Study Of Representation And Contact Detection For Particles And Structural Boundaries In DEM Simulation

Discrete Element Method (DEM) is an effective numerical analysis method for dealing with the dynamic problems of granular system, which is widely applied in various industrial fields involving in granular media, including mechanical engineering, mining engineering, chemical engineering, construction industry and so on, and has achieved a great number of useful research results. With the development of application field of DEM simulations, the non-spherical particles and the complicated structural boundaries are beginning to be involved in DEM simulations. For fulfilling the technical requirements of the non-spherical particles and the complicated structural boundaries in industrial applications of DEM simulations, representation and contact detection for both objects have been studied in this paper, and the following three main problems have been addressed:the problem for the computational efficiency of contact detection among the non-spherical particles; the technical problem for representing the complicated structural boundaries with regular shapes and irregular shapes; and the problem for the computational efficiency of contact detection between the non-spherical particles and the complicated structural boundaries. For the problems as above stated, the following four aspects of research work have been done in this paper.(1) An algorithm for contact detection among the non-spherical particles by means of two-level-grid-searching has been proposed in this paper, where the non-spherical particles are represented by multi-sphere particles. In this algorithm, the bounding spheres are used for multi-sphere particles, and two-level-grid-searching is used in contact detection. In the first-level-grid-searching, global space is partitioned into identical square or cubic cells of size Db, the diameter of the greatest bounding sphere. The bounding spheres of multi-sphere particles are the searching objects in the first-level-grid-searching. In the second-level-grid-searching, if two bounding spheres of two multi-sphere particles are overlapped, two local spaces of these multi-sphere particles are partitioned into identical square (2-dimension) or cubic (3-dimension) cells of size d, the diameter of the greatest element sphere. The element spheres in the overlap region of these two local spaces are the searching objects in the second-level-grid-searching. Compared with Abbaspour-Fard's approach, this algorithm largely improves the memory efficiency of contact detection, while basically maintains the time efficiency of contact detection. Therefore, this algorithm is an effective solution to deal with the contact problem for the non-spherical particles.(2) A method for representing the complicated structural boundaries by combining mathematical equations and triangle meshes has been developed in this paper. In this method, regular shapes are described by mathematical equations, while irregular shapes are modeled by triangle meshes. Two connection types between regular shape and irregular shape have been dealt with by this method, the first type is the connection on the end plane of regular shape with irregular shape; the second type is the connection on the surface of revolution of regular shape with irregular shape. When structural boundaries are represented by mathematical equations and triangle meshes, gaps or protuberances can exist at the connection boundaries between regular shapes and irregular shapes. Through the identifications, expressions and treatments for gaps or protuberances, the original structural shapes can be replaced by the geometrical shapes composed by regular shapes described with mathematical equations and irregular shapes described with triangle meshes, so the complicated structural boundaries can be effectively represented by this method. Compared with means of triangulation for total structure, this method is more time efficient in the contact detection between particles and structural boundaries, and uses much less triangle meshes in representation of the complicated structural boundaries.(3) An algorithm for contact detection between the non-spherical particles and the complicated structural boundaries by means of two-level-grid-searching has been presented in this paper. In this algorithm, the non-spherical particles are represented by multi-sphere particles, and the complicated structural boundaries are represented by combining mathematical equations and triangle meshes. Through two-level-grid-searching, the contact detection between the non-spherical particles and the complicated structural boundaries can be converted to the contact detection of multi-sphere particles with regular shapes and the contact detection of multi-sphere particles with irregular shapes. Compared with the approach that the structure is totally represented by triangle meshes, and grid-searching is directly implemented for each element sphere of multi-sphere particles and for each triangle mesh of the complicated structural boundaries in global space, this algorithm consumes much less memory and time in contact detection between the non-spherical particles and the complicated structural boundaries. So, this algorithm provides an effective technical means for the development of application field of DEM simulations.(4) The applications of DEM simulations in the analysis of working process and the optimal design for structures of the excavator bucket are detailedly explained in this paper. Through DEM simulations, the velocity distributions of particles, payload of bucket, energy consumptions and the maximum contact forces on bucket are analyzed under the different operating parameters for bucket, particle shapes, and structures parameters of bucket respectively. The numerical results showed that DEM simulations can provide some useful references for the reasonable selections of operating parameters for bucket, can bring the benefits to the understanding and predictions of the working performances of bucket under different particle shapes, and can provide the numerical basis for the reasonable design of bucket structures. Ultimately, the optimization of bucket structures can be achieved through DEM simulations.