Polygon‐based contact resolution for superquadrics
Polygon‐based contact resolution for superquadrics
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DOI：
10.1002/nme.1569
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发表时间：
2006-04
影响因子：
2.9
通讯作者：
K. Han;Y. Feng;D. Owen
中科院分区：
文献类型：
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作者：
K. Han;Y. Feng;D. Owen
离散元建模中离散对象的表示是一个基本问题，它直接影响到离散元实现的效率和粒子系统的动态行为。圆盘和球体是最常用的几何形状，因为它们几何简单，计算效率高，但它们不能提供滚动运动的阻力。因此，引入了一些非圆形/球形物体，如多边形/多面体、超二次曲面或形成不规则形状的圆盘/球体的群集。当使用超二次曲面作为离散单元时，接触分辨率的瓶颈与寻找两个非线性函数的交点有关，这是一个非常昂贵的操作，有时可能会找不到解。本文提出了一种高效鲁棒的二维超二次曲面接触分辨率算法，该算法通过自适应采样将任意超二次曲面逼近为一个凸多边形；然后，通过裁剪两个多边形，采用高效的线性算法搜索多边形的交点和重叠区域；采用新建立的角/角接触模型确定接触力和接触方向。重要的是要强调，所提出的方法也可以扩展到一般的非圆离散对象的情况。通过数值算例验证了该算法的性能。版权所有©2005 John Wiley & Sons， Ltd
The representation of discrete objects in the discrete element modelling is a fundamental issue, which has a direct impact on the efficiency of discrete element implementation and the dynamic behaviour of particulate systems. Disks and spheres are the most commonly used geometric shapes due to their geometric simplicity and computational efficiency, but they are unable to provide resistance to rolling motion. For this reason, some non‐circular/spherical objects, such as polygons/polyhedrons, superquadrics, or the clustering of disks/spheres to form irregular shapes, are introduced. When superquadrics are used as discrete elements, the bottleneck of contact resolution is associated with the searching for intersections of two non‐linear functions, which is a very expensive operation and may sometimes fail in finding the solution. In this work, an efficient and robust algorithm is proposed for contact resolution of 2D superquadrics, in which any superquadric is approximated with a convex polygon through adaptive sampling; then by clipping two polygons, an efficient linear algorithm is performed to search for intersections and overlap area of the polygons; the contact forces and directions are determined by employing a newly established corner/corner contact model. It is important to highlight that the proposed methodology can also be extended to general non‐circular discrete object cases. The performance of the algorithm is demonstrated via numerical examples. Copyright © 2005 John Wiley & Sons, Ltd.