beams, columns, shafts, arches, rings, etc.) (74K10) Finite element methods applied to problems in solid mechanics (74S05)
Cites Work
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- Modeling nonlinear problems in the mechanics of strings and rods. The role of the balance laws
- A hybrid-mixed finite element formulation for the geometrically exact analysis of three-dimensional framed structures
- Exact theory of stress and strain in rods and shells
- The interpolation of rotations and its application to finite element models of geometrically exact rods
- A comparison of finite elements for nonlinear beams: the absolute nodal coordinate and geometrically exact formulations
- A frame-invariant scheme for the geometrically exact beam using rotation vector parametrization
- Finite rotations in the description of continuum deformation
- 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 a stress resultant geometrically exact shell model. IV: Variable thickness shells with through-the-thickness stretching
- Finite rotation analysis and consistent linearization using projectors
- The (symmetric) Hessian for geometrically nonlinear models in solid mechanics: Intrinsic definition and geometric interpretation
- On the choice of finite rotation parameters
- Work-conjugacy between rotation-dependent moments and finite rotations.
- The vectorial parameterization of rotation
- Energy-dissipative momentum-conserving time-stepping algorithms for the dynamics of nonlinear cosserat rods
- Finite-element formulation of geometrically exact three-dimensional beam theories based on interpolation of strain measures.
- On a stress resultant geometrically exact shell model. III: Computational aspects of the nonlinear theory
- Geometrically exact 3D beam theory: Implementation of a strain-invariant finite element for statics and dynamics
- A consistent strain-based beam element with quaternion representation of rotations
- An introduction to continuum mechanics
- Total Lagrangian Reissner's geometrically exact beam element without singularities
- A beam finite element non-linear theory with finite rotations
- Effective modelling of spatial buckling of beam assemblages, accounting for warping constraints and rotation-dependency of moments
- Unconditionally stable algorithms for rigid body dynamics that exactly preserve energy and momentum
- Large displacement analysis of three-dimensional beam structures
- Interpolation of rotational variables in nonlinear dynamics of 3D beams
- Objectivity of strain measures in the geometrically exact three-dimensional beam theory and its finite-element implementation
- On the role of geometrically exact and second-order theories in buckling and post-buckling analysis of three-dimensional beam structures
- 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
- On the Parametrization of the Three-Dimensional Rotation Group
- Nonlinear problems of elasticity
- A total Lagrangian, objective and intrinsically locking‐free Petrov–Galerkin SE(3) Cosserat rod finite element formulation
- A family of total Lagrangian Petrov-Galerkin Cosserat rod finite element formulations
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