Integrating CAD and Numerical Analysis: 'Dirty Geometry' handling using the Finite Cell Method
Integrating CAD and Numerical Analysis: 'Dirty Geometry' handling using the Finite Cell Method
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DOI：
10.1016/j.cma.2019.04.017
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发表时间：
2018-10
期刊：
影响因子：
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通讯作者：
B. Wassermann;S. Kollmannsberger;Shuohui Yin;L. Kudela;E. Rank
中科院分区：
文献类型：
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作者：
B. Wassermann;S. Kollmannsberger;Shuohui Yin;L. Kudela;E. Rank
本文提出了一种计算机辅助设计（CAD）和有限单元法（FCM）的集成与“脏几何”模型的计算方法。FCM是一种基于高阶有限元的虚拟域方法，它将物理模型嵌入到虚拟域中，可以在不考虑物理域边界的情况下进行离散。真实的几何形状是由边界切割的元素的精确数值积分捕获的。因此，一个有效的点隶属度分类算法，确定内部和外部状态的集成点相对于物理域是在FCM的核心操作。为了处理“脏几何”，即不精确或有缺陷的几何模型，提出了一种对大多数CAD模型缺陷不敏感的分段三角形相交算法和泛洪填充算法的组合来识别集成点的隶属关系。因此，本方法允许直接计算几何和拓扑缺陷的模型。数值算例表明了该方法的实际应用潜力和优点。
This paper proposes a computational methodology for the integration of Computer Aided Design (CAD) and the Finite Cell Method (FCM) for models with “dirty geometries”. FCM, being a fictitious domain approach based on higher order finite elements, embeds the physical model into a fictitious domain, which can be discretized without having to take into account the boundary of the physical domain. The true geometry is captured by a precise numerical integration of elements cut by the boundary. Thus, an effective Point Membership Classification algorithm that determines the inside–outside state of an integration point with respect to the physical domain is a core operation in FCM. To treat also “dirty geometries”, i.e. imprecise or flawed geometric models, a combination of a segment-triangle intersection algorithm and a flood fill algorithm being insensitive to most CAD model flaws is proposed to identify the affiliation of the integration points. The present method thus allows direct computations on geometrically and topologically flawed models. The potential and merit for practical applications of the proposed method is demonstrated by several numerical examples.