非连续变形分析中块体大转动问题研究

原有非连续变形分析（DDA）采用一阶近似后的位移增量表达式更新块体构形，推导相关子矩阵，且对不同时步计算出的应变增量直接叠加，当模拟的块体发生大转动时往往会产生较大误差。为考虑块体转动与变形的耦合作用，引入先变形、后转动的块体位移增量表达式。重新推导了惯性力子矩阵，将块体转动时的离心力与科氏力加到荷载矩阵中。计算时对应变分量及其相关变量进行坐标变换与修正，并采用新引入的位移增量表达式计算块体顶点位移，进行后接触修正与更新块体构形。数值算例表明，改进后的程序能够消除转动带来的误差，自动考虑了块体转动时离心力和科氏力引起的变形，应变计算精度更高。改进方法克服了块体体积自由膨胀、应变场畸变等问题，给出了合理的块体应变。

Study on large rotation problem of a block in discontinuous deformation analysis

The original discontinuous deformation analysis (DDA) takes the first-order approximation of the incremental displacement to update block configuration, deduces related sub-matrices, and directly superimposes the incremental strains calculated at different time steps, which generates significant errors when simulating large rotation of a block. In order to consider the coupling effect of block rotation and deformation, a modified incremental displacement formulation is introduced, which calculates the displacements caused by the strains before the rigid-body rotation term. The sub-matrix of the inertial force is then modified, and the centrifugal and Coriolis forces are added to the load matrix. In the calculation, the coordinate transformation is carried out for the strain components and its related variables, and the newly introduced displacement formulation is used to calculate the displacements of block vertices. After that, the post-adjustment and post-contact adjustment are used to update the block configuration. The numerical examples indicate that the modified DDA can eliminate the errors caused by large rotation, automatically consider the deformation caused by centrifugal and Coriolis forces of the rotating block, and the precision of strain calculation is higher than that of original DDA. The modified codes overcome the free volume expansion and strain distortion problems, and give a reasonable block strain.