关键词: 开合迭代, 接触约束, 块体位移, 势能函数, 变尺度法

Abstract: To resolve problem of poor convergence in open-close iteration of discontinuous deformation analysis, an improved DDA method based on approximated step function and Lagrange interpolation is developed based on the relationship between the state of contact constraints within blocks and the block displacement. Hyperbolic tangent function is used to approximate the step function. The state of contact constraints within blocks is represented by block displacement using step function, which replaces the function of open-close iteration and avoids the problem of poor convergence in open-close iteration. The potential energy function of block system only containing the block displacement as unknown variable is derived with the principle of Lagrange interpolation. The extremum of general potential energy function is analyzed to obtain the block displacement. With the model of sliding block and underground chamber respectively, computational accuracy and computational speed of the improved DDA method are analyzed, and the correctness and the iterative stability of the improved DDA method is verified. Research shows that the improved DDA method based on approximated step function and Lagrange interpolation produces high precision, and it has a more stable and more robust computing convergence compared with the traditional DDA. Therefore, the improved DDA method based on approximated step function and Lagrange interpolation is a stable and effective numerical method and it provides a new approach for solving the problem of poor convergence in open-close iteration of discontinuous deformation.

Key words: open-close iteration, contact constraint, block displacement, potential energy function, variable metric method