B211 CAによる堆積粒子の掘削シミュレーション(粒状体関連)

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The granular media with cohesive and heterogeneous characteristics such as soil and sand grains is deformed plastically, which issues very difficult problem on the analytical investigation. Particularly, it is a strong demand for qualitative understanding of the dynamic behavior of soils by the actions of cutting blade in the field of construction machinery, such as dozers typically. Conventional soil mechanics theory seems less applicable for such large deformation problem, while the experimental estimation would be a rather reliable way to understand their nature. Moreover, the shape of the cutting blade affects much on the soil excavation, however, for the most part it is designed in a empirical sense. In the present study, we simulated two dimensionally the dynamic behavior of granular media which is piled in layers by a cutting blade using Cellular Automata (CA). CA are the discrete system which consists of finite state variables arranged on uniform spatial grids (cells). State variable varies within a finite set of values in order to express the physical state of components of the system to be analyzed. Moreover, the states of each cell are updated synchronously according to the local interaction rules at every discrete time step. That is, the state of a cell at a given time step only depends on the previous state of itself and also that of nearby neighbor cells. Compared with the conventional method such as DEM, it is addressed that the modeling techniques with CA provide advantages on the point of computation efficiency and numerical stability due to the discrete treatment of time and space. It is also attractive for its simple strategy, however, rules must be defined along with physical consideration as carefully as we derive differential equations in the ordinary analysis. Likewise the state variables can be given certain physical quantities, on the other hand, regularly divided space into rectangle or triangle grids requires spatial averaging process. In the present CA model, the two dimensional space is divided into triangular grids, where particles are distributed two dimensionally on cellular space. Two state variables are defined for the model ; The first one represents cell condition which distinguishes four kinds of physical state such as wall, blade, particle and vacant space represented as integers 0, 1, 2, 3, respectively. The second variable applies additionally to the particle and blade state cells, which represents moving direction vector of particles and blade. The triangular arrangement of cell grids allows six neighbors present around each cell. Therefore, the particles are movable into six directions, hence the identical variation of vector states exist. The traveling speed of particles is given definitely to move on single cell distance per calculation step according to the vector state if movable . On the other hand, the blade state cells is designed so that the traveling speed can be changed, however, the speed cannot exceed 1 cell per calculation step. Hence the blade speed always become at most equal, or below particle movement. The local interaction rules are defined based on the two assumptions, which are related to the determination of moving vector of particle cells due to the force action of blade, and also the free drop direction of particles. The simulations are performed for the two cases. The first one investigates the effect of blade angle, which compares three of 30, 60 and 90 (vertical) attitudes. Also, the second simulation demonstrates the traveling speed effect of blade, where the angle is fixed to 60 deg. The calculation is performed for the three 1cell/1 step, 1cell/5step, and also 1cell/10step cases respectively. The simulation results showed acceptable patterns in qualitative sense, that the particles swell up and crumble down the surface. It is said that the present CA model provides the basic idea for understanding dynamic behavior of granular media, and also the model can easily be extended to more practical scenario.
一般社団法人日本機械学会の論文
2001-11-14

B211 CAによる堆積粒子の掘削シミュレーション(粒状体関連)

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