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。 Aiming at the difficult convergence problem of opening and closing iterations in discontinuous deformation analysis, an improved DDA method based on approximation step function and Lagrange interpolation is proposed based on the relationship between the contact constraint state and block displacement. The hyperbolic tangent function is used to approximate the step function, and the step function is used to express the contact state of the block with the displacement of the block, so as to replace the opening and closing iteration and avoid the difficult convergence problem of the opening and closing iteration. The Lagrange interpolation principle is used to deduce the potential energy function of the bulk system, which contains only the displacement of the block, and the extreme value of the global potential function is obtained by using the scaling method to get the displacement of the block. Combining the model of slider and the model of underground cavern respectively, the calculation accuracy and speed of the improved DDA method are analyzed, and the correctness and stability of the improved DDA method are verified. The results show that the improved DDA method based on approximation step function and Lagrange interpolation has higher precision and has more stable and more robust computational convergence than the traditional DDA method. Therefore, the improved DDA method based on approximation step function and Lagrange interpolation is a stable and effective numerical method, which provides a new idea for solving the problem of difficult convergence of opening and closing iterations in discontinuous deformation.