研究業績

2022


  1. Zhiyuan Jia, Yangjun Luo, Akihiro Takezawa, Xiaopeng Zhang, Topology optimization for realizing tailored self-collimation in phononic crystals, International Journal for Numerical Methods in Engineering, in press.
  2. Heng Zhang, Akihiro Takezawa, Xiaohong Ding, Xiaopeng Zhang, Shipeng Xu, Hao Li, Shuya Nozawa, Shinji Nishiwaki, Robust topology optimization of biodegradable composite structures under uncertain degradation rates, Composite Structures, 291, 115593, 2022.
  3. 竹澤 晃弘, 構造設計による金属積層造形の熱変形低減, 軽金属, 72, pp. 234-239, 2022.
  4. J. Nomura, A. Takezawa, H. Zhang, M. Kitamura, Design optimization of functionally graded lattice infill total hip arthroplasty stem for stress shielding reduction, Proc. Inst. Mech. Eng. H, 236, pp. 515-525, 2022.
  5. 柳原 一貴, 宇惠野 章, 竹澤 晃弘, 傾斜機能ラティス構造による構造体表面の接触反力最適化, 精密工学会誌, 88, pp. 352-358, 2022.
  6. H. Guo, K. Ichikawa, H. Sakai, H. Zhang, X. Zhang, K. Tsuruta, K. Makihara, A. Takezawa, Numerical and Experimental Analysis of Additively Manufactured Particle Dampers at Low Frequencies, Powder Technology, 396B, pp. 696-709, 2022.
  7. 本田 正徳, 目良 貢, 河村 力, 竹澤 晃弘, 北村 充, スパースモデリングを用いた構造物の設計形状における重要部位の抽出手法に関する研究, 日本機械学会論文集, 88, 21-00289, 2022.


2021


  1. H. Zhang, A. Takezawa, X. Ding, H. Guo, W. Ni, X. Zhang, Topology optimization of composite macrostructure with multi-phase viscoelastic composite microstructures for enhanced structural damping, Composite Structures, 278, 114712, 2021.
  2. A. Takezawa, Q. Chen, A. C. To, Optimally Variable Density Lattice to Reduce Warping Thermal Distortion of Laser Powder Bed Fusion, Additive Manufacturing, 48B, 102422, 2021.
  3. 野沢 修矢, Zhang Heng, 宇恵野 章, 柳原 一貴, 竹澤 晃弘, 動的問題における繊維強化複合材のトポロジー最適化, 日本機械学会論文集, 87, 21-00234, 2021.
  4. H. Zhang, A. Takezawa, X. Ding, S. Xu, P. Duan, H. Li, H. Guo, Bi-material microstructural design of biodegradable composites using topology optimization, Materials & Design, 209, 109973, 2021.
  5. Q. Chen, H. Taylor, A. Takezawa, X. Liang, X. Jimenez, R. Wicker, A. C. To, Island scanning pattern optimization for residual deformation mitigation in laser powder bed fusion via sequential inherent strain method and sensitivity analysis, Additive Manufacturing, 46, 102116, 2021.
  6. 宇惠野 章, Guo Honghu, 森豊 亮太, 竹澤 晃弘, 北村 充, ラティス体積分率分布最適化と金属積層造形による傾斜機能構造体の温度分布設計, 精密工学会誌, 87, pp. 827-833, 2021.
  7. H. Zhang, A. Takezawa, X. Ding, S. Xu, H. Li, H. Guo, Topology optimization of degradable composite structures with time changeable stiffness, International Journal for Numerical Methods in Engineering, 122, pp. 4751-4773, 2021.
  8. 本田 正徳, 河村 力, 竹澤 晃弘, 北村 充, 高強度・薄板中空フレーム曲げ強度の質量効率を向上させる断面形状の研究, 日本機械学会論文集, 87, 21-00096, 2021.
  9. M. Honda, C. Kawamura, I. Kizaki, Y. Miyajima, A. Takezawa, M. Kitamura, Construction of Design Guidelines for Optimal Automotive Frame Shape Based on Statistical Approach and Mechanical Analysis, Computer Modeling in Engineering & Sciences, 128, pp. 731-742, 2021.
  10. A. Ueno, H. Guo, A. Takezawa, R. Moritoyo, M. Kitamura, Temperature Distribution Design Based on Variable Lattice Density Optimization and Metal Additive Manufacturing, Symmetry, 13, 1194, 2021.
  11. 市川 和男, 阪井 博行, 小湊 裕允, 大瀬戸 将輔, Guo Honghu, 竹澤 晃弘, 北村 充, 微細粒を用いた粒状体ダンパの振動減衰性に関する研究, 日本機械学会論文集, 87, 20-00389, 2021.
  12. A. M. Vilardell, A. Takezawa, A. du Plessis, N. Takata, P. Krakhmalev, M. Kobashi, M. Albu, G. Kothleitner, I. Yadroitsava, I. Yadroitsev, Mechanical behavior of in-situ alloyed Ti6Al4V(ELI)-3 at. Cu lattice structures manufactured by laser powder bed fusion and designed for implant applications, Journal of the Mechanical Behavior of Biomedical Materials, 113, 104130, 2021.


