Several Boundaries Algorithm Research And Software Design Based On Three-dimensional Discrete Element Method

In the field of modern engineering, always using finite element method to solve complex problems of engineering mechanics (FEA,Finite Element Analysis). Using this method, the solving domain will be seen as composing of many coadjacent subdomain that called finite element, assume a suitable approximate solution for each unit, and then general solution of the field that meet the conditions is obtained, thus the problem is solved. Not only because of the finite element has character of high precision for calculation, but also to adapt to a variety of complex engineering problems, it has become an effective means of engineering analysis. However, in the field of industrial and agricultural production, there is a large number of granular materials, the movement ruler of which is not only like the solids, but also like liquid with fluidity, Using of finite element methods can not solve the problem. Similar phenomenon also involves many aspects, for example, the cultivation of food crops, harvesting, drying, transportation, processing and packaging. There are many areas of industrial production too, such as pharmaceuticals, metallurgy, cement, etc, these fields exist a large number of granular materials.In seventies of the 20th century, Cundall put forward Discrete Element Method(DEM) which applies to the rock mechanics, the basic idea originates from earlier molecular dynamics, It was originally used for analysis of slope movement with cracked rock. Discrete Element Method takes granular materials as a collection of limited basic discrete components, for the particle system, a single particle is a unit, the act of granular groups is described in accordance with the force of inter-cell interaction and Newton's Laws of MotionIn order to apply Discrete Element Method to practice, after several years of efforts by all members of the team, in the aspects of theoretical research for calculation and application on Discrete Element Method, collating experimental data of simulation, we accumulated rich experience, especially in the aspect of calculation and simulation software design based on Discrete Element Method, we made great progress. The software has been achieved the function that extraction three-dimensional discrete element boundary on front-end through the graphical database is integrated. Thereby, a software system which can integrate mechanical components design and mechanical components performance analysis is built. The system carry out dynamic simulation for the work process of mechanical components through the CAD model of mechanical components, From the analysis of its work, improve the deign of mechanical components. The mechanical components design technology and design methods which are already existed can not achieve it.This article is based on that the experience in the designing simulation software with DEM and results of research on theory of calculate, algorithm, application of DEM was summarized sufficiently, takes Three-dimensional Discrete Element Method (TDEM) simulation software developed by team as studying object, has main objective of enriching the type of boundary for simulation and increasing the function of the boundary, focus on studying and realizing modeling complex boundary as well as enhancing existing boundaries based on TDEM, improves further three-dimensional simulation software developed by the team.When modeling boundary in the method based on graphic element, some of practical mechanical components may be similar to the ellipsoid, some of which may be similar spiral. These models can not be combined by simple graphic element, they can be accurately expressed by spiral or ellipsoid only. Thereby, in this article, elliptical boundary and spiral boundary are modeled. Taking the coordinate transformation method, establish local coordinate for two kinds of boundary model, simplify mathematical equations of two kinds of boundary model, and establish the relationship between local coordinate of two kinds of boundary and global coordinate, realize modeling of two kinds of boundary in any space. At the same time, I analyze deeply the collision process that spherical particle contacts with the surface of two kinds of boundary, select the appropriate method, solve the nonlinear equation of spherical particle in contact with two kinds of boundary, such as solution 6-th degree equation in one variable when making contact detection between spherical particle and elliptical boundary, differential equation when making contact detection between spherical particle and spiral boundary etc, so I obtain geometric quantity when spherical particle contacts with elliptical boundary and spiral boundary finally.Upon completion of building physical model, at the same time, this article studies the OpenGL interface and graphics. Based on the method drawing ellipsoid put forward by our team, through rigorous mathematical derivation, identify the steps must be followed and parameters for every step that elliptical boundary moves to any position in space through translation and rotation, draw the precise elliptical boundary in arbitrary position finally. This article also uses general OpenGL graphics of curve, with the method of connecting points and lines, draw a spiral model, to make simulation tests of collision between spherical particles and complex boundary possible.The team has successfully achieved the virtual boundary of disc and virtual boundary of cylinder, and the experiments verify that they are necessary and have many functions.However, the theory and algorithm of virtual boundary of polygon and polyhedron has not studied by the team yet, virtual boundary of polygon and virtual boundary of polyhedron apply in many types of mechanical components. In order to increase the function of the existing boundary, this article puts forward and builds virtual boundaries of polygon and polyhedron, which can be attached to plane and three-dimensional boundary. Also, this article designs the algorithm of contact judgment between spherical particles and two types of virtual boundary, and improves algorithm, such as improving general solution method for the intersection point of two straight lines, to reduce the volume of code and improve the efficiency of code. To make movement of virtual boundaries and boundaries synchronized, this article designs update algorithm of coordinate parameter for virtual boundary when it moves, makes translation, rotation as well as complex movement of every point on virtual polygon and virtual polyhedron synchronized.On the basis of above work, using of VC ++ 6.0 development tool, in accordance with the modular design concept, the above-mentioned functions and algorithms was realized. Then using software that has been finished, I simulate the process that spherical particles contact with four kinds of boundary, and therefore validates the correctness and efficiency of the method established in this article with instances.This article has much positive sense to the perfection of the software, enriching the function of software, making the software adaptable and the establishment of general digital design methods of the relative mechanical parts.