Application of Meshless Local Petrov-Galerkin (MLPG) Method in Cloth Simulation
Weiran Yuan; Yujun Chen; Andr ' e Gagalowicz; and Kaixin Liu

Source CMES: Computer Modeling in Engineering & Sciences, Vol. 35, No. 2, pp. 133-156, 2008
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Keywords Cloth Simulation, MLPG, Large Deformation, Thin Shells.
Abstract In this paper we present an approach to cloth simulation which models the deformation based on continuum mechanics and discretized with Meshless Local Petrov-Galerkin (MLPG) Method. MLPG method, which involves not only a meshless interpolation for trial functions, but also a meshless integration of the local weak form, has been considered as a general basis for the other meshless methods. By this way, the mechanical behavior of cloth is consistent and united, which is independent of the resolutions. At the same time, point sampled models, which neither have to store nor to maintain globally consistent topological information, are available for MLPG method. We use Kirchhoff-Love (KL) thin shell theory as the basis of the cloth model. Compared to finite element methods, MLPG method provides higher continuity in the displacement field which meets the requirement of the KL model. When large deformation is involved, the nonlinear equations make the simulations become costly. We use corotational formulation to attach the parameterized local coordinate system of nodes. In addition, the rotation fields are computed by an efficient iteration scheme. This allows us to use stable corotated linear strains. As for the collision solution, since the conventional mesh-based collision detection methods fail to work in meshless methods. We developed a novel shape function based collision detection method for the meshless parametric surface. The experimental results show that our cloth simulator based on MLPG method can produce vivid results and can be applied especially in the computer cloth animation.
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