研究者詳細 - 加藤　準治

Multiscale Topology Optimization Applying FFT-Based Homogenization

Matsui, M; Hoshiba, H; Nishiguchi, K; Ogura, H; Kato, J

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING 126 巻 ( 4 ) 2025年2月

出版者・発行元：International Journal for Numerical Methods in Engineering

Advances in 3D-printing technology have enabled the fabrication of periodic microstructures that exhibit characteristic mechanical performances. In response, multiscale topology optimization, which finds the optimal design of microstructure for the macrostructure geometry and performance requirements, has become a hot topic in the field of structural optimization. While the basic optimization framework based on the homogenization theory spanning macro and microscales is available, it is computationally expensive and not easily applicable in practical scenarios such as high-resolution design for precision modeling and reliable design considering non-linearities. To address this issue, we focus on a homogenization analysis using a fast Fourier transform as an alternative approach to conventional finite element analysis and develop an optimization method with fast computing speed and low memory requirements. In this paper, we define a simple stiffness maximization problem with linear elastic materials and conduct two and three-dimensional optimization analyses to evaluate the validity and performance of the proposed method. We discuss the advantages of computational cost, the influence of the filtering process, and the appropriate setting of material contrast.

DOI： 10.1002/nme.70009

TOPOLOGY OPTIMIZATION INCLUDING CONSTRAINTS FOR UNIFORM REACTION FORCES DISTRIBUTION Open Access

Liu G., Hoshiba H., Nishiguchi K., Kato J.

Journal of Japan Society of Civil Engineers 13 巻 ( 2 ) 頁： n/a 2025年

記述言語：英語出版者・発行元：Journal of Japan Society of Civil Engineers

The present study proposes a method to maximize the stiffness of a structure considering the uniform distribution of reaction forces. The variance of the reaction forces at the Dirichlet boundary is introduced to evaluate the uniformity of the reaction forces. Several formulations for optimal topology design are provided by introducing the constraints of variance of reaction forces. Multi-objective optimization considering mean compliance minimization and uniform distribution of force transmission is proposed by dimensionless quantity description. Sensitivity analysis is then derived based on the adjoint variable method and verified by the finite differentiation approximation(FDA). Several numerical examples verify the effectiveness of the proposed method.

DOI： 10.2208/journalofjsce.24-15005

Eulerian elastoplastic simulation of vehicle structures by building-cube method on supercomputer Fugaku

トポロジー最適化技術を用いた落橋防止ブラケットの設計および評価 Open Access

北田幸夫, 黒川貴大, 吉居翔太朗, 松村寿男, 松岡勤, 加藤準治

構造工学論文集Ａ 71A 巻 ( 0 ) 頁： 59 - 69 2025年

トポロジー最適化技術を適用した落橋防止ブラケットの形状設計

北田幸夫, 黒川貴大, 松村寿男, 加藤準治

鋼構造論文集 31 巻 ( 123 ) 頁： 123_69 - 123_80 2024年9月

Nishiguchi K., Takeuchi S., Sugiyama H., Okazawa S., Katsuhara T., Yonehara K., Kojima S., Kawahara K., Hoshiba H., Kato J.

ACM International Conference Proceeding Series 頁： 145 - 153 2024年1月

担当区分：最終著者記述言語：英語掲載種別：研究論文（国際会議プロシーディングス）出版者・発行元：ACM International Conference Proceeding Series

This paper presents a novel numerical method for the elastoplastic simulation of vehicle component structures under large deformation problems, such as crash-worthiness analysis. Elastoplastic simulation of vehicle structures is essential for designing safer and more efficient vehicles, but poses significant challenges for a conventional finite element method (FEM) due to the limitation of parallel performance and mesh distortion at large deformations. To overcome these challenges, we propose using the cell-centered finite-volume method (CCFVM) in the Eulerian description and the building-cube method (BCM). The Eulerian CCFVM is a robust scheme for solving large deformations of the continuum by spatially fixed collocated Cartesian mesh, which enables a simpler data structure than conventional FEM. The BCM is a hierarchical Cartesian mesh approach in which the computational domain is divided into cubic regions with adaptive refinement suitable for parallel computing. The combination of Eulerian CCFVM and BCM enables us to perform high-fidelity simulations of vehicle component structures. We demonstrate the validity and scalability of the present method by computing a three-point bending test of vehicle component structures using different geometries, such as impact beams. The numerical results show good agreement with the reference results obtained by LS-DYNA, a commercial FEM code. We also achieve a weak scaling of 73.5% in an elastoplastic simulation of about 540 million cell mesh using 131,072 cores of supercomputer Fugaku. The proposed method is expected to contribute to the development of geometrically complex crushable structures by giga-casting and 3D printing, which are emerging manufacturing techniques for vehicle structures.

DOI： 10.1145/3635035.3635038

Generative model of three-dimensional shapes incorporating structural mechanics

Toida I., Nishiguchi K., Chiba N., Wada Y., Yokota R., Hoshiba H., Kato J.

Transactions of the Japan Society for Computational Engineering and Science 2024 巻 ( 1 ) 頁： 20241010 - 20241010 2024年

記述言語：日本語出版者・発行元：Transactions of the Japan Society for Computational Engineering and Science

We propose a deep generative model for 3D shapes that incorporates structural mechanics parameters, and a dataset of 6667 shapes created by topology optimization. Our model is based on DeepSDF, a decoder-type neural network that implicitly represents shapes as signed distance functions (SDFs). We extend DeepSDF to condition the shape generation on structural mechanics parameters, such as strain energy, load direction, volume, and dimension. We also introduce positional encoding to improve the spatial resolution of the model. Our dataset consists of various 3D shapes computed by a linear topology optimization method using the Building-Cube method. We use the strain energy as a quantitative indicator of the structural performance of the shapes. We train our model on the dataset and evaluate its ability to generate 3D shapes reflecting structural mechanics parameters. Our results indicate that our model can produce 3D shapes with high fidelity and diversity, and achieve an average reconstruction accuracy of 88.8% for the test shapes. Our model and dataset open up new possibilities for 3D shape generation and structural design using deep learning.

