From geometric design to numerical analysis: A direct approach using the Finite Cell Method on Constructive Solid Geometry
From geometric design to numerical analysis: A direct approach using the Finite Cell Method on Constructive Solid Geometry
复制标题
DOI：
10.1016/j.camwa.2017.01.027
复制
发表时间：
2017-10
期刊：
影响因子：
--
通讯作者：
B. Wassermann;S. Kollmannsberger;Tino Bog;E. Rank
中科院分区：
文献类型：
--
作者：
B. Wassermann;S. Kollmannsberger;Tino Bog;E. Rank
在过去的十年中，人们越来越努力地改进和简化从计算机辅助设计（CAD）建模到数值模拟的过程。从一个模型到另一个模型的过渡，即网格划分，是一个瓶颈。已经开发了几种方法来克服这一耗时的步骤，例如等几何分析（IGA），它将用于几何描述的形状函数（通常是b样条和NURBS）直接应用于数值分析。与IGA处理边界表示模型（B-Rep）相比，我们的方法侧重于参数化体积模型，如构造实体几何（CSG）。这些模型有几个优点，因为它们的几何描述本质上是水密的，它们提供了模型内部的描述。为了能够使用这些模型的明确的数学描述，我们采用有限单元法（FCM）。在这里，唯一必要的输入是一个可靠的声明，一个（积分）点是在几何模型的内部还是外部。本文主要讨论了这种隶属点检验在各种几何对象上的应用，如扫描和放样，以及一些几何操作，如倒角或倒角。结果表明，基于这些目标的构造方法信息，可以有效地、鲁棒地进行隶属点检验。
During the last ten years, increasing efforts were made to improve and simplify the process from Computer Aided Design (CAD) modeling to a numerical simulation. It has been shown that the transition from one model to another, i.e. the meshing, is a bottle-neck. Several approaches have been developed to overcome this time-consuming step, e.g. Isogeometric Analysis (IGA), which applies the shape functions used for the geometry description (typically B-Splines and NURBS) directly to the numerical analysis. In contrast to IGA, which deals with boundary represented models (B-Rep), our approach focuses on parametric volumetric models such as Constructive Solid Geometries (CSG). These models have several advantages, as their geometry description is inherently watertight and they provide a description of the models’ interior. To be able to use the explicit mathematical description of these models, we employ the Finite Cell Method (FCM). Herein, the only necessary input is a reliable statement whether an (integration-) point lies inside or outside of the geometric model. This paper mainly discusses such point-in-membership tests on various geometric objects like sweeps and lofts, as well as several geometric operations such as filleting or chamfering. We demonstrate that, based on the information of the construction method of these objects, the point-in-membership-test can be carried out efficiently and robustly.