2020


  1. A. Takezawa, A. C. To, Q. Chen, X. Liang, F. Dugast, X. Zhang, M. Kitamura, Sensitivity analysis and lattice density optimization for sequential inherent strain method used in additive manufacturing process, Computer Methods in Applied Mechanics and Engineering, 370, 113231, 2020.
  2. D. Woo, M. Kitamura, A. Takezawa, Method to systemically order welding sequence to efficiently mitigate welding displacement of a general ship grillage structure, Ships and Offshore Structures, 15, pp. 753-768, 2020.
  3. 竹澤晃弘, アディティブマニュファクチャリングによる最適化構造の創製, 精密工学会誌, 86, pp. 405-408, 2020.
  4. H. Guo, A. Takezawa, M. Honda, C. Kawamura, M. Kitamura, Finite element simulation of the compressive response of additively manufactured lattice structures with large diameters, Computational Materials Science, 175, 109610, 2020.
  5. D. Woo, M. Kitamura, A. Takezawa, Systematic method for positioning clamps and strongbacks based on their influence on welding displacements, Ocean Engineering, 202, 107084, 2020.
  6. A. Takezawa, X. Zhang, T. Tanaka, M. Kitamura, Topology optimisation of a porous unit cell in a fluid flow considering Forchheimer drag, International Journal of Computational Fluid Dynamics, 34, pp. 50-60, 2020.


2019


  1. 佐藤 泰貴, 大槻 真嗣, 馬場 満久, 戸部 裕史, 石村 康生, 北薗 幸一, 竹澤 晃弘, 金属3Dプリンタにより造形した月惑星探査機用着陸衝撃吸収材の力学特性 , 日本航空宇宙学会論文集, 67, pp. 218-224, 2019.
  2. A. Takezawa, X. Zhang, M. Kitamura, Optimization of an Additively Manufactured Functionally Graded Lattice Structure with Liquid Cooling Considering Structural Performances, International Journal of Heat and Mass Transfer, 143C, 118564, 2019.
  3. 竹澤晃弘, 金属3Dプリンティングにおけるトポロジー最適化の活用法, 機械技術, 67, pp. 28-33, 2019.
  4. 竹澤晃弘, トポロジー最適化と金属AM を用いた冷却ラティス構造の開発, 砥粒加工学会誌, 63, pp. 353-356, 2019.
  5. A. M. Vilardell, A. Takezawa, A. du Plessis, N. Takata, P. Krakhmalev, M. Kobashi, I. Yadroitsava, I. Yadroitse, Topology optimization and characterization of Ti6Al4V ELI cellular lattice structures by laser powder bed fusion for biomedical applications., Materials Science and Engineering: A, 766, 138330, 2019.
  6. A. Takezawa, X. Zhang, M. Kato, M. Kitamura, Method to Optimize an Additively-Manufactured Functionally-Graded Lattice Structure for Effective Liquid Cooling, Additive Manufacturing, 28, pp. 285-298, 2019.
  7. G. L. Putra, M. Kitamura, A. Takezawa, Structural optimization of stiffener layout for stiffened plate using hybrid GA, International Journal of Naval Architecture and Ocean Engineering, 11, pp. 809-818, 2019.
  8. X. Zhang, A. Takezawa, Z. Kang, A phase-field based robust topology optimization method for phononic crystals design considering uncertain diffuse regions, Computational Materials Science, 160, pp. 159-172, 2019.
  9. A. Takezawa, T. Yamamoto, X. Zhang, K. Yamakawa, S. Nakano. M. Kitamura, An objective function for the topology optimization of sound-absorbing materials, Journal of Sound and Vibration, 443, pp. 804-819, 2019.
  10. A. Takezawa, X. Zhang, Y. Koizumi, Numerical study on the effective stiffness of topology-optimized lattice structures made of orthotropic crystal grains with optimal orientation, Computational Materials Science, 159, pp. 202-209, 2019.
  11. X. Zhang, A. Takezawa, Z. Kang, Robust topology optimization of vibrating structures considering random diffuse regions via a phase-field method, Computer Methods in Applied Mechanics and Engineering, 344, pp. 766-797, 2019.
  12. L. Suo, Z. Lei, S. Zhao, Z. Wu. A. Takezawa, Study on sliding-window length based on Rayleigh backscattering spectrum correlation in distributed optical-fiber strain measurement, Optical Fiber Technology, 47, pp. 126-132, 2019.
  13. L. Suo, Z. Lei, S. Zhao, Z. Wu. A. Takezawa, Reliability-Guided Rayleigh Backscattering Spectrum Correlation Method for Distributed Strain Measurements in Optical Fibers, Journal of Modern Optics, 66, pp. 512-520, 2019.
  14. Z. Liu, S. Cho, A. Takezawa, X. Zhang, M. Kitamura, Two-stage layout-size optimization method for prow stiffeners, International Journal of Naval Architecture and Ocean Engineering, 11, pp. 44-51, 2019.


