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Improvement in 3D topology optimization with h-adaptive refinement using the Cartesian grid Finite Element Method
International Journal for Numerical Methods in Engineering ( IF 2.9 ) Pub Date : 2021-02-14 , DOI: 10.1002/nme.6652
David Muñoz 1 , José Albelda 1 , Juan José Ródenas 1 , Enrique Nadal 1
Affiliation  

The growing number of scientific publications on topology optimization (TO) shows the great interest that this technique has generated in recent years. Among the different methodologies for TO, this article focuses on the well-known solid isotropic material penalization (SIMP) method, broadly used because of its simple formulation and efficiency. Even so, the SIMP method has certain drawbacks, namely: lack of precision in definition of the edges of the optimized geometry and final results strongly influenced by the discretization used for the finite element (FE) analyses. In this article, we propose a combination of techniques to limit the effect of these drawbacks and, thus, to improve the behavior of TO. All these techniques are based on the use of the Cartesian grid finite element method (cgFEM), an immersed boundary method whose Cartesian grid structure and hierarchical data structure makes it specially appropriate for TO. All the proposed techniques are framed under the concept of mesh refinement. First, we propose the use of two meshes, the FE analysis mesh, and a finer mesh for integration and evaluation of sensitivities, to improve the resolution of the final solution at a marginal computational cost. Then we propose two h-adaptive mesh refinement strategies. The first one will tend to refine the elements having intermediate density values and will have the effect of sharpening the definition of the edges of the optimized geometry. We will clearly show that if the accuracy of the FE analyses is not taken into account, stress constrained TO will generate solutions that, once manufactured, will not satisfy the constraints. Hence, we also propose an h-refinement strategy based on the estimation of the discretization error in energy norm.

中文翻译:

使用笛卡尔网格有限元方法通过 h 自适应细化改进 3D 拓扑优化

越来越多的关于拓扑优化 (TO) 的科学出版物表明,近年来这种技术引起了极大的兴趣。在 TO 的不同方法中,本文重点介绍了众所周知的固体各向同性材料惩罚 (SIMP) 方法,该方法因其简单的公式和效率而被广泛使用。即便如此,SIMP 方法也有一定的缺点,即:优化几何边缘的定义缺乏精度,最终结果受到有限元 (FE) 分析所使用的离散化的强烈影响。在本文中,我们提出了一种技术组合来限制这些缺点的影响,从而改善 TO 的行为。所有这些技术都基于使用笛卡尔网格有限元法 (cgFEM),一种浸入式边界方法,其笛卡尔网格结构和分层数据结构使其特别适用于 TO。所有提出的技术都是在网格细化的概念下构建的。首先,我们建议使用两个网格,有限元分析网格和一个更精细的网格来集成和评估灵敏度,以边际计算成本提高最终解决方案的分辨率。然后我们提出两个h - 自适应网格细化策略。第一个将倾向于细化具有中间密度值的元素,并将具有锐化优化几何边缘定义的效果。我们将清楚地表明,如果不考虑 FE 分析的准确性,应力约束 TO 将生成解决方案,一旦制造,将不满足约束条件。因此,我们还提出了一种基于能量范数离散化误差估计的h细化策略。
更新日期:2021-02-14
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