【作者】 王建全；

【导师】 林皋； 刘君；

【作者基本信息】 大连理工大学 ， 水工结构工程， 2006， 博士

【摘要】 非连续变形分析（DDA）方法是一种模拟分析非连续介质（如块体或散粒体系统）的有效的数值方法。为了模拟离散系统的力学行为，不仅需要根据材料的物理和几何特性来给出各个物体的图形，而且需要准确地模拟物体之间的相互作用。DDA目前已经广泛的用在二维工程问题的非连续变形分析中，但对于三维问题，由于缺少一种可靠的三维块体间接触判断的方法而导致DDA方法迟迟不能用于三维工程问题的分析中。由三维不规则多面体组成的块体系统的接触检索目前不仅制约着3D-DDA方法的发展，同时也是所有分析非连续块体系统（尤其是岩体系统）的数值方法所共同面临的主要困难之一。接触检索算法的任务是判断和区分接触类型、定位接触位置、描述并跟踪接触状态的变化过程。在实际的数值计算中，接触检索可以通过接触判断和接触传递两个步骤来实现。 本文对已有的接触判断算法的优、缺点进行了分析，提出了建立正确接触判断算法所应该遵循的原则。同时提出了一种新的三维接触判断算法一切割体法，此方法结合了已有几种主要方法的优点。它对于块体的接触范围有明确的定义，而且将块体的接触范围分为4个区域。无论一个块体在何处与另外一个块体产生接触，这个块体上参与接触的部分一定落入这4个区域之中的某一个中。此方法通过将两个块体上参与接触的两个几何元素的类型组合而得到块体对之间的接触类型，同时建立了从块体的切割体信息集合到参与接触的几何元素类型集合之间的一一映射关系。 由于程序中采用分时步计算的方式来实现DDA分析，因此前后时步之间块体系统的接触信息的传递也非常重要，如果不能正确传递接触信息，便无法跟踪和更新块体系统中接触状态的变化。在罚方法和点接触模型的基础上，本文提出了接触传递的具体算法以实现在块体系统运动过程中将接触信息从当前时步传递到下一时步。此外，在计算技巧方面，由于确定接触点对位置时经常涉及到对细部范围内点、线、面各元素之间的相互关系及距离的精细计算，为了统一解决计算过程中的困难，以便准确地确定接触点位置，本文提出了环路搜索法。 对三维DDA理论中各项子矩阵和系统方程的推导和建立做了介绍和完善。基于Visual C⁺⁺平台，本文开发了三维DDA的可视化分析程序3DP DDA，程序中的接触算法即采用切割体法。此程序被设计在PC机上运行，它可以给出块体系统（如岩石块体系统）中各个块体运动过程的实时的可视化模拟结果，输出的数据结果中包括各块体的位移、变形、应力、应变，以及块体间的接触力、相对滑动和接触开合的位移值。更多还原

【Abstract】 Discontinuous Deformation Analysis (DDA) is a powerful numerical method for simulating the discontinuous media composed of blocks or particles. To simulate and analysis the natural physical process of such systems, it needs not only to render realistic images according the material’s physical and geometric properties, but also needs to model objects interactions precisely. DDA has been widely applied to the 2D analysis of discontinuous deformation of rock blocky systems in rock engineering, while for 3D problems, the lack of reliable 3D contact detection algorithms for polyhedron blocks turns out to be the main obstacle. Contact detection is a key problem, at present, encountered by all numerical methods during modeling and analyzing practical 3D blocky systems in rock engineering. A contact detection algorithm must judge and distinguish reliably and correctly the different contact types, find the locations and determine, update the states of contacts of blocky systems. During numerical modeling, the contact detection inludes the contact judge and the contact transfer.Advantages and shortcomings of the existent contact judge schemes are discussed. The principle only according to which a correct contact judge algorithm be bring out is represented. And a new approach, namely Incision Body (IB) scheme is put forward, which combines the advantages of the existent methods. The scheme defined a contact scope for a block and, at the same time, divided the scope into four sections. No matter where a block contacts with another block, the contact part of the block must fall into one of four sections of another block. The contact type between two blocks is formed through combining the two geometry types of two contact components of the two blocks. The contact component of a block was determined by the information of incision body of the block, and a one-to-one mapping from the incision body to the contact component is established.Contact transfer is very important when analyzing discontinuous media using a DDA computer program because the analysis is implemented step-by-step with several time increments. If the contact informations of a blocky system are transferred inaccuratly, the tracking and updating of contacts will be failed. Block contact constraints are enforced using the penalty method and the point-to-face model is adopted as contact model. Subsequently, a contact transfer algorithm is presented to fulfill the transfer of contact informations from current time step to next time step. Furthermore, there are numerous difficulties in更多还原