Flexible Multibody Dynamics and Absolute Nodal Coordinate Formulation
Summary
Flexible multibody dynamics is a discipline that combines modelling of rigid bodies with the deformation of elastic components to capture the complex kinematics and kinetics of real-world systems. The Absolute Nodal Coordinate Formulation (ANCF) offers a continuum-based finite element approach in which global position and slope vectors serve as primary degrees of freedom, enabling the analysis of large deformations and rotations without resorting to incremental linearisation. By yielding canonical ordinary differential equations, ANCF circumvents the need for inertia shape integrals and differential-algebraic systems typical of alternative methods such as the Floating Frame of Reference Formulation (FFRF). This capability has fostered robust modelling of beams, cables and shells with advanced material laws, while preserving computational efficiency via modal reduction and mesh adaptation. Applications span from soft robotic actuators and biomechanical structures to aerospace deployable elements and civil engineering systems, where accurate representation of dynamic behaviour under significant load and motion is imperative.
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Flexible Multibody Dynamics and Absolute Nodal Coordinate Formulation publication trend
The graph below shows the total number of articles in flexible multibody dynamics and absolute nodal coordinate formulation across all publications each year (not limited to Nature Index journals).
Technical terms
Flexible multibody dynamics: The study of mechanical systems composed of interacting rigid and deformable bodies undergoing large motions and elastic deformations.
Absolute Nodal Coordinate Formulation (ANCF): A finite element methodology using global nodal positions and slopes to model three-dimensional continuum mechanics under large deformations without incremental updates.
Floating Frame of Reference Formulation (FFRF): A formulation that separates rigid-body motion and local elastic deformation, leading to a differential-algebraic system under small strain assumptions.
Modal reduction: A simulation technique that projects high-order elastic behaviour onto a reduced set of mode shapes to lower computational complexity.
Locking phenomenon: Numerical stiffness artefacts in finite element formulations that inhibit realistic deformation due to element formulation or mesh configuration.
Arbitrary Lagrangian–Eulerian (ALE) formulation: A computational framework permitting mesh movement independent of material flow, enhancing accuracy in large deformation analyses.
References
- Nearly incompressible nonlinear material models in the large deformation analysis of beams using ANCF. Nonlinear Dynamics (2015).
- Inertia forces and shape integrals in the floating frame of reference formulation. Nonlinear Dynamics (2017).
- Numerical integration algorithms and constraint formulations for an ALE-ANCF cable element. Mechanism and Machine Theory (2022).
- Analysis of high-order quadrilateral plate elements based on the absolute nodal coordinate formulation for three-dimensional elasticity. Advances in Mechanical Engineering (2017).
- Performance review of locking alleviation methods for continuum ANCF beam elements. Nonlinear Dynamics (2022).
- A Variable-Length Rational Finite Element Based on the Absolute Nodal Coordinate Formulation. Machines (2022).
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