DOI： 10.11421/jsces.2024.20241010

量子アニーリングおよび一般化Benders分解法を用いたトポロジー最適化に関する基礎的研究

芳賀栞, 山本佳士, 野々部宏司, 村松眞由, 加藤準治

AI・データサイエンス論文集 5 巻 ( 3 ) 頁： 719 - 729 2024年

記述言語：日本語出版者・発行元：公益社団法人土木学会

本研究は，最終的に，局所最適解に陥ることなく，より良い最適解を高速で探索可能な，量子アニーリングを用いたトポロジー最適化手法の確立を目標としている．その基礎的な段階として，二次元トラスのトポロジー最適化を，量子アニーリングおよび一般化Benders分解法を用いて行う手法を実装するとともに，同手法の検証を行ったものである．特に既往の研究では実施されていない条件下で検証を実施するとともに，各種計算条件が計算結果に与える影響を評価した．検証の結果，提案手法は妥当な最適計算が可能であること，および提案手法で妥当な計算結果を得るためには，体積制約に関するペナルティ係数および最適計算過程の反復ステップにおける体積変化分の設定が特に重要であることが分かった．

DOI： 10.11532/jsceiii.5.3_719

Topology optimization of connectable microstructure using enlarged connective domain 査読有り

Matsui, M; Hoshiba, H; Kamada, H; Ogura, H; Kato, J

STRUCTURAL AND MULTIDISCIPLINARY OPTIMIZATION 66 巻 ( 8 ) 2023年8月

記述言語：英語掲載種別：研究論文（学術雑誌）出版者・発行元：Structural and Multidisciplinary Optimization

Advances in 3D-printing technology have made it possible to manufacture structures containing periodic microstructures (lattice structures) and obtain superior mechanical performance that cannot be provided with uniform solids. To achieve the best performance, microstructures with different properties should be optimally designed and arranged in the right places within the macrostructure. However, in most of the basic approaches with homogenization theory, each microstructure is analyzed and optimized separately under periodic boundaries, so connectivity with adjacent microstructures is not considered (or guaranteed). Consequently, unrealistic discontinuous structures are often obtained, resulting in poor mechanical performance and manufacturability. To address this problem, we propose a method to introduce an "enlarged connective domain" around the boundary when dividing the macrostructure into multiple domains with different microstructures in advance. The microstructure of the enlarged connective domain is formed by combining the unit cells of adjacent microstructures, which allows micro-scale connectivity to be reflected in the macrostructure. Therefore, this method improves the mechanical connectivity between microstructures through the original optimization process of maximizing the performance of the entire macrostructure. This paper demonstrates that the proposed method improves connectivity and mechanical performance by performing optimization analyses for two- and three-dimensional problems. In addition, we focus on the width (volume ratio) of the connective domain as a design parameter that specifies the degree to which connectivity is considered and discuss how to set the parameter appropriately.

DOI： 10.1007/s00158-023-03613-w

固体材料および材料界面の強度を考慮したマルチマテリアルトポロジー最適化査読有り

渡邉大貴, 干場大也, 西口浩司, 加藤準治

日本計算工学会論文集 2023 巻 ( 0 ) 頁： 20230001 - 20230001 2023年2月

担当区分：責任著者記述言語：日本語出版者・発行元：一般社団法人日本計算工学会

本研究では，固体材料と材料界面の両方の強度を考慮したマルチマテリアルトポロジー最適化手法を提案する．ヤング率と強度の複数の材料物性を同時に考慮するために，係数が等価に与えられるDMO材料内挿関数を適用する．応力制約付きトポロジー最適化の特異点問題を緩和するために，DMO材料内挿関数に適応した応力定義を提案する．さらに，材料界面を密度法ベースの手法で表現するために，2段階の密度フィルタリングを用いたgraded interfaceと呼ばれる手法を応用的に導入する．界面に引張/圧縮非対称応力規準を適用することにより，材料界面の引張の負担が軽減されるような最適化計算結果を得ることが可能となる．本研究で提案した手法の妥当性について，3つの構造モデルで検証を行う．

DOI： 10.11421/jsces.2023.20230001

FFT 均質化アルゴリズムに基づく高解像度マルチスケールトポロジー最適化査読有り

松井聖圭, 干場大也, 小倉大季, 加藤準治

土木学会論文集 79 巻 ( 15 ) 頁： n/a 2023年

記述言語：日本語掲載種別：研究論文（学術雑誌）出版者・発行元：公益社団法人土木学会

近年，積層造形技術の発展により，構造物の形状（マクロ構造）だけでなく材料の微視構造（ミクロ構造）を制御し，所望の特性を持つ材料を製造することが可能になりつつある．そのため，最適なミクロ構造を設計するマルチスケールトポロジー最適化が注目を集めているが，これを実設計に適用するには課題が多い．特に，ミクロ構造解析の高い計算コストは，高解像度での解析や非線形問題への拡張の妨げとなっている．本研究は，これを解決するため，高速フーリエ変換を用いた均質化手法に着目し，より高速で省メモリな新しい最適化手法を開発する．線形弾性材料を想定した剛性最大化問題を対象に，従来手法との比較に基づく性能検証を行い，提案手法の妥当性を確認するとともに，計算コスト削減への効果について検証する．