2018


  1. 竹澤晃弘, トポロジー最適化と金属積層造形の金型開発への応用, ぷらすとす, 1, pp. 758-762, 2018.
  2. A. Takezawa, K. Yonekura, Y. Koizumi, X. Zhang, M. Kitamura, Isotropic Ti-6Al-4V lattice via topology optimization and electron beam melting, Additive Manufacturing, 22, pp. 634-642, 2018.
  3. X. Zhang, A. Takezawa, Z. Kang, Topology optimization of piezoelectric smart structures for minimum energy consumption under active control, Structural and Multi-disciplinary Optimization, 58, pp. 185-199, 2018.
  4. J. Liu, A. T. Gaynor, S. Chen, Z. Kang, K. Suresh, A. Takezawa, L. Li, J. Kato, J. Tang, C. C. L. Wang, L. Cheng, X. Liang, A. C. To, Current and future trends in topology optimization for additive manufacturing, Structural and Multi-disciplinary Optimization, 57, pp. 2453-2483, 2018.
  5. X. Zhang, J. He, Z. Kang, A. Takezawa, Robust topology optimization of phononic crystals with random field uncertainty, International Journal for Numerical Methods in Engineering, 115, pp. 1154-1173, 2018.
  6. A. Takezawa, K. Takenaka, X. Zhang, Inverse analysis of giant macroscopic negative thermal expansion of Ca2RuO4-y ceramics based on elasticity and structural topology optimization, Applied Physics Express, 11, 55801, 2018.
  7. A. Takezawa, J. W. Lee, M. Kitamura, Design methodology of magnetic fields and structures for magneto-mechanical resonator based on topology optimization, Optimization and Engineering, 19, pp. 19-38, 2018.


2017


  1. A. Takezawa, M. Kobashi, Design methodology for porous composites with tunable thermal expansion produced by multi-material topology optimization and additive manufacturing, Composites Part B: Engineering, 131, pp. 21-29, 2017.
  2. A. Takezawa, Y. Koizumi, M. Kobashi, High-stiffness and strength porous maraging steel via topology optimization and selective laser melting, Additive Manufacturing, 18, pp. 194-202, 2017.
  3. 西津卓史,谷次智弥,竹澤晃弘,米倉一男,渡邊修,北村充, トポロジー最適化と積層造形を活用したラティス構造の創出手法, 日本機械学会論文集, 83, 16-00581, 2017.
  4. 竹澤晃弘, AM技術を活かすトポロジー最適化, スマートプロセス学会誌, 6, pp. 119-124, 2017.
  5. 竹澤晃弘, ここまできたCAE 第5回 最適設計, KANRIN, 72, pp. 45-48, 2017.
  6. T. Nishizu, A. Takezawa, M. Kitamura, Eigenfrequecy-based Damage Identification Method for Non-destructive Testing Based on Topology Optimization, Engineering Optimization, 49, pp. 417-433, 2017.
  7. A. Takezawa, M. Kobashi, Y. Koizumi, M. Kitamura, Porous metal produced by selective laser melting with effective isotropic thermal conductivity close to the Hashin-Shtrikman bound, International Journal of Heat and Mass Transfer, 105, pp. 564-572, 2017.


