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 wrinkl...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.展开更多
基金the US Army Research Office under the ARO grant award W911NF0910306the Department of Mathematics,National Taiwan University and to acknowledge the generous support from National Science Council of The Republic of China,Grant NSC 101-2811-M-002-006 on his sabbatical visit during which this work is accomplished.
文摘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.
