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

I M Khan1, W Ahn, K S Anderson

  • 1Department of Mechanical Aerospace and Nuclear Engineering, Rensselaer Polytechnic Institute, 110 8th Street, Troy, NY 12180 USA.

International Journal of Non-Linear Mechanics
|October 15, 2013
PubMed
Summary
This summary is machine-generated.

A new interpolating spline method models multi-flexible-body systems efficiently. This approach surpasses the flexible divide-and-conquer (FDCA) method in speed while maintaining accuracy for complex systems.

Keywords:
Divide-and-Conquer AlgorithmInterpolating SplinesLogarithmic ComplexityMulti-Flexible-Body Systems

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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.