Consider using beam elements in absolute nodal coordinate formulation

[stfnp]

Instead of rotation angles, beam elements based on ANCF use the slopes of the beam axis at the nodes to describe the kinematic configuration of the beam.

Advantages over the current approach (floating frame of reference/co-rotational formulation):

• Truly "large deformation". Very few elements needed to approximate the large limb deformation, compared to the co-rotational elements
• Exact, constant mass matrices. Great improvement over lumped mass matrices, especially if fewer elements are being used.
• Slopes as generalized coordinates should reduce the need for trigonometric functions by a lot, possibly better performance

Disadvantages:

• Slopes are sometimes not as intuitive as angles
• More coordinates, 8 for a planar beam element instead of 6. Could be worth it if fewer elements are needed overall.

Alternatives:

• Co-rotational formulation
• Geometrically exact formulation
• Large rotation vector formulation -...

Links:

[0] State of the Art of ANCF Elements Regarding Geometric Description, Interpolation Strategies, Definition of Elastic Forces, Validation and the Locking Phenomenon in Comparison with Proposed Beam Finite Elements

[1] Definition of the Slopes and the Finite Element Absolute Nodal Coordinate Formulation

[2] Three Dimensional AbsoluteNodal Coordinate Formulationfor Beam Elements: Theory

[3] A two-dimensional shear deformable ANCF consistent rotation-based formulation beam element

[4] A Higher-Order Variable Cross-Section Viscoelastic BeamElement Via ANCF for Kinematic and DynamicAnalyses of Two-Link Flexible Manipulators

[5] Review on the Absolute NodalCoordinate Formulation for Large Deformation Analysisof Multibody Systems

[6] An Internal Damping Model for the Absolute Nodal Coordinate Formulation

[7] Computer Implementation of the Absolute Nodal CoordinateFormulation for Flexible Multibody Dynamics

[9] Efficient Evaluation of the Elastic Forces and the Jacobianin the Absolute Nodal Coordinate Formulation

[10] Computational Continuum Mechanics (Book)

[11] A Higher-Order Variable Cross-Section Viscoelastic Beam Element Via ANCF for Kinematic and Dynamic Analyses of Two-Link Flexible Manipulators

[12] Efficient Evaluation of the Elastic Forces and the Jacobianin the Absolute Nodal Coordinate Formulation

[13] On the Co-rotational Beam Element Formulation in Large Deformation Analysis (good general overview)

[14] A TWO-DIMENSIONAL SHEAR DEFORMABLE BEAM FOR LARGEROTATION AND DEFORMATION PROBLEMS

[14] An Accurate Singularity-FreeFormulation of a Three-Dimensional CurvedEuler–Bernoulli Beam forFlexible Multibody DynamicAnalysis

[15] Development of simple models for the elastic forces in the absolute nodal co-ordinate formulation

Open source implementations:

• HOTINT
• Project Chrono

[stfnp]

With the same logic, the string elements could be replaced by higher-order elements that have some flexural motion (as opposed to the straight bar elements currently used). This would make contact handling harder, because node-to-line contact is no longer good enough, but could be worth it. Either look into it as part of this issue or create a new one once this is closed.