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

Open Access

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