A Logarithmic Complexity Floating Frame of Reference Formulation with Interpolating Splines for Articulated...

Area of Science:

• Multibody dynamics
• Computational mechanics
• Applied mathematics

Background:

• Modeling multi-flexible-body systems with large rotations and translations is computationally challenging.
• Existing methods like the flexible divide-and-conquer (FDCA) may require sub-structuring for accuracy.
• Deformable systems with complex geometries require robust modeling techniques.

Purpose of the Study:

• To introduce an interpolating spline-based approach for modeling multi-flexible-body systems within the divide-and-conquer (DCA) framework.
• To enhance the capability of the DCA scheme for simulating deformable systems.
• To compare the efficiency and accuracy of the new spline-based method against the FDCA.

Main Methods:

• Utilizes the floating frame of reference formulation.
• Employs piecewise spline functions to construct and solve non-linear equations of motion.
• Applies the divide-and-conquer (DCA) scheme for parallel computation.

Main Results:

• The interpolating spline-based approach demonstrates comparable accuracy to the FDCA.
• The new method is significantly more efficient than the FDCA.
• The approach effectively models thin 1D flexible bodies with large motions and irregular shapes.

Conclusions:

• The interpolating spline-based DCA approach extends modeling capabilities for deformable multi-body systems.
• This method offers a more efficient alternative to FDCA for complex flexible mechanisms.
• The algorithm preserves the inherent logarithmic complexity of DCA for parallel implementation.