A design-through-analysis approach using the Finite Cell Method (ECCOMAS Congress 2016)
A design-through-analysis approach using the Finite Cell Method (ECCOMAS Congress 2016)
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DOI：
10.7712/100016.1984.8920
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发表时间：
2018-09
期刊：
影响因子：
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通讯作者：
B. Wassermann;Tino Bog;S. Kollmannsberger;E. Rank
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文献类型：
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作者：
B. Wassermann;Tino Bog;S. Kollmannsberger;E. Rank
现代三维计算机辅助设计（CAD）系统主要使用两种类型的几何模型。通常，对象是由边界表示（B-Rep）定义的，其中只存储对象的表面及其相应的边和节点。关于数值模拟的一个缺点是B-Rep模型不一定是无懈可击的。这些“脏几何”在计算分析中造成了很大的困难，因为即使是基本的几何操作，如成员点测试也会失败，更不用说经典的边界符合有限元方法所要求的网格划分了。另外，对象可以用构造实体几何（CSG）表示，这与过程建模（PM）密切相关。在此上下文中，模型是使用对原语的布尔操作创建的。然后将建模过程存储为序列（PM），或者存储为构造树（CSG）。与B-Rep模型相比，CSG模型本质上是不透水的。要在水密CSG模型上运行有限元模拟，可能有两种选择：(i)可以将其转换为b -代表模型以获得有限元网格；（ii）可以通过应用嵌入式域方法（如有限单元法（FCM））直接使用其隐式描述。在这篇文章中，我们提出了一种使用CSG和FCM的设计贯穿分析方法。快速可靠的隶属点检验是FCM的关键，它可以直接从CSG模型中推导出来。我们提出了建模方法的概要，成员点测试作为csg操作序列的实现，并讨论了机械工程中复杂相关模型的优点和局限性。
Modern 3D Computer-Aided-Design (CAD) systems use mainly two types of geometric models. Classically, objects are defined by a Boundary Representation (B-Rep), where only the objects' surfaces with their corresponding edges and nodes are stored. One disadvantage concerning a numerical simulation is that B-Rep models are not necessarily watertight. These 'dirty geometries' cause major difficulties in computational analysis because even basic geometric operations such as point-in-membership tests fail, not to mention meshing as required by classical boundary conforming finite element methods. Alternatively, objects may be represented by Constructive Solid Geometry (CSG), which is strongly related to Procedural Modeling (PM). In this context, the model is created using Boolean operations on primitives. The modeling process is then either stored as a sequence (PM), or as a construction tree (CSG). In contrast to B-Rep models, CSG models are intrinsically water-tight. To run a finite element simulation on a water-tight CSG model, two alternatives are possible: (i) it can either be converted to a B-Rep-model to obtain a finite element mesh or (ii) its implicit description can be used directly by applying an embedded domain approach, like the Finite Cell Method (FCM). In this contribution, we present a design-through analysis methodology using CSG and FCM. A crucial point in FCM is a fast and reliable point-in-membership test which can be directly derived from the CSG model. We present the outline of the modeling approach, the realization of the point-in-membership test as a sequence of CSG-operations, and discuss advantages and limitations on complex models of relevance in mechanical engineering.