Faculty Profiles - KATO Junji

Multiscale Topology Optimization Applying FFT-Based Homogenization

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

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING Vol. 126 ( 4 ) 2025.2

Publisher：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 Guangwei, HOSHIBA Hiroya, NISHIGUCHI Koji, KATO Junji

Journal of JSCE Vol. 13 ( 2 ) page： n/a 2025

Language：English Publisher：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

Design and evaluation of bridge collapse protection brackets using topology optimization techniques Open Access

Kitada Yukio, Kurokawa Takahiro, Yoshii Shotaro, Matsumura Toshio, Matsuoka Tsutomu, Kato Junji

Journal of Structural Engineering, A Vol. 71A ( 0 ) page： 59 - 69 2025

Language：Japanese Publisher：Japan Society of Civil Engineers

A lightweight and highly rigid shape for a bridge collapse protection bracket was developed using topology optimization. The design was refined for compatibility, manufacturability, and cost-effectiveness, resulting in a commercially viable product. This paper aims to verify the final design, demonstrating a balance between weight reduction and performance. A full-scale product was fabricated using a 3D sand mold layering machine based on the final design, and its performance was validated through experimentation. A comparative analysis with computational results also confirmed the performance and safety of the final design.

DOI： 10.11532/structcivil.71a.59

Open Access

SHAPE DESIGN OF BRIDGE COLLAPSE PROTECTION BRACKET APPLYING TOPOLOGY OPTIMIZATION TECHNIQUES

KITADA Yukio, KUROKAWA Takahiro, MATSUMURA Toshio, KATO Junji

Kou kouzou rombunshuu Vol. 31 ( 123 ) page： 123_69 - 123_80 2024.9

Language：Japanese Publisher：Japanese Society of Steel Construction

A lightweight and exceptionally rigid cast metal configuration has been carrying out technological development through the implementation of a topology optimization technique for a bracket designed for a bridge collapse prevention system. Nonetheless, the configuration derived from rudimentary unitary analysis did not result in optimal performance when subjected to combined analysis replicating the installation state. Consequently, for the purpose of enhancing performance, formulated an optimization method encompassing meticulously devised analytical conditions. The configuration obtained through this method is approximately 30% lighter than the conventional shape, while maintains equivalent or heightened rigidity.

DOI： 10.11273/jssc.31.123_69

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

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 page： 145 - 153 2024.1

Authorship：Last author Language：English Publishing type：Research paper (international conference proceedings) Publisher：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 Issei, Nishiguchi Koji, Chiba Naoya, Wada Yuji, Yokota Rio, Hoshiba Hiroya, Kato Junji

Transactions of the Japan Society for Computational Engineering and Science Vol. 2024 ( 1 ) page： 20241010 - 20241010 2024

Language：Japanese Publisher：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

Fundamental study on topology optimization using quantum annealing and generalized Benders decomposition

HAGA Shiori, YAMAMOTO Yoshihito, NONOBE Koji, MURAMATSU Mayu, KATO Junji

Artificial Intelligence and Data Science Vol. 5 ( 3 ) page： 719 - 729 2024

Language：Japanese Publisher：Japan Society of Civil Engineers

The goal of this research is to establish a topology optimization method using quantum annealing that can search for a better optimal solution at high speed without falling into a local optimum. As a fundamental step, we have implemented and verified a method for topology optimization of two-dimensional trusses using quantum annealing and generalized Benders decomposition. In particular, the method was verified under conditions that have not been used in previous studies, and the effects of various calculation conditions on the results were evaluated. The verification results show that the proposed method is capable of performing reasonable optimal calculations, and that the penalty coefficient for the volume constraint and the setting of the volume change in the iterative step of the optimal calculation process are particularly important to obtain reasonable calculation results with the proposed method.

