Shape and topology optimization based on the convected level set method

The aim of this research is to construct a shape optimization method based on the convected level set method, in which the level set function is defined as a truncated smooth function obtained by using a sinus filter based on a hyperbolic tangent function. The local property of the hyperbolic tangen...

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Vydáno v:	Structural and multidisciplinary optimization Ročník 54; číslo 3; s. 659 - 672
Hlavní autoři:	Yaji, Kentaro, Otomori, Masaki, Yamada, Takayuki, Izui, Kazuhiro, Nishiwaki, Shinji, Pironneau, Olivier
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	Berlin/Heidelberg Springer Berlin Heidelberg 01.09.2016 Springer Nature B.V Springer Verlag
Témata:	Computational Mathematics and Numerical Analysis Computer Science Engineering Engineering Design Evolution Hyperbolic functions Mathematical analysis Numerical Analysis Research Paper Shape optimization Theoretical and Applied Mechanics Topology optimization Mesh adaptation Shape sensitivity Convective reinitialization Shape optimization Hyperbolic tangent level set function set function Hyperbolic tangent level
ISSN:	1615-147X, 1615-1488
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Abstract	The aim of this research is to construct a shape optimization method based on the convected level set method, in which the level set function is defined as a truncated smooth function obtained by using a sinus filter based on a hyperbolic tangent function. The local property of the hyperbolic tangent function dramatically reduces the generation of red the error between the specified profile of the hyperbolic tangent function and the level set function that is updated using a time evolution equation. In addition, the small size of the error facilitates the use of convective reinitialization, whose basic idea is that the reinitialization is embedded in the time evolution equation, whereas such treatment is typically conducted in a separate calculation in conventional level set methods. The convected level set method can completely avoid the need for additional calculations when performing reinitialization. The validity and effectiveness of our presented method are tested with a mean compliance minimization problem and a problem for the design of a compliant mechanism.
AbstractList	The aim of this research is to construct a shape optimization method based on the convected level set method, in which the level set function is defined as a truncated smooth function obtained by using a sinus filter based on a hyperbolic tangent function. The local property of the hyperbolic tangent function dramatically reduces the generation of red the error between the specified profile of the hyperbolic tangent function and the level set function that is updated using a time evolution equation. In addition, the small size of the error facilitates the use of convective reinitialization, whose basic idea is that the reinitialization is embedded in the time evolution equation, whereas such treatment is typically conducted in a separate calculation in conventional level set methods. The convected level set method can completely avoid the need for additional calculations when performing reinitialization. The validity and effectiveness of our presented method are tested with a mean compliance minimization problem and a problem for the design of a compliant mechanism.
Author	Izui, Kazuhiro Otomori, Masaki Yaji, Kentaro Nishiwaki, Shinji Pironneau, Olivier Yamada, Takayuki
Author_xml	– sequence: 1 givenname: Kentaro surname: Yaji fullname: Yaji, Kentaro email: yaji.kentarou.74v@st.kyoto-u.jp organization: Department of Mechanical Engineering and Science, Graduate School of Engineering, Kyoto University – sequence: 2 givenname: Masaki surname: Otomori fullname: Otomori, Masaki organization: AISIN AW Co., LTD. Fujii-cho – sequence: 3 givenname: Takayuki surname: Yamada fullname: Yamada, Takayuki organization: Department of Mechanical Engineering and Science, Graduate School of Engineering, Kyoto University – sequence: 4 givenname: Kazuhiro surname: Izui fullname: Izui, Kazuhiro organization: Department of Mechanical Engineering and Science, Graduate School of Engineering, Kyoto University – sequence: 5 givenname: Shinji surname: Nishiwaki fullname: Nishiwaki, Shinji organization: Department of Mechanical Engineering and Science, Graduate School of Engineering, Kyoto University – sequence: 6 givenname: Olivier surname: Pironneau fullname: Pironneau, Olivier organization: Sorbonne Universités, UPMC Univ Paris 06, UMR 7598, Laboratoire Jacques-Louis Lions (LJLL)
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Keywords	Mesh adaptation Shape sensitivity Convective reinitialization Shape optimization Hyperbolic tangent level set function set function Hyperbolic tangent level
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Snippet	The aim of this research is to construct a shape optimization method based on the convected level set method, in which the level set function is defined as a...
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SubjectTerms	Computational Mathematics and Numerical Analysis Computer Science Engineering Engineering Design Evolution Hyperbolic functions Mathematical analysis Numerical Analysis Research Paper Shape optimization Theoretical and Applied Mechanics Topology optimization
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Title	Shape and topology optimization based on the convected level set method
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