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Dual form of discontinuous deformation analysis

机译：不连续变形分析的双重形式

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Discontinuous deformation analysis (DDA) is a numerical method for analyzing dynamic behaviors of an assemblage of distinct blocks, with the block displacements as the basic variables. The contact conditions are approximately satisfied by the open-close iteration, which needs to fix or remove repeatedly the virtual springs between blocks in contact. The results from DDA are strongly dependent upon stiffness of these virtual springs. Excessively hard or soft springs all incur numerical problems. This is believed to be the biggest obstacle to more extensive application of DDA. To avoid the introduction of virtual springs, huge efforts have been made with little progress related to low efficiency in solution. In this study, the contact forces, instead of the block displacements, are taken as the basic variables. Stemming from the equations of momentum conservation of each block, the block displacements can be expressed in terms of the contact forces acting on the block. From the contact conditions a finite-dimensional quasi-variational inequality is derived with the contact forces as the independent variables. On the basis of the projection-contraction algorithm for the standard finite-dimensional variational inequalities, an iteration algorithm, called the compatibility iteration, is designed for the quasi-variational inequality. The main processes can be highly parallelized with no need to assemble the global stiffness matrix. A number of numerical tests, including those very challenging, suggest that the proposed procedure has reached practical level in accuracy, robustness and efficiency, and the goal to abandon completely virtual springs has been reached. (C) 2016 Elsevier B.V. All rights reserved.
机译：不连续变形分析（DDA）是一种数值方法，用于分析以块位移为基本变量的不同块体组合的动态行为。接触条件可以通过开闭迭代大致满足，该迭代需要反复固定或移除接触块之间的虚拟弹簧。 DDA的结果在很大程度上取决于这些虚拟弹簧的刚度。过多的硬弹簧或软弹簧都会引起数值问题。相信这是DDA广泛应用的最大障碍。为了避免引入虚拟弹簧，已经做出了巨大的努力，而解决方案效率低下的进展却很少。在这项研究中，将接触力而不是滑块位移作为基本变量。从每个块的动量守恒方程式得出，块位移可以用作用在块上的接触力表示。根据接触条件，以接触力为自变量，推导了有限维的拟变分不等式。在标准有限维变分不等式的投影-收缩算法的基础上，设计了一种用于拟变分不等式的迭代算法，称为兼容性迭代。主要过程可以高度并行化，而无需组装整体刚度矩阵。大量的数值测试，包括那些非常具有挑战性的数值，表明所提出的程序在准确性，鲁棒性和效率上已达到实用水平，并且已经达到了完全放弃虚拟弹簧的目标。 （C）2016 Elsevier B.V.保留所有权利。

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