DOI： 10.2208/jscejj.22-15026

脆性–延性複合構造物のトポロジー最適化のための拡張 SIMP 材料モデルおよび感度解析法の提案査読有り

藤原睦樹, 干場大也, 西口浩司, 加藤準治

土木学会論文集 79 巻 ( 15 ) 頁： n/a 2023年

担当区分：責任著者記述言語：日本語掲載種別：研究論文（学術雑誌）出版者・発行元：公益社団法人土木学会

高強度かつ高靭性な構造は工学的に理想的な構造である．一部の複合構造物では，延性材料と脆性材料という性質の異なる 2 種類の材料を組み合わせることで，構造全体で高い強度と靭性を両立している．本研究では，そのような複合構造物を対象として，強度および靭性を最大化するためのトポロジー最適化手法を提案する．この手法は，強度を担う脆性損傷材料と靭性を担う von Mises 弾塑性材料からなる 2 相構造を想定し，数理構造の異なる 2 つの材料構成則を部分的に組み合わせた特殊な材料表現法を用いるものである．本論文では，本手法に関する一連の定式化について記述し，数例の数値計算結果を示す．

DOI： 10.2208/jscejj.22-15028

トポロジー最適化技術を用いた仮設ブラケットの設計及び評価査読有り

北田幸夫, 黒川貴大, 長崎怜, 松村寿男, 中村将章, 加藤準治

構造工学論文集Ａ 69A 巻 ( 0 ) 頁： 26 - 34 2023年

Large-Scale Topology Optimization for Unsteady Flow Using the Building-Cube Method 査読有り

Katsumata R., Nishiguchi K., Shimada T., Hoshiba H., Kato J.

Transactions of the Japan Society for Computational Engineering and Science 2023 巻 ( 0 ) 頁： 20230007 - 20230007 2023年

記述言語：日本語掲載種別：研究論文（学術雑誌）出版者・発行元：Transactions of the Japan Society for Computational Engineering and Science

In recent years, topology optimization methods have been applied not only to structural problems but also to fluid flow problems. Most of the previous studies assume steady-state flow. In contrast, this paper focuses on topology optimization for unsteady flow, which is more general from an engineering point of view. However, unsteady flow topology optimization involves solving the governing and adjoint equations of a time-evolving system, which requires a huge computational cost for topology optimization with a fine mesh. Therefore, we propose a large-scale unsteady flow topology optimization based on the building-cube method (BCM), which is suitable for massively parallel computing. BCM is one of the hierarchical Cartesian mesh methods and is confirmed to have very good scalability. The governing equations are discretized by a cell-centered finite volume method based on the BCM. The objective sensitivity is obtained by the continuous adjoint method. Several numerical examples are demonstrated to discuss its applicability to large-scale computations.

DOI： 10.11421/jsces.2023.20230007

固体材料および界面物性を考慮したマルチマテリアルトポロジー最適化査読有り

渡邉大貴, 干場大也, 西口浩司, 加藤準治

日本計算工学会論文集 2022 巻 ( 0 ) 頁： 20220017 - 20220017 2022年11月

担当区分：責任著者記述言語：日本語掲載種別：研究論文（学術雑誌）出版者・発行元：一般社団法人日本計算工学会

本研究では，固体材料と界面の物理的性質を考慮したマルチマテリアルトポロジー最適化手法を提案する．材料界面を定義するために，Helmholtz型偏微分方程式に基づいた拡張2段階フィルタリングが導入される．さらに，このアプローチに基づき界面領域の幅を制御することができる．マルチマテリアルトポロジー最適化で生じる問題の非凸性に対処するため，固体材料の材料体積比が相互に独立な材料内挿関数を使用し，これにより構成材料の可換性を担保させた．2つの異なる構造モデルにおいて，平均コンプライアンスの最小化問題の最適化計算を行った．この問題を解くために，目的関数と制約条件の感度を導出した．いくつかの数値例を通して，本提案手法の有用性を示す．

DOI： 10.11421/jsces.2022.20220017

非定常熱伝導問題における二相材料トポロジー最適化およびその性能検証査読有り

高荒圭佑, 干場大也, 西口浩司, 加藤準治

日本計算工学会論文集 2022 巻 ( 0 ) 頁： 20220007 - 20220007 2022年8月

担当区分：責任著者記述言語：日本語掲載種別：研究論文（学術雑誌）出版者・発行元：一般社団法人日本計算工学会

熱伝導問題に対するトポロジー最適化の分野では，理論的な扱いやすさから，大抵は定常熱伝導問題を仮定している．しかし，鋳造金型や電子機器の放熱部品など，温度の空間分布だけでなく，その時間的推移も重要な設計問題では，非定常状態を考慮したトポロジー最適化手法が必要となる．このような背景から，本研究では，非定常熱伝導問題を扱いながら，目標とする時間・空間における温度を評価するような特殊な目的関数を用い，これを最小化する最適化問題を設定する．この最適化問題を，勾配情報に基づいた最適化アルゴリズムを用いて解く．またその際重要となる感度の精度検証を行う．最後に，提案手法の性能と非定常熱問題の一般的な問題について，一連の数値例を通して議論する．

DOI： 10.11421/jsces.2022.20220007

Two-scale topology optimization for transient heat analysis in porous material considering the size effect of microstructure 招待有り

Sukulthanasorn, N; Hoshiba, H; Nishiguchi, K; Kurumatani, M; Fleischhauer, R; Ushijima, K; Kaliske, M; Terada, K; Kato, J

STRUCTURAL AND MULTIDISCIPLINARY OPTIMIZATION 65 巻 ( 7 ) 2022年7月

記述言語：日本語掲載種別：研究論文（学術雑誌）出版者・発行元：Structural and Multidisciplinary Optimization

This paper presents a two-scale topology optimization framework for determining the optimal microstructure in porous material under transient heat conduction and transfer. The new optimization model, which can consider the surface area directly from microstructure topology as the size-dependent term, is introduced to enhance the heat transfer performance. In more detail, a homogenization method capable of considering the size-dependent microscopic heat transfer effect is adopted to express the microscopic material responses. A well-known material interpolation, referred to as the SIMP approach, and the design-dependent linear function are used for interpolating intermediate material properties. The minimal transient heat compliance is chosen as an objective function in this optimization problem. For the sensitivity analysis, a coupled-adjoint variable method is adopted to derive transient sensitivity formulation. The analysis shows that the proposed topology optimization model captures not only the transient heat but also the size effect of the microstructure in a transient heat analysis in porous material.