2016


  1. Y. Koizumi, A. Okazaki, A. Chiba, T. Kato, A. Takezawa, Cellular Lattices of Biomedical Co-Cr-Mo-Alloy Fabricated by Electron Beam Melting with the Aid of Shape Optimization, Additive Manufacturing, 12, pp. 305-313, 2016.
  2. A. Takezawa, M. Daifuku, Y. Nakano, K. Nakagawa, T. Yamamoto, M. Kitamura, Topology optimization of damping material for reducing resonance response based on complex dynamic compliance, Journal of Sound and Vibration, 365, pp. 230-243, 2016.
  3. 槙原幹十朗,吉水謙司,竹澤晃弘, 振動ハーベスティングにおける発電エネルギ増加制御の研究, 日本機械学会論文集, 82, 15-00499, 2016.
  4. M. Daifuku, T. Nishizu, A. Takezawa, M. Kitamura, H. Terashita, Y. Ohtsuki, Design methodology using topology optimization for anti-vibration reinforcement of generators in a ship's engine room, Proceedings of the Institution of Mechanical Engineers - Part M: Journal of Engineering for the Maritime Environment, 230, pp. 216-226, 2016.


2015


  1. 野波諒太,北村充,竹澤晃弘,平川真一, 補強材のレイアウトを考慮した船体構造最適化に関する研究, 日本船舶海洋工学会論文集, 22, pp. 129-135, 2015.
  2. 野波諒太,北村充,竹澤晃弘, Hybrid GAを用いたスティフナーを有する大型構造物の最適化に関する研究, 日本機械学会論文集, 81, 15-00437, 2015.
  3. 西津卓史,竹澤晃弘,北村充, トポロジー最適化を用いた熱伝導制約下での熱変形最小化, 日本機械学会論文集, 81, 15-00111, 2015.
  4. 中野陽平, 竹澤晃弘, 槙原幹十朗, 北村充, エネルギー回生式セミアクティブ振動制御装置に対するSRS制約を導入した圧電アクチュエータ最適配置, 日本機械学会論文集, 81, 15-00191, 2015.
  5. A. Takezawa, M. Kobashi, M. Kitamura, Porous composite with negative thermal expansion obtained by photopolymer additive manufacturing, APL Materials, 3, 76103, 2015.
  6. K. Makihara, A. Takezawa, D. Sigeta, Y. Yamamoto, Power evaluation of advanced energy-harvester using graphical analysis, Mechanical Engineering Journal, 2, 14-00444, 2015.


2014


  1. A. Takezawa, M. Haraguchi. T. Okamoto, M. Kitamura, Cross-sectional optimization of whispering-gallery mode sensor with high electric field intensity in the detection domain, IEEE Journal of Selected Topics in Quantum Electronics, 20, 5300110, 2014.
  2. 竹澤晃弘, トポロジー最適化と金属3D プリンタを用いたポーラス材料の設計・製造, 日本機械学会誌, 117, pp. 697, 2014.
  3. 北村充, 上重嘉史,竹澤晃弘, 部材接合部の応力評価を可能とするはり・シェル要素の開発, 日本船舶海洋工学会論文集, 19, pp. 111-121, 2014.
  4. A. Takezawa, G.H. Yoon, S.H. Jeong, M. Kobashi, M. Kitamura, Structural topology optimization with strength and heat conduction constraints, Computer Methods in Applied Mechanics and Engineering, 276, pp. 341-361, 2014.
  5. M. Daifuku, A. Takezawa, M. Kitamura, H. Terashita, Y. Ohtsuki, Smooth operators iron out engine room vibrations, The Naval Architect, February 2014, pp. 62-64, 2014.
  6. S.H. Jeong, G.H. Yoon, A. Takezawa, D.H. Choi, Development of a novel phase-field method for local stress-based shape and topology optimization, Computers & Structures, 132, pp. 84-98, 2014.
  7. A. Takezawa, M. Kitamura, S.L. Vatanabe, E.C.N. Silva, Design methodology of piezoelectric energy-harvesting skin using topology optimization, Structural and Multi-disciplinary Optimization, 49, pp. 281-297, 2014.
  8. A. Takezawa, K. Makihara, N. Kogiso, M. Kitamura, Layout optimization methodology of piezoelectric transducers in energy-recycling semi-active vibration control systems, Journal of Sound and Vibration, 333, pp. 327-344, 2014.
  9. A. Takezawa, M. Kitamura, Phase field method to optimize dielectric devices for electromagnetic wave propagation, Journal of Computational Physics, 257A, pp. 216-240, 2014.
  10. A. Takezawa, M. Kitamura, Enhancement of non-resonant dielectric cloaks using anisotropic composites, AIP Advances, 4, 17106, 2014.


