Numerical integration of discontinuities on arbitrary domains based on moment fitting
Numerical integration of discontinuities on arbitrary domains based on moment fitting
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DOI：
10.1007/s00466-016-1273-3
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发表时间：
2016-03
影响因子：
4.1
通讯作者：
Meysam Joulaian;Simeon Hubrich;A. Düster
中科院分区：
文献类型：
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作者：
Meysam Joulaian;Simeon Hubrich;A. Düster
基于网格的离散化方法不符合所考虑问题的几何形状，当涉及到被边界或内部界面破坏的有限元积分时，需要特殊处理。为此，我们提出了一种数值方法，适合于集成破碎的元素与少量的积分点。在这种方法中，这是基于矩拟合的方法，一个单独的求积规则被设置为每个切割元素。该方法需要一个B-REP表示的破碎的元素，这可以通过处理从CAD软件获得的三角形表面或通过利用从计算机断层扫描得到的体素模型来实现。本文中提出的数值例子表明，所提出的方法提供了各种各样的几何情况下非常准确的结果，需要一个相当低的积分点。
Discretization methods based on meshes that do not conform to the geometry of the problem under consideration require special treatment when it comes to the integration of finite elements that are broken by the boundary or internal interfaces. To this end, we propose a numerical approach suitable for integrating broken elements with a low number of integration points. In this method, which is based on the moment fitting approach, an individual quadrature rule is set up for each cut element. The approach requires a B-rep representation of the broken element, which can be either achieved by processing a triangulated surface obtained from a CAD software or by taking advantage of a voxel model resulting from computed tomography. The numerical examples presented in this paper reveal that the proposed method delivers for a wide variety of geometrical situations very accurate results and requires a rather low number of integration points.