DOI： 10.1007/s00158-022-03257-2

Heat-transfer and pressure drop characteristics of micro-lattice materials fabricated by selective laser metal melting technology 査読有り国際共著

Takarazawa, S; Ushijima, K; Fleischhauer, R; Kato, J; Terada, K; Cantwell, WJ; Kaliske, M; Kagaya, S; Hasumoto, S

HEAT AND MASS TRANSFER 58 巻 ( 1 ) 頁： 125 - 141 2022年1月

記述言語：英語掲載種別：研究論文（学術雑誌）出版者・発行元：Heat and Mass Transfer/Waerme- und Stoffuebertragung

This paper describes the findings of a numerical and experimental study on the heat transfer coefficient and pressure drop in micro-lattice blocks fabricated by selective laser metal melting and subjected to forced air convection. In particular, the influence of the unit-cell topology on the thermofluid performance of the lattice structure is examined in detail. In the present numerical study, five lattice block designs (BCC, BCCZ, FCC, FCCZ and F2BCC) are considered for investigation. Regarding effective thermal conductivity, the FCC and FCCZ lattices offer the best performance among the various lattices. In terms of heat transfer capacity per unit mass, the BCC and BCCZ lattices exhibit superior characteristics relative to the other lattices. Also, F2BCC lattice offers the lowest pressure loss for a given relative density. In addition, it is found that the heat transfer coefficients obtained by experiment lie between two numerical results having different strut diameter, which is due to the fact that the equivalent strut diameter in the as-manufactured samples is greater, due to the present of additional metal particles fused onto the surfaces of some struts. Moreover, it is found from our experimental investigation that the heat transfer coefficient h for the BCCZ is approximately 1.3 times higher than that for the BCC lattice for the same pressure loss.

DOI： 10.1007/s00231-021-03083-0

Transient thermal porous structure designed by two-scale concurrent topology optimization 査読有り

Sukulthanasorn N., Kurumatani M., Nishiguchi K., Kato J., Terada K.

Transactions of the Japan Society for Computational Engineering and Science 2022 巻 ( 0 ) 頁： 20220004 - 20220004 2022年

記述言語：英語掲載種別：研究論文（学術雑誌）出版者・発行元：Transactions of the Japan Society for Computational Engineering and Science

The present paper proposes the novel design framework for thermal porous structure based on two-scale concurrent topology optimization subject to transient heat analysis. The optimization model considers the heat transfer through the microstructure surface to enhance the heat dissipation performance design. In particular, a well-known homogenization method incorporated the size-dependent term of microscopic heat transfer is exploited to obtain the material properties. Meanwhile, the unsteady-state heat condition is applied to the macrostructure. Furthermore, the heat compliance objective function and the derived analytical sensitivity formulations are adopted to determine the two-scale optimal topologies. As a numerical result, the concurrent design of micro-and macrostructures show the remarkable transient effect. It is also indicated that the microstructure size and the volume constraint are significant parameters for the design of heat performance.

DOI： 10.11421/jsces.2022.20220004

非定常熱・流体問題のトポロジー最適化

高荒圭佑, 干場大也, 高瀬慎介, 西口浩司, 加藤準治

理論応用力学講演会講演論文集 66 巻 ( 0 ) 頁： 27 2022年

記述言語：日本語出版者・発行元：日本学術会議「機械工学委員会・土木工学・建築学委員会合同IUTAM分科会」

トポロジー最適化は，数理的な手法に基づいて所望の性能を最大化する構造を導く手法であり，様々な設計問題へ応用されている．中でも熱単一場のトポロジー最適化の研究は，基礎方程式の単純さから，これまでに多くの研究がなされている．近年では，単一場のみならず対流熱伝達を考慮した熱・流体連成問題の研究が盛んである．しかし，これら先行研究の多くは，定常流れを対象としている．実際の工学設計では，非定常的な流れ場や温度分布の時間推移を考慮すべき場合がほとんどである．そこで本研究では，非定常の熱・流体トポロジー最適設計法を開発することを目的とする．手法としては，密度法による材料表現を基本として，有限要素法における非定常熱・流体問題の支配方程式を用いて既存手法を拡張する．また，増分解析をもって解かれる時間依存の感度解析の精度および最適化計算のパフォーマンスについて数値的に検証する．

DOI： 10.11345/japannctam.66.0_27

Building-cube法を用いた大規模非定常流トポロジー最適化

勝又稜平, 西口浩司, 嶋田宗将, 干場大也, 加藤準治

理論応用力学講演会講演論文集 66 巻 ( 0 ) 頁： 25 2022年

記述言語：日本語出版者・発行元：日本学術会議「機械工学委員会・土木工学・建築学委員会合同IUTAM分科会」

近年，トポロジー最適化手法は，構造問題だけでなく，流体問題にも採用されるようになってきている．しかし，非定常流に対するトポロジー最適化では，特に高レイノルズ数の流れに対しては詳細なメッシュ分割が必要となり，膨大な計算コストが必要となる．一方，近年の並列計算機の指数関数的性能向上により，高解像度の計算メッシュを用いた超並列計算が可能となっている．そこで我々は，超並列計算に適したbuilding-cube法（BCM）を用いた非定常非圧縮性流れトポロジー最適化手法を提案する．トポロジー最適化における非定常Navier-Stokes方程式は，BCMに基づくセル中心有限体積法により離散化する．目的汎関数の感度は随伴変数法に基づく連続的感度解析によって求める．

