Automatic image-based analyses using a coupled quadtree-SBFEM/SCM approach
Automatic image-based analyses using a coupled quadtree-SBFEM/SCM approach
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DOI：
10.1007/s00466-017-1424-1
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发表时间：
2017-10-01
影响因子：
4.1
通讯作者：
Duczek, Sascha
中科院分区：
文献类型：
--
作者：
Gravenkamp, Hauke;Duczek, Sascha
基于四叉树的区域分解算法为基于图像的自动分析提供了一种创建网格的有效选择。尺度边界有限元方法在不引入悬挂节点的情况下，只需对每个子域的边界进行离散化，即可直接对此类网格进行计算。然而，由于边界的不精确表示，依赖于基于四叉树的几何近似的数值方法的收敛往往是次优的。为了解决这一问题，提出了一种将谱单元方法(SCM)与标准有限元方法相结合的方法。其基本思想是将每个未切割的四叉树单元视为一个SBFEM多边形，而所有已切割的四叉树单元则使用SCM进行计算。这种方法不仅减少了所需的自由度数，而且还避免了在所有未切割的四叉树单元中进行二维求积。数值算例包括复杂几何结构的静力分析、简谐分析、模态分析和暂态分析，突出了这种新方法的性能。
Quadtree-based domain decomposition algorithms offer an efficient option to create meshes for automatic image-based analyses. Without introducing hanging nodes the scaled boundary finite element method (SBFEM) can directly operate on such meshes by only discretizing the edges of each subdomain. However, the convergence of a numerical method that relies on a quadtree-based geometry approximation is often suboptimal due to the inaccurate representation of the boundary. To overcome this problem a combination of the SBFEM with the spectral cell method (SCM) is proposed. The basic idea is to treat each uncut quadtree cell as an SBFEM polygon, while all cut quadtree cells are computed employing the SCM. This methodology not only reduces the required number of degrees of freedom but also avoids a two-dimensional quadrature in all uncut quadtree cells. Numerical examples including static, harmonic, modal and transient analyses of complex geometries are studied, highlighting the performance of this novel approach.