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Subdivision method for rational ANCF circular elements.

Manyu Shi1, Manlan Liu1,2, Yaxiong Liu1

  • 1School of Mechanical and Electrical Engineering, Xi'an University of Architecture and Technology, Xi'an, 710055, China.

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|July 2, 2025
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Summary
This summary is machine-generated.

This study introduces a novel method for subdividing Rational NURBS (Non-Uniform Rational B-Spline) curves, ensuring geometric accuracy. The approach refines elements in dense parameter regions for improved computational efficiency and accuracy.

Keywords:
Element subdivisionMapping relationshipParameterizationRational absolute nodal coordinate formulation (RANCF)Subdivision elements definition

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Area of Science:

  • Computational geometry
  • Computer-aided design
  • Numerical analysis

Background:

  • Non-Uniform Rational B-Spline (NURBS) curves are fundamental in geometric modeling.
  • Existing node insertion algorithms may face challenges with diverse element definitions and parameter distributions.
  • Distortion in the subdivision of non-uniformly parameterized elements necessitates improved methods.

Purpose of the Study:

  • To develop a precise method for calculating node coordinates and weights in subdivided elements without altering geometric properties.
  • To address and control distortions during the subdivision of non-uniformly parameterized elements.
  • To establish criteria for subdividing Rational NURBS (RANCF) elements based on physical space arc length.

Main Methods:

  • Utilizing a node insertion algorithm for NURBS curves.
  • Introducing a distribution density function for element parameter points.
  • Establishing a calculation method for parameter space subdivision nodes corresponding to physical space arc length.

Main Results:

  • The proposed method enables precise subdivision of differently parameterized arc elements in physical space.
  • Numerical computation results guided the determination of subdivision criteria for RANCF elements.
  • Local refinement in regions with denser parameter point distribution was found to be effective.

Conclusions:

  • The developed method ensures the geometric properties and parameter distribution of RANCF elements are maintained during subdivision.
  • The approach effectively controls distortions in the subdivision process for non-uniformly parameterized elements.
  • Local refinement based on parameter point density enhances both computational accuracy and efficiency.