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An interface-enriched generalized finite element method for level set-based topology optimization
Structural and Multidisciplinary Optimization ( IF 3.9 ) Pub Date : 2020-12-04 , DOI: 10.1007/s00158-020-02682-5
S. J. van den Boom , J. Zhang , F. van Keulen , A. M. Aragón

During design optimization, a smooth description of the geometry is important, especially for problems that are sensitive to the way interfaces are resolved, e.g., wave propagation or fluid-structure interaction. A level set description of the boundary, when combined with an enriched finite element formulation, offers a smoother description of the design than traditional density-based methods. However, existing enriched methods have drawbacks, including ill-conditioning and difficulties in prescribing essential boundary conditions. In this work, we introduce a new enriched topology optimization methodology that overcomes the aforementioned drawbacks; boundaries are resolved accurately by means of the Interface-enriched Generalized Finite Element Method (IGFEM), coupled to a level set function constructed by radial basis functions. The enriched method used in this new approach to topology optimization has the same level of accuracy in the analysis as the standard finite element method with matching meshes, but without the need for remeshing. We derive the analytical sensitivities and we discuss the behavior of the optimization process in detail. We establish that IGFEM-based level set topology optimization generates correct topologies for well-known compliance minimization problems.



中文翻译:

基于水平集拓扑优化的富接口广义有限元方法

在设计优化过程中,对几何图形的平滑描述非常重要,尤其是对于那些对界面解决方式敏感的问题,例如波传播或流体-结构相互作用。与丰富的有限元公式结合使用时,边界的水平集描述可提供比传统的基于密度的方法更平滑的设计描述。然而,现有的丰富方法具有缺点,包括不适条件和规定基本边界条件的困难。在这项工作中,我们介绍了一种新的丰富的拓扑优化方法,该方法克服了上述缺点。边界可通过富界面的广义有限元方法(IGFEM)精确解析,该方法与由径向基函数构造的水平集函数耦合。在这种新的拓扑优化方法中使用的丰富方法在分析中的精度与带有匹配网格的标准有限元方法的分析水平相同,但无需重新网格化。我们得出分析灵敏度,并详细讨论优化过程的行为。我们确定基于IGFEM的级别集拓扑优化可为已知的合规性最小化问题生成正确的拓扑。

更新日期:2020-12-04
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