DOI： 10.11345/japannctam.66.0_25

オイラー型有限体積法による流体と粘性-超弾性体の連成解析

西口浩司, 竹内秀輔, 嶋田宗将, 勝又稜平, 干場大也, 加藤準治

理論応用力学講演会講演論文集 66 巻 ( 0 ) 頁： 15 2022年

記述言語：日本語出版者・発行元：日本学術会議「機械工学委員会・土木工学・建築学委員会合同IUTAM分科会」

本研究では，マーカー粒子を用いたオイラー型セル中心有限体積法による粘性-超弾性解析手法を提案することを目的とする．本手法の有用性を示すため，粘弾性体（熱可塑性エラストマー）からなる衝撃吸収構造と空気の連成解析に適用する．

DOI： 10.11345/japannctam.66.0_15

Building-cube法を用いた非定常・非圧縮性流体の大規模トポロジー最適化

非定常熱・流体連成問題のトポロジー最適化

高荒圭佑, 干場大也, 高瀬慎介, 西口浩司, 加藤準治

最適化シンポジウム講演論文集 2022.14 巻 ( 0 ) 頁： U00045 2022年

勝又稜平, 西口浩司, 嶋田宗将, 干場大也, 加藤準治

最適化シンポジウム講演論文集 2022.14 巻 ( 0 ) 頁： U00058 2022年

FFT均質化アルゴリズムに基づく弾塑性マルチスケールトポロジー最適化の基礎的検討

松井聖圭, 干場大也, 小倉大季, 西口浩司, 加藤準治

最適化シンポジウム講演論文集 2022.14 巻 ( 0 ) 頁： U00052 2022年

A new constraint on principal stress direction variance to improve load bearing capacity

Kamada, H; Kato, J; Uozumi, H; Kikawa, K

STRUCTURAL AND MULTIDISCIPLINARY OPTIMIZATION 64 巻 ( 5 ) 頁： 3209 - 3225 2021年11月

記述言語：日本語出版者・発行元：Structural and Multidisciplinary Optimization

The present study addresses a simplified topology optimization method to improve load bearing capacity. Topology optimization taking account of structurally nonlinear and complex behavior is an important topic from the viewpoint of mechanics. However, most methodologies require complex analytical derivation of sensitivity analysis and high computational cost to obtain the optimal solution. In light of this, we propose a practical design method employing the principal direction of Cauchy stress and the directional statistics, to improve load bearing capacity indirectly with much lower computational cost than those based on complex nonlinear structural analysis. Finally, we discuss setting of optimization problems, and demonstrate the accuracy and performance of the proposed method with a series of numerical examples.

DOI： 10.1007/s00158-021-03079-8

Robust topology optimization based on finite strain considering uncertain loading conditions

Nishino, T; Kato, J

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING 122 巻 ( 6 ) 頁： 1427 - 1455 2021年3月

記述言語：日本語出版者・発行元：International Journal for Numerical Methods in Engineering

The present study proposes a method of robust topology optimization assuming uncertainties in the magnitude and direction of loads applied to a geometrically nonlinear structure. The objective function is the sum of the expected value and the standard deviation of end-compliance of a structure with a compressible Neo-Hookean hyperelasticity. In this study, quadratic approximation of the end-compliance with respect to random variables is employed to reduce computational cost. To ensure its accuracy, a complete analytical formulation is derived, and the performance and limitation of the proposed method are deeply discussed. The performance of the proposed method is verified and its numerical examples emphasize the importance of considering geometrical nonlinearity to obtain robust structures with respect to uncertainties of loading conditions. Finally, we have obtained a finding that the optimized network system consisting of thin members plays a significant role in the improvement of robustness of structures.

DOI： 10.1002/nme.6584

速度場の界面不連続性を考慮した陰的オイラー型構造-流体連成解析

西口浩司, 嶋田宗将, 干場大也, 加藤準治

計算力学講演会講演論文集 2021.34 巻 ( 0 ) 頁： 228 2021年

トポロジー最適化による構造強度向上を目的とした主応力方向分散制約の提案査読有り

鎌田浩基, 加藤準治, 京谷孝史

日本計算工学会論文集 2020 巻 ( 0 ) 頁： 20200006 - 20200006 2020年4月

Finite thermo-elastic decoupled two-scale analysis 査読有り Open Access

Fleischhauer, R; Thomas, T; Kato, J; Terada, K; Kaliske, M

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING 121 巻 ( 3 ) 頁： 355 - 392 2020年2月

記述言語：英語掲載種別：研究論文（学術雑誌）出版者・発行元：International Journal for Numerical Methods in Engineering

Engineering structures are often characterized by different structural properties, depending on the length scale under consideration. Fiber reinforced composites are determined, eg, by a heterogeneous microstructure, but are sufficiently described by homogeneous characteristics at their macroscopic level. Moreover, different loading situations, eg, of thermal or mechanical nature, require the consideration of multiphysical equilibrium states. The challenging engineering task is the computation of the effective material properties of these different loading scenarios. The contribution at hand introduces a finite thermo-elastic two-scale analysis, where the effective macroscopic material properties are computed in a decoupled manner with respect to the different length scales.

