著者

真鍋 匡利 山田 崇恭 泉井 一浩 西脇 眞二

出版者

一般社団法人 日本機械学会

雑誌

日本機械学会論文集A編 (ISSN:18848338)

巻号頁・発行日

vol.77, no.784, pp.2054-2066, 2011 (Released:2011-12-25)

参考文献数

35

被引用文献数

1 3

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Topology optimization for structures has been applied to nonlinear structural problems, however conventional topology optimization methods for structures with geometrical nonlinearity encounter difficulties during nonlinear analysis using the FEM (Finite Element Method), due to the use of a mesh. In this study, we propose a new level set-based topology optimization method considering geometrical nonlinearity using a mesh-free/particle technique, for optimizing elastic structures that undergo large deformation. In the proposed method, the MPS (Moving Particle Semiimplicit) method, a particle method, is used for the response analysis, since it does not rely on a mesh for geometrically nonlinear analysis. In this paper, first, a topology optimization problem is formulated based on the level set method and a method for regularizing the optimization problem by the Tikhonov regularization method is explained. The reactiondiffusion equation that updates the level set function is then derived and an optimization algorithm, which uses the FEM to solve the equilibrium equations and the reaction-diffusion equation when updating the level set function, is constructed. Next, the particle interaction model and the treatment of geometrical nonlinearity in the MPS method are shown, and the implementation of combining the level set-based topology optimization and the MPS methods is explained. Finally, several numerical examples are provided to demonstrate the effectiveness of the proposed method of topology optimization for geometrically nonlinear problems.

著者

伊藤 瑛里 西脇 眞二 泉井 一浩 山田 孝之

出版者

一般社団法人 日本機械学会

雑誌

年次大会

巻号頁・発行日

vol.2020, 2020

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<p>This paper proposes a scheme for imposing geometrical constraints in topology optimization to obtain structures considering the visibility of the product user, based on a fictitious physical model. First, a level set-based topology optimization method is concisely introduced, and geometrical requirements for the visibility are clarifid. A fictitious physical model described by a steady-state advection-dffusion equation is then constructed based on the requirements. In this model, virtual heat sources correspond to material domains and the advection direction is aligned with a radial direction around a view point. The visibility is evaluated by the values of the fictitious physical model, and the regions to see, where the value of the fictitious physical field is high, represent blind area. Next, an optimal problem is introduced based on the fictitious physical model. Finally, in the numerical examples, the proposed method yields optimal structure considering the visibility, confirming the validity and the utility of the proposed method.</p>

著者

古口 睦士 矢地 謙太郎 山田 崇恭 泉井 一浩 西脇 眞二

出版者

日本計算工学会

雑誌

日本計算工学会論文集 (ISSN:13478826)

巻号頁・発行日

vol.2015, pp.20150002-20150002, 2015-01-30 (Released:2015-01-30)

