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Contact Modeling Algorithms for Fiber Dynamics Simulations
123 Seiten, Dissertation Technische Universität Kaiserslautern (2016), Softcover, A5
In the production of technical textiles, nonwovens are produced by overlaying thousands of fibers, which are subjected to a turbulent airflow. During this process, fibers can collide with surrounding machine parts.
Simulations of the production process need to handle contact forces arising from these collisions. In this thesis, I address the problem of including contacts between fibers and machine geometry into the simulation. State of the art methods based on penalty forces or explicitly computed collision response impulses are fast to compute, but fail to always satisfy the non-penetration constraint. I provide an efficient contact detection, together with a robust and accurate method for contact handling, using an implicitly formulated non-penetration constraint in the fiber dynamics. The surface of the machine geometry is smoothed to provide C^1 continuous normals, ensuring locally quadratic convergence of the underlying Newton solver for fiber dynamics. Fiber dynamics are thus faster to compute than using non-smooth implicit constraints. The contact simulation is implemented in a software tool and has been applied to simulate artificial test cases as well as industrial production processes.
I present a novel method to smooth a solid given as a polyhedral mesh. The surface is represented implicitly as the zero level-set of a signed distance field, and a convolution-based smoothing is applied. A feature size parameter controls the strength of the smoothing effect. The resulting distance field is globally C^2 continuous. In contrast, using standard surface smoothing methods and applying an implicitization yields a distance field which is only locally smooth in the neighborhood of the surface. The method works for meshes of arbitrary topology, preserves local shape features such as convexity, and the result is independent of the mesh's tesselation. I employ linearizations to the convolution kernel, as well as the implicit function representing the solid. The latter is linearized using the straight skeleton. The resulting function and its derivatives can be analytically evaluated in closed form. I give a qualitative and quantitative analysis of the approximation quality of this method with respect to the feature size parameter. For contact detection, only the sign of the distance function needs to be evaluated. Based on a tight bound of the approximation quality, I present a fast algorithm to compute this sign.