2013


  1. 西津卓史,竹澤晃弘,北村充, トポロジー最適化と固有振動数解析に基づく非破壊検査での損傷同定手法, 日本船舶海洋工学会論文集, 18, pp. 73-80, 2013.
  2. A. Takezawa, M. Kitamura, Sensitivity analysis and optimization of vibration modes in continuum systems, Journal of Sound and Vibration, 332, pp. 1553-1566, 2013.


2012


  1. A. Takezawa, M. Kitamura, Cross-Sectional Shape Optimization of Whispering-Gallery Ring Resonators, IEEE/OSA Journal of Lightwave Technology, 30, pp. 2776-2782, 2012.
  2. L.A.M. Mello, A. Takezawa, E.C.N. Silva, Designing piezoresistive plate-based sensors with distribution of piezoresistive material using topology optimization, Smart Materials and Structures, 21, 85029, 2012.
  3. A. Takezawa, M. Kitamura, Topology optimization of compliant circular-path mechanisms based on an aggregated linear system and singular value decomposition, International Journal for Numerical Methods in Engineering, 89, pp. 706-725, 2012.
  4. A. Takezawa, M. Kitamura, Geometrical design of thermoelectric generators based on topology optimization, International Journal for Numerical Methods in Engineering, 90, pp. 1363-1392, 2012.


2011


  1. M. Kitamura, K. Hamada, A. Takezawa, T. Uedera, Shape Optimization System of Bottom Structure of Ship Incorporating Individual Mesh Subdivision and Multi-Point Constraint, International Journal of Offshore and Polar Engineering, 21, pp. 209-215, 2011.
  2. A. Takezawa, S. Nii, M. Kitamura, N. Kogiso, Topology optimization for worst load conditions based on the eigenvalue analysis of an aggregated linear system, Computer Methods in Applied Mechanics and Engineering, 200, pp. 2268-2281, 2011.
  3. T. Yamada, K. Izui, S. Nishiwaki, M. Yoshimura, A. Takezawa, A Structural Optimization Method Incorporating Level Set Boundary Expressions Based on the Concept of the Phase Field Method, Journal of Environment and Engineering, 6, pp. 567-578, 2011.
  4. 新居悟,竹澤晃弘,北村充,小木曽望, 縮約された線形システムを用いた不確定荷重に対するロバストトポロジー最適化, 日本機械学会論文集A編, 77, pp. 472-482, 2011.


2010


  1. T. Yamada, K. Izui, S. Nishiwaki, A. Takezawa, Topology optimization method based on the level set method incorporating a fictitious interface energy, Computer Methods in Applied Mechanics and Engineering, 199, pp. 2876-2891, 2010.
  2. 竹澤晃弘, Phase-Field法による形状最適化, 計算工学, 15, pp. 20-23, 2010.
  3. A. Takezawa, S. Nishiwaki, M. Kitamura, Shape and topology optimization based on the phase field method and sensitivity analysis, Journal of Computational Physics, 229, pp. 2697-2718, 2010.
  4. 竹澤晃弘,金野有里,北村充,濱田邦裕,大槻康明, トポロジー最適化を用いたブリッジウィングの防振設計に関する研究, 日本船舶海洋工学会論文集, 10, pp. 205-212, 2010.
  5. A. Takezawa, S. Nishiwaki, M. Kitamura, E.C.N. Silva, Topology optimization for designing strain-gauge load cells: Structural and Multi-disciplinary Optimization, Structural and Multi-disciplinary Optimization, 42, pp. 387-402, 2010.
  6. 竹澤晃弘,西脇眞二,北村充, フェーズフィールド法と感度解析に基づく構造最適化, 日本機械学会論文集A編, 76, pp. 1-9, 2010.