参考文献数

24

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構造最適化は, 数値解析による性能評価と数学的な最適化手法により, 最大限の性能を有する構造を求める手法で, 寸法最適化, 形状最適化, トポロジー最適化に大別される. このうちトポロジー最適化は, 構造の形状だけなく形態の変更も可能な最も自由度の高い手法で, 大幅な性能向上が期待できる. 構造最適化は, 当初構造問題への適用に限られていたが, 近年では様々な物理問題に適用されてきている. 流体問題への適用は, 電磁波問題などと比較するとやや古く, ストークス流を対象に流体に作用する抗力の最小化を目的とし, その形状感度を導出することにより最適形状を得る手法や, 変動拘束された境界を含む領域において粘性流体を対象とした散逸エネルギー最小化の構造最適化の手法が提案されている. しかしながら, これらの手法は, 対象とする設計領域における物体と流体の境界を変動させることにより最適構造を得る, いわゆる形状最適化の手法であるため大幅な性能向上が期待できないうえ, 最適構造が初期構造に強く依存する欠点を持つ. これに対して, 流体問題へのトポロジー最適化の展開も報告されている. その報告の例としては, 設計領域全体を多孔質体と仮定し, 物体領域と流体領域の境界で流速が零になるように仮想的な外力を与えることで物体と流体を区別し, 散逸エネルギーを最小化する最適構造を得る手法が挙げられる. トポロジー最適化の基本的な考え方は, 固定設計領域を導入し, 物体の有無を示す特性関数により構造最適化の問題を材料分布問題に置き換えることである. このため, 構造の形状だけでなく形態の変化も可能となるが, 特性関数が設計領域内のいたるところで無限小の範囲で不連続になる可能性を持つ不適切な問題(ill-posed problem)となる. この問題を解決するためには, 大域的な意味において不連続な関数を連続な関数に置き換える設計変数の緩和を行う. この緩和方法には, 均質化法や密度法などが提案されているが, どちらの手法においても, 最適構造の境界が明確にならない, いわゆるグレースケールを許容する欠点を持つ. 他方, 新たな構造最適化の手法として, レベルセット法に基づく形状最適化が提案されている. この手法では, レベルセット関数と呼ばれるスカラー関数を用いて, 設計領域中の物体の有無をその符号で示し, 零等位面を境界として表現するため, グレースケールを含まない明瞭な境界を有した最適構造が得られる利点がある. しかしながら, この方法は基本的には形状最適化の考え方に基づいており, 新たに境界が生成されるような構造の形態の変化を許容しない. この問題を本質的に解決する手法として, レベルセット法による境界表現を行いながら, トポロジー導関数の考え方に基づき設計変数を更新することにより, 形態変更を可能とした新しいトポロジー最適化の手法が提案されている. そこで本研究ではこの形態変更を可能とした新しい最適化の手法に基づき, ナビエ・ストークス方程式を支配方程式とする内部流れにおいて, エネルギー損失の最小化を目的としたトポロジー最適化の手法を構築する. トポロジー最適化は, 状態場および感度解析のための随伴場の計算に, 何らかの数値解析法を必要とする. その代表的な数値解析法として有限体積法が挙げられる. 有限体積法は, 離散化した各要素内において保存則を満たすように定式化した数値解析手法で, 状態方程式に存在する対流項や拡散項をガウスの積分定理により領域積分から境界積分に変換でき, 数値積分においても中点公式を用いる. また, 非構造格子を扱える汎用性の高さという利点もあり, 流れ場の数値解析法として広く利用されている. そこで本研究では, 状態場と感度解析には有限体積法を用いた新しい方法を開発することにより, 明確な形状表現を可能にしながら大規模問題への展開可能な方法論を構築する. 随伴方程式は連続系に基づき導出し, 有限体積法により離散化して数値安定性に優れている半陰解法のSIMPLE法(Semi-Implicit Method for Pressure Linked Equation) を用いて解析している. また, 最適化の過程におけるレベルセット関数を更新には, 時間発展方程式の数値解析法として有限体積法を適用した方法を構築する. これにより, 時間発展方程式の離散化の過程で弱形式による複雑な展開は必要としないうえ, 時間項については数値安定性のよいオイラー陰解法を適用することにより, 時間発展方程式の計算効率は状態場および随伴場と同様に向上させることができる.

著者

松木 貴広 山田 崇恭 泉井 一浩 西脇 眞二

出版者

一般社団法人 日本機械学会

雑誌

計算力学講演会講演論文集 2013.26 (ISSN:24242799)

巻号頁・発行日

pp._2203-1_-_2203-3_, 2013-11-02 (Released:2017-06-19)

著者

山田 崇恭 西脇 眞二 伊賀 淳郎 泉井 一浩 吉村 允孝

出版者

一般社団法人 日本機械学会

雑誌

日本機械学会論文集 C編 (ISSN:03875024)

巻号頁・発行日

vol.75, no.759, pp.2868-2876, 2009-11-25 (Released:2017-06-09)

