The elastic distortion problem with large rotation in discontinuous deformation analysis
The elastic distortion problem with large rotation in discontinuous deformation analysis
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DOI：
10.1016/j.compgeo.2015.06.001
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发表时间：
2015-09
影响因子：
5.3
通讯作者：
Jian Hong Wu
中科院分区：
文献类型：
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作者：
Jian Hong Wu
传统的非连续变形分析（DDA）由于采用线性位移函数来模拟具有刚体和弹性行为的块体的行为，在旋转计算过程中会导致块体体积的变化，即所谓的自由膨胀。研究表明，线性位移函数也会产生未解的弹性变形，特别是当块体在每个计算步骤中经历大的旋转时。该变形干扰了开闭迭代中的接触判断以及每个计算步骤结束时的顶点坐标、应力、速度等的更新计算。一个新的程序遵循原始DDA的流程图，但它采用了额外的代码来进行顶点坐标、应力和速度更新中的坐标变换计算。当顶点坐标被更新时，在位移函数中涉及块旋转项之前计算由应变引起的顶点位移，以减轻弹性变形。此外，新的代码编译公式转换应力和速度与块旋转。新的DDA确保了旋转弹性计算的正确性，以解决实际的落石问题，在每个计算步骤中的大旋转角。
Conventional discontinuous deformation analysis (DDA) results in a change of block volume, which is known as free expansion, during rotation calculations because of the use of a linear displacement function to simulate the behavior of a block with a rigid body and elastic behaviors. This study demonstrates that the linear displacement function also generates unsolved elastic distortion, especially when the block undergoes large rotation in each calculation step. The distortion disturbs the contact judgment in the open–close iteration and update calculations of vertex coordinates, stresses, velocities, etc. at the end of each calculation step. A new procedure follows the flow chart of the original DDA, but it adopts additional codes for the coordinate-transformation calculations in vertex coordinate, stress, and velocity updates. When the vertex coordinates are updated, vertex displacements caused by strains are calculated before involving the block-rotation term in the displacement function to mitigate the elastic distortion. In addition, new codes compile formulas to transform stresses and velocities with block rotation. The new DDA ensures the correctness of rotating elastic calculations to solve practical falling rock problems with a large rotational angle in each calculation step.