DOI： 10.11532/jsceiii.5.3_719

Topology optimization of connectable microstructure using enlarged connective domain Reviewed

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

STRUCTURAL AND MULTIDISCIPLINARY OPTIMIZATION Vol. 66 ( 8 ) 2023.8

Language：English Publishing type：Research paper (scientific journal) Publisher：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

Multi-material topology optimization considering strengths of solid materials and interface Reviewed

WATANABE Daiki, HOSHIBA Hiroya, NISHIGUCHI Koji, KATO Junji

Transactions of the Japan Society for Computational Engineering and Science Vol. 2023 ( 0 ) page： 20230001 - 20230001 2023.2

Authorship：Corresponding author Language：Japanese Publisher：JAPAN SOCIETY FOR COMPUTATIONAL ENGINEERING AND SCIENCE

The present study proposes a multi-material topology optimization method considering the strengths both of solid materials and interface. In order to consider multiple factors of Young’s modulus and strength at the same time, the DMO material interpolation function that the coefficients are given equivalently is applied. To resolve the singularity problem, we propose the stress definition adapted to the DMO material interpolation function. Furthermore, the graded interface with a two-step density filter is introduced to represent the interface on a density-based method. The tension/compression asymmetric interfacial strength criteria makes it possible to obtain an optimal layout in which the interface is not subjected to tensile strain. The validity of the method proposed in this study is verified with three structural models.

DOI： 10.11421/jsces.2023.20230001

HIGH-RESOLUTION MULTI-SCALE TOPOLOGY OPTIMIZATION USING FFT-BASED HOMOGENIZATION Reviewed

MATSUI Masayoshi, HOSHIBA Hiroya, OGURA Hiroki, KATO Junji

Japanese Journal of JSCE Vol. 79 ( 15 ) page： n/a 2023

Language：Japanese Publishing type：Research paper (scientific journal) Publisher：Japan Society of Civil Engineers

Thanks to the development of additive manufacturing technology, it is becoming possible to produce materials with desired mechanical properties defined by their periodic microstructures. To design optimal microstructures, multi-scale topology optimization has been paid attention to in many engineering fields. However, its high computational cost prevents practical use, such as high-resolution 3D analysis for precision modeling and non-linear analysis assuming actual materials. In this study, to solve this problem, we focus on the homogenization approach using fast Fourier transform and develop a new optimization method with fast computing speed and low memory requirement. By performing stiffness maximization analyses with linear elastic materials, we demonstrate the validity and efficiency of the proposed method.

DOI： 10.2208/jscejj.22-15026

AN EXTENDED SIMP MODEL AND SENSITIVITY FORMULATION FOR TOPOLOGY OPTIMIZATION OF BRITTLE-DUCTILE COMPOSITE STRUCTURES Reviewed

FUJIWARA Mutsuki, HOSHIBA Hiroya, NISHIGUCHI Koji, KATO Junji

Japanese Journal of JSCE Vol. 79 ( 15 ) page： n/a 2023

Authorship：Corresponding author Language：Japanese Publishing type：Research paper (scientific journal) Publisher：Japan Society of Civil Engineers

A structure with high strength and toughness is an ideal structure for engineering. Some existing composite structures demonstrate these performances with the proper combination of ductile and brittle materials. In this study, we propose a topology optimization method to maximize the strength and toughness of such composite structures by assuming a two-phase structure consisting of a brittle damage material for strength and a von-Mises elastoplastic material for toughness. It uses a unique material representation method, which partially combines two material constitutive laws with different mathematical structures. In this paper, a series of formulations of the method are described, and some numerical results are presented.

DOI： 10.2208/jscejj.22-15028

Design and evaluation of temporary brackets using topology optimization techniques Reviewed

Kitada Yukio, Kurokawa Takahiro, Nagasaki Ren, Matsumura Toshio, Nakamura Masaaki, Kato Junji

Journal of Structural Engineering, A Vol. 69A ( 0 ) page： 26 - 34 2023

Language：Japanese Publishing type：Research paper (scientific journal) Publisher：Japan Society of Civil Engineers

The present paper aims at the development of temporary brackets used for erection of additional girders for bridge maintenance construction. A lightweight and highly rigid shape made of casting without welding joints is derived using topology optimization techniques. First, FEA (finite element analysis) of the current shape is performed, and topology analysis is performed using the result as a standard for comparison. After that, we use a three-dimensional sand mold additive manufacturing a test body, performance is evaluated through a full-scale loading test. From experimental results, the effectiveness of the optimal shape using the topology optimization technique is evaluated.

