三维连续与非连续变形分析

THREE DIMENSIONAL CONTINUOUS AND DISCONTINUOUS DEFORMATION ANALYSIS

将石根华博士所提出的二维非连续变形分析——Discontinuous Deformation Analysis（DDA）方法扩展到三维情况,并对三维不连续块体进行有限元网格剖分,即块体之间的接触采用DDA描述,块体内部的位移场和应力场则采用有限单元法描述,从而将三维DDA与有限元方法结合起来,增强了DDA方法与有限元方法解决实际工程问题的能力,实现了三维连续与非连续变形分析.给出了基本公式的推导过程和各子矩阵的形式.典型接触、碰撞算例证明了所提出方法的有效性和正确性.

The Finite Element Method (FEM) is a very important numerical analysis method and widely used in modeling continuous body. But conventional FEM cannot satisfactorily solve or fit some requirements of the reality, such as the discontinuity.The Discontinuous Deformation Analysis (DDA) method developed by Dr. Shi in 1992 can be used for large displacement and deformation modeling such as simulation of rigid body movements like Distinct Element Method (DEM) as well as for stress-strain analysis like FEM.Three-dimensional DDA also choose the complete first order polynomial as displacement func-tion for a block as like two-dimensional DDA, no matter how irregular the shape of the block is. As a result, the stress field and the deformation ability of the DDA block are restricted.In order to refine stress field and to enhance deformation ability of DDA blocks, the eight-node brick element mesh is incorporated into three-dimensional DDA blocks in this paper. The contacts between blocks are described by DDA while the stress field and displacement field inside blocks are described by FEM. So that the ability of modeling block's deformation and stress filed distribution are enhanced and this numerical model combines both three-dimensional continuous and discontinuous computations for large displacement and deformation solutions. The system variables have become nodal displacements from center of gravity of DDA block. However the equilibrium equations are still derived by minimizing total potential energy of the system. This method is also adopts step-by-step time marching for both static and dynamic calculations. At the end of each time step, the equilibrium condition, the no-tension, no-penetration constraint conditions, and the Coulomb's friction law are satisfied at all contacts. The formulations of imple-menting finite element mesh into three-dimensional DDA blocks are presented and several classic contact-impact examples prove the validity of the method proposed by this paper.