基于逼近阶跃函数和拉格朗日插值的改进DDA方法

发布时间：2019-06-12 13:17

【摘要】：针对非连续变形分析中开合迭代难以收敛的难题,基于块体接触约束状态和块体位移之间的关系,提出了基于逼近阶跃函数和拉格朗日插值的改进DDA方法。采用双曲正切函数来逼近阶跃函数,利用阶跃函数将块体接触约束状态用块体位移来表达,以此来替代开合迭代,避免了开合迭代难以收敛的难题。利用拉格朗日插值原理,推导得到只含有块体位移为未知量的块体系统势能函数,并利用变尺度法来求解总体势能函数的极值以得到块体位移。分别结合滑块模型和地下洞室模型,分析了改进DDA方法的计算精度和计算速度,验证了文中提出的改进DDA方法的正确性和稳定性。研究表明:基于逼近阶跃函数和拉格朗日插值的改进DDA方法具有较高的精度,且相比较传统DDA方法而言,具有更为稳定的和更为强健的计算收敛性。因此,基于逼近阶跃函数和拉格朗日插值的改进DDA方法是一种稳定有效的数值计算方法,为解决非连续变形中开合迭代难以收敛的问题提供了新思路。
[Abstract]:In order to solve the problem that it is difficult to converge in open and close iterations in discrete deformation analysis, an improved DDA method based on approximate step function and Lagrangian interpolation is proposed based on the relationship between block contact constraint state and block displacement. The hyperbolic tangent function is used to approximate the step function, and the block contact constraint state is expressed by the block displacement by using the step function to replace the open and close iteration, which avoids the problem that the open and close iteration is difficult to converge. Based on the Lagrangian interpolation principle, the potential energy function of the block system with only block displacement as unknown is derived, and the variable scale method is used to solve the extreme value of the total potential energy function to obtain the block displacement. Combined with slider model and underground caverns model, the calculation accuracy and speed of the improved DDA method are analyzed, and the correctness and stability of the improved DDA method proposed in this paper are verified. The results show that the improved DDA method based on approximate step function and Lagrangian interpolation has higher accuracy, and has more stable and stronger convergence than the traditional DDA method. Therefore, the improved DDA method based on approximate step function and Lagrangian interpolation is a stable and effective numerical method, which provides a new idea for solving the problem that it is difficult to converge in open and close iterations in discrete deformation.
【作者单位】：武汉大学水资源与水电工程科学国家重点实验室;长江勘测规划设计研究有限责任公司;
【基金】：国家重点基础研究计划(973)项目(No.2015CB057904) 国家自然科学基金(No.51579191)~~
【分类号】：TU45

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