2009


  1. 竹澤晃弘,西脇眞二,北村充, フェーズフィールド法に基づく構造最適化:ペリメータ制約効果の検証とコンプライアントメカニズム創生問題・固有振動数最大化問題への拡張, 日本機械学会論文集A編, 75, pp. 1784-1793, 2009.
  2. 岡本由仁,山田崇恭,泉井一浩,西脇眞二,竹澤晃弘, レベルセット法に基づく熱電効果を利用した熱アクチュエータ設計問題に関するトポロジー最適化, 日本計算工学会論文集, 2009, 20090024, 2009.
  3. K.V. Karottu, K. Hamada, A. Takezawa, M. Kitamura, Optimization of Block Division Using Nodal Cut Set Method, Ship Technology Research, 56, pp. 142-153, 2009.
  4. K. Hamada, A. Takezawa, M. Kitamura, K. Kanaikari, A Multi-step Design Optimization Method for Mid-ship Section, Ship Technology Research, 56, pp. 110-120, 2009.
  5. 山田崇恭,西脇眞二,泉井一浩,吉村允孝,竹澤晃弘, レベルセット法による形状表現を用いたフェーズフィールド法の考え方に基づくトポロジー最適化, 日本機械学会論文集A編, 75, pp. 550-558, 2009.


2008


  1. 竹澤晃弘,西脇眞二,北村充, トポロジー最適化法を用いたひずみゲージ式変換器構造の最適化, 日本機械学会論文集A編, 74, pp. 1459-1468, 2008.
  2. 竹澤晃弘,西脇眞二,北村充,Silva, E. C. N., 特異値分解に基づく多軸荷重変換器構造のトポロジー最適化, 日本機械学会論文集C 編, 74, pp. 2462-2470, 2008.
  3. 北村充,上寺哲也,濱田邦裕,竹澤晃弘, 部材認識機能を利用した船体構造の形状最適化システムに関する研究-船体構造二重底部の形状最適化-, 日本船舶海洋工学会論文集, 8, pp. 281-289, 2008.
  4. 竹澤晃弘,最上克哉,西脇眞二,泉井一浩,吉村允孝,北村充, 離散構造要素を用いたバンドギャップ構造の最適化, 日本機械学会論文集C編, 74, pp. 780-788, 2008.
  5. 北村充,濱田邦裕,竹澤晃弘,高木貴弘,金谷勲平,大槻康明, 独立要素分割と多点拘束を利用した船体構造二重底部の形状および寸法最適設計に関する研究, 日本船舶海洋工学会論文集, 7, pp. 89-96, 2008.


2007


  1. A. Takezawa, S. Nishiwaki, K. Izui, M. Yoshimura, Structural optimization based on topology optimization techniques using frame elements considering cross-sectional properties, Structural and Multi-disciplinary Optimization, 34, pp. 41-60, 2007.


2006


  1. A. Takezawa, S. Nishiwaki, K. Izui, M. Yoshimura, Structural Optimization Using Function-Oriented Elements to Support Conceptual Designs, ASME Journal of Mechanical Design, 128, pp. 689-700, 2006.


2005


  1. 竹澤晃弘,斉藤真大,西脇眞二,泉井一浩,吉村允孝, フレーム要素を用いたトポロジー最適化(固有振動数最大化を目的とした場合), 日本機械学会論文集C編, 71, pp. 3018-3025, 2005.
  2. 竹澤晃弘,西脇眞二,泉井一浩,吉村允孝, 離散構造要素を用いたトポロジー最適化(フレーム要素の断面主軸方向を設計変数として考慮した場合), 日本機械学会論文集C編, 71, pp. 172-179, 2005.
  3. A. Takezawa, S. Nishiwaki, K. Izui, M. Yoshimura, H. Nishigaki, Y. Tsurumi, Concurrent design and evaluation based on structural optimization using structural and function-oriented elements at the conceptual design phase, Concurrent Engineering: Research and Applications, 13, pp. 29-42, 2005.


2004


  1. 竹澤晃弘,西脇眞二,泉井一浩,吉村允孝,西垣英一,鶴見康昭, 離散化構造要素を用いたトポロジー最適化, 日本機械学会論文集C編, 70, pp. 1008-1015, 2004.