Packing Random Particles to Use Them as Initial Input of Numerical Analysis of discontinuous Materials

Summary
In this paper, a new algorithm was offered for collision detection and packing random volumes. Among the features of this algorithm is its packing feature which is capable of packing particles with any shape. Then, using PSO algorithm, the optimal state of this packing algorithm was obtained. Finally, in order to validate the optimized algorithm, the results were compared with the results of digital packing algorithm. This comparison showed that the new packing method proposed in this paper (the optimized packing method of using control points) provides good results compared with digital packing method.
 
Introduction
Unlike dynamic packing methods, geometric packing methods allow the rapid packing of a large number of particles; these packing structures can be used as the initial state (initial input) in numerical analysis of discontinuous materials. Geometric packing methods, in fact, improve the efficiency of the particles preparation phase for numerical analysis and dynamic simulation. For example, sorting and preparation of hundreds of particles through using dynamic methods may take several hours, while using geometric methods, it may take less than few minutes. The disadvantage of geometric methods is that as the particles do not reach dynamic balance in these methods, no information is obtained about the contact forces. However, geometric methods is close enough to the particles mechanical balance. As a result, the packing structure obtained by these methods can be used as a good starting point for dynamic simulations.
 
Methodology and Approaches
The new packing algorithm offered in this paper is based on control and placement of each shape by using boundary points (the outer surface points of the shape) or all points of the shape. Hence, this algorithm is capable of packing the particles with any shape. This new algorithm was originally designed for collision detection and packing of two random shapes and, then, was generalized to N particles. Finally, using Particle Swarm Optimization (PSO), it was optimized.
 
Results and Conclusions
The new packing algorithm was generalized to N particles and, using the algorithm of PSO, it was optimized. After the optimization of this packing algorithm, it was validated through comparing its results with the results of digital packing method; and it was observed that, in comparison with the digital packing method, the new packing method proposed in this paper (the optimized packing method of using control points) can offer good results. In the optimized packing method of using control points, the following factors have a significant impact on the packing quality and density of particles:

The order of adding particles into the container.
The number of the times the answers are repeated (M), the increase of which leads to the higher density and quality of packing.
Prioritizations of the criteria for the calculation of fitness function (through determining the values of K1 and K2 coefficients).