A topology optimization method based on the level set method incorporating a fictitious interface energy

Takayuki Yamada; Kazuhiro Izui; Shinji Nishiwaki; Akihiro Takezawa

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A topology optimization method based on the level set method incorporating a fictitious interface energy

机译：基于结合虚拟接口能的水平集方法的拓扑优化方法

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摘要

This paper proposes a new topology optimization method, which can adjust the geometrical complexity of optimal configurations, using the level set method and incorporating a fictitious interface energy derived from the phase field method. First, a topology optimization problem is formulated based on the level set method, and the method of regularizing the optimization problem by introducing fictitious interface energy is explained. Next, the reaction-diffusion equation that updates the level set function is derived and an optimization algorithm is then constructed, which uses the finite element method to solve the equilibrium equations and the reaction-diffusion equation when updating the level set function. Finally, several optimum design examples are shown to confirm the validity and utility of the proposed topology optimization method.

机译：本文提出了一种新的拓扑优化方法，该方法可以使用水平集方法并结合从相场方法获得的虚拟界面能量来调整最佳配置的几何复杂度。首先，基于水平集方法提出了拓扑优化问题，并介绍了通过引入虚拟接口能量来对优化问题进行规则化的方法。接下来，导出更新水平集函数的反应扩散方程，然后构造优化算法，该算法在更新水平集函数时使用有限元方法求解平衡方程和反应扩散方程。最后，通过几个优化设计实例证明了所提出的拓扑优化方法的有效性和实用性。

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来源
《Computer Methods in Applied Mechanics and Engineering》 |2010年第48期|p.2876-2891|共16页
作者
Takayuki Yamada; Kazuhiro Izui; Shinji Nishiwaki; Akihiro Takezawa;
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作者单位

Graduate School of Engineering, Kyoto University, Yoshida-honmachi, Sakyo-ku, Kyoto 606-8501, Japan;

Graduate School of Engineering, Kyoto University, Yoshida-honmachi, Sakyo-ku, Kyoto 606-8501, Japan;

Graduate School of Engineering, Kyoto University, Yoshida-honmachi, Sakyo-ku, Kyoto 606-8501, Japan;

Graduate School of Engineering, Hiroshima University, 1-4-7 Kagamiyama, Higashi-Hiroshima, Hiroshima 739-8527, Japan;

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收录信息美国《科学引文索引》(SCI);美国《工程索引》(EI);
原文格式 PDF
正文语种 eng
中图分类
关键词
topology optimization; finite element method; level set method; phase field method; tikhonov regularization method;

机译：拓扑优化;有限元法水平设置方法;相场法tikhonov正则化方法;

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5. Level-Set-XFEM-Density Topology Optimization of Active Structures: Methods and Applications =Level-Set-XFEM-Dichte Topologieoptimierung von Aktiven Strukturen: Methoden und Anwendungen [D] . Geiss, Markus Josef. 2019

机译：活动结构的水平集-XFEM-密度拓扑优化：方法和应用=活动结构的水平集-XFEM-密度拓扑优化：方法和应用
6. Comparative study on gene set and pathway topology-based enrichment methods [O] . Michaela Bayerlová, Klaus Jung, Frank Kramer, 2015

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7. A topology optimization method based on the level set method incorporating a fictitious interface energy [O] . Yamada Takayuki, Izui Kazuhiro, Nishiwaki Shinji, 2010

机译：基于结合虚拟接口能的水平集方法的拓扑优化方法

A topology optimization method based on the level set method incorporating a fictitious interface energy

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