The elastic distortion problem with large rotation in discontinuous deformation analysis |
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| Institution: | 1. Department of Maritime Civilizations, L. H. Charney School of Marine Sciences, University of Haifa, 31905 Haifa, Israel;2. The School of Ocean and Earth, University of Southampton, Southampton SO14 3ZH, UK;3. Dr. Moses Strauss Department of Marine Geosciences, L. H. Charney School of Marine Sciences, University of Haifa, 31905 Haifa, Israel;4. Israel Oceanographic and Limnological Research Institute, 31080 Haifa, Israel;5. The Recanati Institute for Maritime Studies (RIMS), University of Haifa, 31905 Haifa, Israel |
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| Abstract: | 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. |
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| Keywords: | DDA Stress Coordinate transformation Rotation Falling rock |
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