参考文献数

21

被引用文献数

1 2

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In structural designs considering thermal loading, to control thermal stress and minimize decreases in material strength at high temperatures, it is important to maximize the thermal diffusivity of structures, in addition to the usual maximization of stiffness that optimal designs achieve. This paper presents a new level set-based topology optimization method for thermal problems with generic heat transfer boundaries in a fixed design domain that includes design-dependent effects, using level set boundary expressions and the Finite Element Method. First, a topology optimization method using a level set model incorporating fictitious interface energy is briefly discussed. Next, an optimization problem is formulated using the concept of total potential energy to address the design of mechanical structures that aim to minimize the mean temperature of the structure under thermal loading. An optimization algorithm that uses the Finite Element Method when solving the equilibrium equation and updating the level set function is then constructed. Finally, several numerical examples are provided to confirm the utility of the proposed optimization method.

著者

石塚 尚子 野口 悠暉 山田 崇恭 泉井 一浩 西脇 眞二

出版者

一般社団法人 日本機械学会

雑誌

日本機械学会論文集 (ISSN:21879761)

巻号頁・発行日

vol.83, no.853, pp.17-00185-17-00185, 2017 (Released:2017-09-25)

参考文献数

19

被引用文献数

1

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The uniformity of deposition thickness in electroplating processes is vital to the realization of desirable surface qualities of many products. The thickness distribution of deposits varies according to numerous factors, such as the arrangement and shapes of auxiliary cathodes, anodes and shields, and the detailed configuration of the plating process. In recent years, computer analyses such as the Finite Element Method (FEM) have become widespread. Such analytical tools can predict thickness distributions, search for optimal process configurations, and avoid production problems, to some extent, but the selection of the most effective analytical conditions still depends on skilled analysts. This study presents a topology optimization method to achieve uniform deposition thickness, applied to the design of the shields placed in an electroplating bath. The proposed method uses level set boundary expressions and the FEM to analyze the electrochemical field. The Kreisselmeier-Steinhauser (KS) function for the current density distribution on a cathode is employed as an objective function, since current density is nearly proportional to the thickness of the resulting electroplating. The magnitude of the current density on the cathode is set as a constraint so that it does not fall below a certain value, to avoid lengthy plating times that would occur if the current density were too low. Numerical examples are presented to confirm the utility of the proposed method and the results demonstrate that the proposed method can obtain appropriate shapes and arrangements of shields.

著者

佐藤 綾美 岡本 崇 山田 崇恭 泉井 一浩 西脇 眞二

出版者

一般社団法人 日本機械学会

雑誌

日本機械学会論文集 (ISSN:21879761)

巻号頁・発行日

vol.83, no.850, pp.17-00135-17-00135, 2017 (Released:2017-06-25)

参考文献数

17

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We construct a topology optimization method for two dimensional rarefied gas flow problems, based on level-set boundary expressions. The degree of rarefaction is expressed by the Knudsen number, which is the ratio of the mean free path and the characteristic length of the system. As the Knudsen number approaches 0 in the limit, flow behaviors can be described by Navier-Stokes equations and topology optimization methods for such flows have already been proposed. On the other hand, the governing equation for flows which have a large rarefaction is the Boltzmann equation and topology optimization methods for such flows have not been seen. This paper presents the topology optimization method for rarefied gas flows whose Knudsen number is approximately 1, aiming at an application for the design of flow channels in micromachines. We use the Bhatnagar-Gross-Krook (BGK) model of the Boltzmann equation and extend it to the entire design domain that includes both rarefied gas and solid domains. First, we briefly discuss the Boltzmann equation and the level set-based topology optimization method. Second, an optimization problem is formulated to address the design of flow channels that aim to maximize the flow velocity induced along a temperature gradient. Finally, several numerical examples demonstrate the validity and usefulness of the proposed method.

