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Numerical Method of Fabric Dynamics Using Front Tracking and Spring Model

Published online by Cambridge University Press:  03 June 2015

Yan Li ,
I-Liang Chern ,
Joung-Dong Kim  and
Xiaolin Li
Yan Li*
Affiliation:
Department of Applied Mathematics and Statistics, Stony Brook University, Stony Brook, NY 11794-3600, USA
I-Liang Chern*
Affiliation:
Department of Applied Mathematics, Center of Mathematical Modeling and Scientific Computing, National Chiao Tung University, Hsin Chu, 300, Taiwan Department of Mathematics, National Taiwan University, Taipei, 106, Taiwan National Center for Theoretical Sciences, Taipei Office, Taipei, 106, Taiwan
Joung-Dong Kim*
Affiliation:
Department of Applied Mathematics and Statistics, Stony Brook University, Stony Brook, NY 11794-3600, USA
Xiaolin Li*
Affiliation:
Department of Applied Mathematics and Statistics, Stony Brook University, Stony Brook, NY 11794-3600, USA
*
Corresponding author.Email:yli@ams.sunysb.edu
Email:chern@math.ntu.edu.tw
Email:selom114@ams.sunysb.edu
Email:linli@ams.sunysb.edu
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Abstract

We use front tracking data structures and functions to model the dynamic evolution of fabric surface. We represent the fabric surface by a triangulated mesh with preset equilibrium side length. The stretching and wrinkling of the surface are modeled by the mass-spring system. The external driving force is added to the fabric motion through the “Impulse method” which computes the velocity of the point mass by superposition of momentum. The mass-spring system is a nonlinear ODE system. Added by the numerical and computational analysis, we show that the spring system has an upper bound of the eigen frequency. We analyzed the system by considering two spring models and we proved in one case that all eigenvalues are imaginary and there exists an upper bound for the eigen-frequency This upper bound plays an important role in determining the numerical stability and accuracy of the ODE system. Based on this analysis, we analyzed the numerical accuracy and stability of the nonlinear spring mass system for fabric surface and its tangential and normal motion. We used the fourth order Runge-Kutta method to solve the ODE system and showed that the time step is linearly dependent on the mesh size for the system.

Keywords

74B2065D1765Z05Front trackingspring modeleigen frequency
Type
Research Article
Information
Communications in Computational Physics , Volume 14 , Issue 5 , November 2013 , pp. 1228 - 1251
Copyright
Copyright © Global Science Press Limited 2013

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