DOI： 10.11532/structcivil.69a.26

Large-Scale Topology Optimization for Unsteady Flow Using the Building-Cube Method Reviewed

Katsumata Ryohei, Nishiguchi Koji, Shimada Tokimasa, Hoshiba Hiroya, Kato Junji

Transactions of the Japan Society for Computational Engineering and Science Vol. 2023 ( 0 ) page： 20230007 - 20230007 2023

Language：Japanese Publishing type：Research paper (scientific journal) Publisher：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

Multi-material topology optimization considering properties of solid materials and interface Reviewed

WATANABE Daiki, HOSHIBA Hiroya, NISHIGUCHI Koji, KATO Junji

Transactions of the Japan Society for Computational Engineering and Science Vol. 2022 ( 0 ) page： 20220017 - 20220017 2022.11

Authorship：Corresponding author Language：Japanese Publishing type：Research paper (scientific journal) Publisher：JAPAN SOCIETY FOR COMPUTATIONAL ENGINEERING AND SCIENCE

The present study proposes a multi-material topology optimization method considering the physical properties of solid materials and the interface. An extended two-step filtering technique is introduced to define material interface based on Helmholtz-type partial differential equations. Furthermore, the width of the interface region can be controlled based on this approach. To deal with the non-convexity of the problem caused by multi-material topology optimization, a material interpolation function in which the material volume fractions are mutually independent is used: this allows for the commutativity of constituent materials. The minimum mean compliance problem is considered in two different structural models. To solve this problem, sensitivities of the objective function and the constraint condition are derived. The usefulness of the proposed method is verified through several numerical examples.

DOI： 10.11421/jsces.2022.20220017

Study on two-phase material topology optimization for transient heat conduction Reviewed

TAKAARA Keisuke, HOSHIBA Hiroya, NISHIGUCHI Koji, KATO Junji

Transactions of the Japan Society for Computational Engineering and Science Vol. 2022 ( 0 ) page： 20220007 - 20220007 2022.8

Authorship：Corresponding author Language：Japanese Publishing type：Research paper (scientific journal) Publisher：JAPAN SOCIETY FOR COMPUTATIONAL ENGINEERING AND SCIENCE

In the field of topology optimization for heat conduction problems, the steady-state thermal conditions are usually assumed because of its theoretical ease of handling. However, for design problems such as casting dies and heat-dissipating parts, where not only the spatial distribution of temperature but also its temporal transition is important, a topology optimization method considering unsteady-state conditions is required. With this background, the present study deals with an unsteady-state heat conduction problem with a special objective function, namely minimizing temperature at the targeted time and space. The optimization problem is solved using a gradient-based optimization scheme and its accuracy of sensitivities with respect to design variables is investigated. Finally, the performance of the proposed method and a common problem for unsteady-state thermal problems are discussed through a series of the numerical examples.

DOI： 10.11421/jsces.2022.20220007

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

Naruethep Sukulthanasorn, Hiroya Hoshiba, Koji Nishiguchi, Mao Kurumatani, Robert Fleischhauer, Kuniharu Ushijima, Michael Kaliske, Kenjiro Terada, Junji Kato

Structural and Multidisciplinary Optimization Vol. 65 ( 7 ) 2022.7

Language：Japanese Publishing type：Research paper (scientific journal)

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 Reviewed International coauthorship

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

HEAT AND MASS TRANSFER Vol. 58 ( 1 ) page： 125 - 141 2022.1

Language：English Publishing type：Research paper (scientific journal) Publisher：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 Reviewed

Naruethep Sukulthanasorn, Mao Kurumatani, Koji Nishiguchi, Junji Kato, Kenjiro Terada

Transactions of the Japan Society for Computational Engineering and Science Vol. 2022 ( 0 ) page： 20220004 - 20220004 2022

Language：English Publishing type：Research paper (scientific journal) Publisher：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

Large-scale Unsteady Flow Topology Optimization Using Building-cube Method

Katsumata Ryohei, Nishiguchi Koji, Shimada Tokimasa, Hoshiba Hiroya, Kato Junji

NCTAM papers, National Congress of Theoretical and Applied Mechanics, Japan Vol. 66 ( 0 ) page： 25 2022

Language：Japanese Publisher：National Committee for IUTAM

In recent years, topology optimization methods have been adopted not only for structural problems but also for fluid flow problems. Topology optimization for unsteady flows requires a fine mesh, especially for high Reynolds number flows, which is computationally expensive. Therefore, we propose an unsteady incompressible flow topology optimization method based on the building-cube method (BCM), which is suitable for massively parallel computing. The unsteady Navier-Stokes equations in the topology optimization procedure are solved by finite volume discretization, and the sensitivity of the objective function is obtained by continuous sensitivity analysis based on the adjoint variables method.

DOI： 10.11345/japannctam.66.0_25