基于八叉树的全局接触搜索算法研究

摘要

接触搜索是接触-碰撞问题有限元模拟中最为耗时的部分,高效的接触搜索算法是提高数值分析效率的关键.以面心坐标和特征长度表征接触主片,并引入树包围盒和从节点包围盒的概念,基于八叉树算法发展了一种高效的全局接触搜索方法,计算复杂度为O(Nlog8M),其中N为从节点数,M为接触主片数.程序实现时,通过引入接触预搜索和相邻搜索方式加速搜索速度.本文算法基于PANDA-Impact软件实现,并进行了算例验证分析.结果表明,本文算法具有很好的接触搜索效率与适用性,与桶排序算法相比,当接触复杂且规模较大时,本文算法表现出较大的优势.%In finite element simulations,contact searching is the most time-consuming part in the problems involving contact-impact,therefore it is significant to develop an efficient contact-pairs searching method.In this paper a new global searching method based on octree algorithm is developed and implemented in PANDA-Impact program.In the proposed method,centroid of the master segment and relevant characteristic length are used to represent its true geometry.Two new concepts,tree-bounding-box and slave-bounding-box,are presented.The cost of the new contact searching method is of the order of O(Nlog8M),where N is the number of the slave nodes,and M is the number of master segments.In implementation,pre-searching and neighbor-searching are introduced to accelerate the efficiency of contact-searching.The results of typical numerical experiments show that the new contact searching method is very efficient.In dealing with problems involving complex and large amount of contact pairs,the new method has an apparent observable advantage over the bucket sorting method.