DOI： 10.1002/nme.6212

数理的均質化法に基づく材料微視構造のトポロジー最適（特集：モルフォロジクス：形がつくる新しいセラミックスと機能）

加藤準治

日本セラミックス協会誌 ( 55 ) 頁： 377-382 2020年

弾塑性挙動を考慮したトポロジー最適化における解析的感度導出法とその後の展開

加藤準治

計算工学 25 巻 ( 1 ) 頁： 3-7 2020年

数理的均質化法に基づく材料微視構造のトポロジー最適

加藤準治

日本セラミックス協会誌 55 巻頁： 377 - 382 2020年

Microscopic design and optimization of hydrodynamically lubricated dissipative interfaces 査読有り

Cakal, BA; Temizer, I; Terada, K; Kato, J

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING 120 巻 ( 2 ) 頁： 153 - 178 2019年10月

記述言語：英語掲載種別：研究論文（学術雑誌）出版者・発行元：International Journal for Numerical Methods in Engineering

A homogenization-based topology optimization framework is developed, which can endow hydrodynamically lubricated interfaces with a micro-texture, to achieve optimal macroscopic responses by addressing both dissipative and nondissipative physics at the interface. With respect to the homogenization aspects of the problem, the thermodynamic consistency of the two-scale formulation is explicitly analyzed and verified. With respect to the topology optimization aspects, a variational approach to sensitivity analysis is pursued. Subsequently, these are employed in micro-texture design studies, which address microscopic and macroscopic objectives. The influence of dissipation on the optimization results is demonstrated through extensive numerical investigations, which also highlight the importance of working in a sufficiently flexible design space that can deliver nearly optimal micro-texture geometries.

DOI： 10.1002/nme.6129

グランドストラクチャ法に基づくサンドイッチラティス梁の最適化設計に関する研究査読有り

小池雄介, 牛島邦晴, 加藤準治

日本計算工学会論文集 2019 巻 ( 0 ) 頁： 20190006 - 20190006 2019年4月

記述言語：日本語掲載種別：研究論文（学術雑誌）出版者・発行元：一般社団法人日本計算工学会

本研究では，グランドストラクチャ法を利用し，実際の粉末金属積層装置で造形できるラティス構造の最適化設計について検討した．本研究の特徴は，実際に造形装置を使用した際，造形可能な範囲で梁の断面積を変化させるアルゴリズムを構築したこと，また，造形しやすいユニットセル（本論文ではBCCとf2BCC）を用いて最適化を行った点が挙げられる．また，設計変数の目的関数に関する感度計算において，計算効率を上げるため，有限差分法で用いられるコンプライアンスの感度の代わりに，設計変数の剛性マトリックスへの寄与のみに注目して計算を行った．得られた最適形状は，初期形状の違いに関わらず，ほぼ同様の高剛性を示している．検討に用いた3種類のユニットセルで比較すると，様々な体積制約の下で最適化計算を行った結果，f2BCCのユニットを持つラティス構造が，一番すぐれた剛性を示すことが分かった．さらに，得られた最適化形状を用いてSLM装置で積層造形した結果，設計通りの直径の分布を持たせたラティスサンドイッチ構造を造形できた．

DOI： 10.11421/jsces.2019.20190006

幾何学的非線形性と荷重条件の不確かさを考慮したトポロジー最適化査読有り

西野崇行, 加藤準治, 京谷孝史

日本計算工学会論文集 2019 巻 ( 0 ) 頁： 20190004 - 20190004 2019年4月

記述言語：日本語掲載種別：研究論文（学術雑誌）出版者・発行元：一般社団法人日本計算工学会

本研究は，幾何学的非線形挙動を有する構造に対して，外荷重の方向が不確かである場合を想定し，そのロバスト性を向上させるためのトポロジー最適設計法を提案するものである．ここでは，エンドコンプライアンスの期待値と標準偏差の和を目的関数とするが，低い計算コストで精度よく期待値と標準偏差の推定を行うため，エンドコンプライアンスの2次近似式を用いる手法を提案する．そして，近似式による推定値の精度検証およびいくつかの最適化計算例を示し，本手法の妥当性を検証する．

DOI： 10.11421/jsces.2019.20190004

インフィル構造の応力制約付きトポロジー最適化

鎌田浩基, 干場大也, 加藤準治, 京谷孝史

土木学会論文集Ａ２（応用力学） 75 巻 ( 1 ) 頁： 68 - 85 2019年

記述言語：日本語出版者・発行元：公益社団法人土木学会

近年，特殊な機能や特性をもつ多孔質構造の研究開発が盛んに行われている．中でもインフィル構造は，高い座屈性能やロバスト性を潜在的に有することが実験により確認され，その基礎的な最適設計法の開発も進められている．しかし，既往の研究では応力制約などの実用に向けた取り組みはまだ報告されていない．そこで本研究では剛性最大化問題に対して局所的な体積制約と，p-ノルムの考え方に基づいた応力制約を最適化問題に加えることで，応力集中を回避するインフィル構造のトポロジー最適化問題を取り扱う．それに加えて，インフィル構造の最適化問題を解くにあたって生じる特有の問題を解決するための手法として，可変的な影響半径という新しい手法を提案する．また本研究で提案する手法に関し，いくつかの数値計算例を用いてその妥当性の検証を行う．

DOI： 10.2208/jscejam.75.68

OPTIMAL DESIGN OF LATTICE STRUCTURE CONSIDERING CONSTRAINTS THROUGH ADDITIVE MANUFACTURING PROCESS

Koike, Y; Ushijima, K; Kato, J

SECOND INTERNATIONAL CONFERENCE ON SIMULATION FOR ADDITIVE MANUFACTURING (SIM-AM 2019) 頁： 205 - 214 2019年

Optimal design of lattice structure considering constraints through additive manufacturing process Open Access

Koike Y., Ushijima K., Kato J.

2nd International Conference on Simulation for Additive Manufacturing, Sim-AM 2019 頁： 205 - 214 2019年

出版者・発行元：2nd International Conference on Simulation for Additive Manufacturing, Sim-AM 2019

In this research, an optimization design of the lattice structure is investigated, which is based on the ground structure method. In recent years, as a result of rapid development of additional manufacturing technology, it has become possible to manufacture complicated shapes including periodic lattice structure. However, in real metal lattice samples, geometric imperfections may exist in every unit because of the stochastic influence of feasible processing path. In this study, a new ground structure method which does not leave elements with small cross sectional area was proposed. In particular, the effect of geometric constraints caused by additive manufacturing techniques on optimized results are discussed based on the robust topology optimization combining perturbation methods for quantifying uncertainty. In the end, a robust topology optimization was also discussed as a problem to minimize expected value and standard deviation of compliance.

