Dynamics of spatial beams in quaternion description based on the Newmark integration scheme
From MaRDI portal
Publication:1933475
DOI10.1007/s00466-012-0703-0zbMath1398.74201OpenAlexW2005341776MaRDI QIDQ1933475
Eva Zupan, Dejan Zupan, Miran Saje
Publication date: 24 January 2013
Published in: Computational Mechanics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/s00466-012-0703-0
Rods (beams, columns, shafts, arches, rings, etc.) (74K10) Nonlinear elasticity (74B20) Vibrations in dynamical problems in solid mechanics (74H45) Finite element methods applied to problems in solid mechanics (74S05) Finite difference methods applied to problems in solid mechanics (74S20) Quaternion and other division algebras: arithmetic, zeta functions (11R52)
Related Items
On a virtual work consistent three-dimensional Reissner-Simo beam formulation using the quaternion algebra ⋮ Isogeometric collocation for implicit dynamics of three-dimensional beams undergoing finite motions ⋮ A consistent strain-based beam element with quaternion representation of rotations ⋮ Dynamics of spatial beams in quaternion description based on the Newmark integration scheme ⋮ A consistent 3D corotational beam element for nonlinear dynamic analysis of flexible structures ⋮ Explicit isogeometric collocation for the dynamics of three-dimensional beams undergoing finite motions ⋮ An energy-momentum conserving scheme for geometrically exact shells with drilling DOFs ⋮ A Newmark space-time formulation in structural dynamics ⋮ Dynamic and static isogeometric analysis for laminated Timoshenko curved microbeams ⋮ Velocity-based approach in non-linear dynamics of three-dimensional beams with enforced kinematic compatibility ⋮ On conservation of energy and kinematic compatibility in dynamics of nonlinear velocity-based three-dimensional beams
Uses Software
Cites Work
- Unnamed Item
- Unnamed Item
- Multi-body dynamics simulation of geometrically exact Cosserat rods
- Consistent quaternion interpolation for objective finite element approximation of geometrically exact beam
- Integrating rotation from angular velocity
- The quaternion-based three-dimensional beam theory
- The interpolation of rotations and its application to finite element models of geometrically exact rods
- An exact conserving algorithm for nonlinear dynamics with rotational DOFs and general hyperelasticity. I: Rods
- 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
- Kinematics and dynamics of rigid and flexible mechanisms using finite elements and quaternion algebra
- On finite deformations of space-curved beams
- Large rotations revisited application of Lie algebra
- Energy preserving/decaying schemes for nonlinear beam dynamics using the helicoidal approximation
- Energy decaying scheme for nonlinear beam models
- Automatic generation of finite-element code by simultaneous optimization of expressions
- Finite-element formulation of geometrically exact three-dimensional beam theories based on interpolation of strain measures.
- An excursion into large rotations
- Dynamics of spatial beams in quaternion description based on the Newmark integration scheme
- Geometrically exact 3D beam theory: Implementation of a strain-invariant finite element for statics and dynamics
- Rigid body dynamics in terms of quaternions: Hamiltonian formulation and conserving numerical integration
- A beam finite element non-linear theory with finite rotations
- Unconditionally stable algorithms for rigid body dynamics that exactly preserve energy and momentum
- Simo-Vu Quoc rods using Clifford algebra
- 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
- Non‐linear dynamics of three‐dimensional rods: Exact energy and momentum conserving algorithms
- Computational aspects of vector‐like parametrization of three‐dimensional finite rotations
- Critical study of Newmark scheme on manifold of finite rotations