著者

佐藤 勇気 山田 崇恭 泉井 一浩 西脇 眞二

出版者

一般社団法人 日本機械学会

雑誌

日本機械学会論文集 (ISSN:21879761)

巻号頁・発行日

vol.83, no.851, pp.17-00081-17-00081, 2017 (Released:2017-07-25)

参考文献数

29

被引用文献数

2

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This paper proposes a scheme for imposing geometrical constraints in topology optimization for molding and milling so that optimal configurations that guarantee manufacturability can be obtained, based on the fictitious physical model. First, a level set-based topology optimization method is briefly described, and geometrical requirements for molding and milling are clarified. In molding, molded products must embody certain geometrical features so that mold parts can be separated, and milling cannot proceed unless the desired shape allows tool cutting faces to reach the workpiece. A fictitious physical model described by a steady-state advection-diffusion equation is then constructed based on the requirements. In the fictitious physical model, material domains are represented as virtual heat sources and an advection direction is aligned with a prescribed direction, along which mold parts are moved, or attitude in the case of a milling tool. Void regions, where the value of the fictitious physical field is high, represent either undercut geometries which would prevent the mold from being parted, interior voids that cannot be manufactured, or regions that a milling tool cannot reach. Next, a geometrical constraint is formulated based on the fictitious physical model. An optimization algorithm is then constructed. Finally, in the numerical examples, the proposed method yields manufacturable optimal configurations, confirming the validity and the utility of the proposed method.

著者

岸本 直樹 野口 悠暉 佐藤 勇気 泉井 一浩 山田 崇恭 西脇 眞二

出版者

一般社団法人 日本機械学会

雑誌

日本機械学会論文集 (ISSN:21879761)

巻号頁・発行日

vol.83, no.849, pp.17-00069-17-00069, 2017 (Released:2017-05-25)

参考文献数

24

被引用文献数

8

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Topology optimization is the most flexible type of structural optimization method. This method has been applied in a variety of physics problems dealing with a multitude of design problems. In a given design problem, however, the optimization problem often has conflicting evaluative functions, such as the need for high rigidity in combination with minimal weight. The difficulty of simultaneously achieving high performance for two or more functions may be further compounded because current topology optimization methods typically only deal with a single material. On the other hand, when multiple kinds of materials having various properties can be selected for use, the range of a designer's choices is increased and an appropriate solution that greatly improves product functions may be achieved. Thus, this paper presents a new topology optimization method for multi-materials that obtains high-performance configurations. We apply the Multi-Material Level Set (MM-LS) topology description model in the topology optimization method, which uses a total of n level set functions to represent n materials, plus the void phase. The advantage of the MM-LS model is that clear optimal configurations are obtained and the design sensitivity for multi-material structures can be easily calculated. The level set functions that are design variables are updated using the topological derivatives, which also function as design sensitivities, and we derive the topological derivatives for multiple materials. Through several numerical examples, we demonstrate the validity of the proposed method.

著者

小林 正和 吉村 允孝 西脇 眞二 泉井 一浩

出版者

一般社団法人日本機械学会

雑誌

設計工学・システム部門講演会講演論文集 (ISSN:13480286)

巻号頁・発行日

vol.2003, no.13, pp.271-272, 2003-10-30

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Collaborative product design implies that multiple designers will cooperate during the design of a product, by sharing knowledge and information. For practical design teams, expertise in a wide area is needed, but the area that a single designer can proficiently handle is usually quite narrow. Therefore, facilitated collaboration is indispensable to achieve efficient results from a practical design team. In recent years, customer requirements have become increasingly diversified, and companies have focused upon developing unique or increasingly sophisticated products to maintain their market share. As a result, achieving especially creative designs has become more important than ever. An additional aim of collaboration is to maximally assist this type of creative design process. This paper discusses an advanced collaborative system supporting creative design processes that depend on interactive communication among a number of designers. To implement such a system, this paper proposes a method for structurizing and visualizing communication processes.