複合材料の弾塑性挙動を考慮したマルチスケールトポロジー最適化査読有り

干場大也, 小川竣, 加藤準治, 京谷孝史

日本計算工学会論文集 2018 巻 ( 0 ) 頁： 20180015 - 20180015 2018年11月

記述言語：日本語掲載種別：研究論文（学術雑誌）出版者・発行元：一般社団法人日本計算工学会

本研究は, 分離型マルチスケール解析に基づいて材料の弾塑性力学挙動を考慮したミクロ構造のトポロジー最適化法を提案するものである. ここでは, ミクロ構造の材料体積量を制約した上で, マクロ構造のエネルギー吸収性能の最大化を目指すものである. ミクロの材料構成則は等方性のvon Mises弾塑性材料モデルで, マクロの構成則はHillの異方性弾塑性材料モデルを使用した. この研究では, 著者らが提案した感度解析法を拡張してマルチスケールトポロジー最適化に適用するもので, 条件付きではあるものの随伴ベクトルを計算せずに低計算コストで高精度の感度を得る方法を提案している. 最後にいつくかの数値計算例を示してその精度検証を実施し, 高精度の感度が得られることを確認した.

DOI： 10.11421/jsces.2018.20180015

その他リンク： https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-16J02523/

割線剛性を用いた簡便なマルチスケール解析による膨張性地山のトンネル安定性評価査読有り

劉暁東, 鵜之沢均, 加藤準治, 京谷孝史

日本計算工学会論文集 2018年10月

Current and future trends in topology optimization for additive manufacturing 査読有り

Jikai Liu, Andrew T. Gaynor, Shikui Chen, Zhan Kang, Krishnan Suresh, Akihiro Takezawa, Lei Li, Junji Kato, Jinyuan Tang, Charlie C. L. Wang, Lin Cheng, Xuan Liang, Albert. C. To

Structural and Multidisciplinary Optimization 57 巻 ( 6 ) 頁： 2457 - 2483 2018年6月

記述言語：英語掲載種別：研究論文（学術雑誌）出版者・発行元：Springer Verlag

Manufacturing-oriented topology optimization has been extensively studied the past two decades, in particular for the conventional manufacturing methods, for example, machining and injection molding or casting. Both design and manufacturing engineers have benefited from these efforts because of the close-to-optimal and friendly-to-manufacture design solutions. Recently, additive manufacturing (AM) has received significant attention from both academia and industry. AM is characterized by producing geometrically complex components layer-by-layer, and greatly reduces the geometric complexity restrictions imposed on topology optimization by conventional manufacturing. In other words, AM can make near-full use of the freeform structural evolution of topology optimization. Even so, new rules and restrictions emerge due to the diverse and intricate AM processes, which should be carefully addressed when developing the AM-specific topology optimization algorithms. Therefore, the motivation of this perspective paper is to summarize the state-of-art topology optimization methods for a variety of AM topics. At the same time, this paper also expresses the authors’ perspectives on the challenges and opportunities in these topics. The hope is to inspire both researchers and engineers to meet these challenges with innovative solutions.

DOI： 10.1007/s00158-018-1994-3

Multi-phase field topology optimization of polycrystalline microstructure for maximizing heat conductivity 査読有り

Junji Kato, Shun Ogawa, Toshiki Ichibangase, Tomohiro Takaki

Structural and Multidisciplinary Optimization 57 巻 ( 5 ) 頁： 1937 - 1954 2018年5月

掲載種別：研究論文（学術雑誌）

© 2018, Springer-Verlag GmbH Germany, part of Springer Nature. The present study proposes multi-scale topology optimization for polycrystalline microstructures applying a multi-phase field method. The objective function is to maximize the heat compliance of macrostructure and the equality constraint is the material volume of constituents in an alloy consisting of two components with different heat conductivity. Two-scale steady-state heat conduction problem based on a homogenization method is conducted. The Allen-Cahn non-conserved time evolution equation with the additional volume constraint scheme is employed as the optimization strategy for updating the crystal configuration. In the time evolution equation, sensitivities of objective function with respect to phase-field variables are considered to relate topology optimization to the multi-phase field method. It is verified from a series of numerical examples that the proposed method has great potential for the development of material design underlying polycrystalline structure.

DOI： 10.1007/s00158-018-1965-8

Two-scale topology optimization for composite plates with in-plane periodicity 査読有り

Shinnosuke Nishi, Kenjiro Terada, Junji Kato, Shinji Nishiwaki, Kazuhiro Izui

International Journal for Numerical Methods in Engineering 113 巻 ( 8 ) 頁： 1164 - 1188 2018年2月

記述言語：英語掲載種別：研究論文（国際会議プロシーディングス）出版者・発行元：John Wiley and Sons Ltd

This study proposes a two-scale topology optimization method for a microstructure (an in-plane unit cell) that maximizes the macroscopic mechanical performance of composite plates. The proposed method is based on the in-plane homogenization method for a composite plate model in which the macrostructure is modeled using thick plate theory and the microstructures are three-dimensional solids. Macroscopic plate characteristics such as homogenized plate stiffnesses and generalized thermal strains are evaluated through the application of numerical plate tests applied to an in-plane unit cell. To handle large rotations of the composite plates, we employ a co-rotational formulation that facilitates working with the two-scale plate model formulated within a small strain framework. Two types of objective functions are tested in the presented optimization problems: one minimizes the macroscopic end compliance to maximize the macroscopic plate stiffness, whereas the other maximizes components of a macroscopic nodal displacement vector. Analytical sensitivities are derived based on in-plane homogenization formulae so that a gradient-based method can be employed to update the topology of in-plane unit cells. Several numerical examples are presented to demonstrate the proposed method's capability related to the design of optimal in-plane unit cells of composite plates. Copyright © 2017 John Wiley &amp
Sons, Ltd.

