An Advancing Front Packing of Polygons, Ellipses and Spheres
Y.T. Feng, Kue Jin Han, David R. Owen · 2002
The discrete element method has emerged as a powerful numerical simulation tool for a wide variety of industrial problems characterised by discrete/discontinuous features, in which different shaped objects with different sizes have to be considered. The pre-step in the discrete element simulation of practical problems often requires the generation of discrete objects packed in a form that can represent various realistic situations, an issue which appears not well addressed elsewhere. In many practical situations, disks/spheres may be sufficient to represent actual situations but often different size disks/spheres have to be used in the simulation. In other situations, more diverse shaped objects such as ellipses and polygons are necessary. The random packing of disks/spheres is an issue that has attracted a reasonable amount of attention over the last few decades, but nevertheless, preparation of an initial distribution of a large number of such discrete objects in a realistic (random) manner is not trivial. The existing packing algorithms are mainly of a non-constructive nature and therefore may involve substantial computer costs for large scale situations. Furthermore, very limited work has been reported with regard to the development of efficient packing algorithms for other shaped objects such as ellipses and convex polygons. In Feng et al., a novel numerical method is proposed to constructively generate a realistic random packing for different sizes of disks within a domain, motivated by the idea of the advancing front technique employed in mesh generation procedures. There are two different implementation versions of the algorithm, termed the closed form and open form. The closed form ignores the existence of the boundaries of the domain or container to be filled, while the open form takes the restriction of the boundaries into consideration when generating the disks. The algorithm has proved to be very effective, having a linear complexity and taking only several seconds to generate 1,000,000 disks with graded size distribution. The main purpose of the present paper is to extend the same methodology to other shaped discrete objects including elliptic particles and convex polygons, and as well to 3D spheres with different sizes. Computational issues unique to each special case are addressed briefly.