DOI： 10.1002/nme.5545

Micro-macro concurrent topology optimization for nonlinear solids with a decoupling multiscale analysis 査読有り

Junji Kato, Daishun Yachi, Takashi Kyoya, Kenjiro Terada

International Journal for Numerical Methods in Engineering 113 巻 ( 8 ) 頁： 1189 - 1213 2018年2月

記述言語：英語掲載種別：研究論文（国際会議プロシーディングス）出版者・発行元：John Wiley and Sons Ltd

The present study proposes a method of micro-macro concurrent topology optimization for a two-phase nonlinear solid to minimize the end compliance of its macrostructure undergoing large deformation. To reduce the computational costs to solve a 2-scale boundary value problem under geometrically nonlinear setting, we use the so-called method of decoupling multiscale structural analysis, in which the microscopic and macroscopic boundary value problems are decoupled in the homogenization process. An isotropic hyperelasticity model is used for the constitutive model for microstructures, while an orthotropic one is assumed to represent the macroscopic material behavior. Owing to this decoupling framework, the micro-macro concurrent optimization problem can be split into 2 individual problems at the microscale and macroscale for the sake of algorithmic simplicity. Also, a 2-scale adjoint sensitivity analysis can be performed within the framework of computational homogenization. It is verified from a series numerical examples that the proposed method is capable of computing the optimal structures at both microscale and macroscale, according to the level of applied load.

DOI： 10.1002/nme.5571

弾塑性挙動を考慮したインフィル構造最適化に関する検証

鎌田浩基, 干場大也, 加藤準治, 京谷孝史

最適化シンポジウム講演論文集 2018.13 巻 ( 0 ) 頁： 113 2018年

多孔質充填構造のトポロジー最適化に関する研究

鎌田浩基, 干場大也, 加藤準治, 京谷孝史

計算力学講演会講演論文集 2018.31 巻 ( 0 ) 頁： 312 2018年

荷重条件の不確かさと幾何学的非線形性を考慮したトポロジー最適化

西野崇行, 干場大也, 加藤準治, 京谷孝史

計算力学講演会講演論文集 2018.31 巻 ( 0 ) 頁： 277 2018年

積層造形下での制約を考慮したラティス構造の最適化設計

小池雄介, 牛島邦晴, 加藤準治

計算力学講演会講演論文集 2018.31 巻 ( 0 ) 頁： 134 2018年

振動抑制を目的としたトポロジー最適化

遠藤拓真, 干場大也, 加藤準治, 京谷孝史

計算力学講演会講演論文集 2018.31 巻 ( 0 ) 頁： 291 2018年

Micro-texture design and optimization in hydrodynamic lubrication via two-scale analysis 査読有り

A. Waseem, I. Temizer, J. Kato, K. Terada

STRUCTURAL AND MULTIDISCIPLINARY OPTIMIZATION 56 巻 ( 2 ) 頁： 227 - 248 2017年8月

記述言語：英語掲載種別：研究論文（学術雑誌）出版者・発行元：SPRINGER

A novel computational surface engineering framework is developed to design micro-textures which can optimize the macroscopic response of hydrodynamically lubricated interfaces. All macroscopic objectives are formulated and analyzed within a homogenization-based two-scale setting and the micro-texture design is achieved through topology optimization schemes. Two non-standard aspects of this multiscale optimization problem, namely the temporal and spatial variations in the homogenized response of the micro-texture, are individually addressed. Extensive numerical investigations demonstrate the ability of the framework to deliver optimal micro-texture designs as well as the influence of major problem parameters.

DOI： 10.1007/s00158-017-1713-5

Phase-field topology optimization model that removes the curvature effects 査読有り

Tomohiro Takaki, Junji Kato

Mechanical Engineering Journal 2017年4月

記述言語：英語掲載種別：研究論文（学術雑誌）出版者・発行元：一般社団法人日本機械学会

The conventional phase-field topology optimization (PFTO) models minimize not only the objective function but also the interface energy. In the present study, a new PFTO model, which minimizes only the objective function, is developed by removing the curvature effect from the conventional PFTO model. Simulations of elastic strain energy minimization under a constant-volume constraint condition of a cantilever are performed using the developed and conventional PFTO models. From the simulation results, we confirm that the developed PFTO model that removes the curvature effects can efficiently optimize only the objective function.

DOI： 10.1299/mej.16-00462

Multiscale stability analysis of a tunnel in swelling rockmass applying secant stiffness

Xiaodong Liu, Junji Kato, Takashi Kyoya

4th ISRM Young Scholars Symposium on Rock Mechanics, YSS 2017 2017-May 巻頁： 284 - 287 2017年

掲載種別：研究論文（国際会議プロシーディングス）

Damage of tunnels often occurs in Japan caused by swelling smectite rockmass. For an effective countermeasure against the damage, mechanical interaction between tunnel lining and swelling rock mass are analyzed by a two-scale analysis based on a homogenization theory in this study. In the microscopic scale, swelling of smectite minerals and damage process of surrounding intact rocks induced by the swelling of smectite minerals are analyzed by a 3D continuous damage model. This microscopic analysis provides the averaged volumetric change and the damaged macroscopic stiffness of the representative volumetric element (RVE) of rock mass. In the macroscopic scale, therefore, stress distribution within/around the tunnel lining can be reasonably analyzed by using the averaged secant stiffness and its volumetric strain of the RVE. The mechanical interaction between the tunnel lining and swelling rock mass is discussed and examined as some case studies are carried out.