In this paper, we propose a robust shape optimization method for a linear elastic structure with unknown loadings. The concept of principal compliance for minimizing the maximal compliance in the unknown loadings is applied to a shape optimization problem of a linear elastic structure. The principal compliance minimization problem is transformed to the equivalent maximization problem of the fundamental eigenvalue, and the problem is formulated as the distributed-parameter shape optimization problem based on the variational method. The derived shape gradient function is applied to the H1 gradient method to determine the optimal shape variation, or the optimal free-form of the linear elastic structure. With this method, the optimal shape can be obtained without shape parameterization, while maintaining the surface smoothness. It is confirmed that the obtained shape has high and uniform stiffness in all directions. We confirm the proposed method is effective for designing the robust shape with high stiffness of a linear elastic structure with unknown loadings.

Designing composite structures to satisfy specific requirements has been an important topic for a long time. In this study, we review a free-form optimization method for the optimal shape design of composite structures composed of dissimilar materials in terms of the stiffness problem, the shape identification problem, and the vibration control problem. The free-form optimization method is based on the H¹ gradient method, in which the shape gradient functions are theoretically derived using the material derivative method, and applied to the design boundaries as traction forces. We set the interface and surface of composite structures as the design boundaries, and consider the volume constraints of the dissimilar materials in each design problem. At last, we give some numerical examples to verify the validity of the proposed free-form optimization method.

The shape optimization has an effect of leveling stress distribution in the structures of many types, and the reduction of the peak stress amplitude has an influence on the improvement of its durability. The leveling effect of the shape optimization is investigated, on the stress distribution of the Michell truss under the dynamic loading with sweep excitation. The number of troughs and peaks can be divided into 2(two) groups, i.e. troughs and peaks with elastic strain only, and troughs and peaks with plastic strain accumulation, which leads us to apply the Palmgren-Miner rule directly. In this paper, the effect of leveling stress distribution in the Michall truss is reported, regarding the improvement of durability evaluation.

Various kinds of working fluid are used in precision machining of materials including glass, ceramic, casting, aluminum and so on. The working fluid is contaminated by sludge like cutting dust during machining process and contaminated fluid may cause scratch on the surface of the product or shorten the lifetime of processing machines. Hence filtering of working fluid is very important process in manufacturing. An unique filter system with translucent body having backwashing function has been developed. The purpose of the study is improvement of the efficiency of filtering. The filter system contains a part called “cone” to control flow of liquid in the system. The shape optimization of the cone was performed to improve the efficiency of the filtering using MPS method based CFD software Particleworks and optimization software Optimus. As the result, improvement of pressure distribution in the filter system was achieved.

The main topic of this study is a shape design of a noise eliminating duct. In order to enhance the noise muffling performance of an eliminating duct, jumps in the cross-section or bends are adapted to the duct. However, jumps in the cross-section or bends interrupt the flow of wind and impair air permeability. Thus, the noise muffling performance and ventilation performance of a noise eliminating are related to the trade-off. In order to realize a duct with high muffling capability and high ventilation performance, the shape optimization method using multi-objective genetic algorithm (MOGA) is used to decide optimal shape of the eliminating duct in this study.

Shape optimization of a traditional ejector with a high flow rate ratio of suction and driving is carried out with CFD in order to maximize the ejector efficiency. Three different commercial optimization algorithms are then evaluated: a genetic algorithm, a hybrid algorithm of global and local exploration, and a combined algorithm of hybrid and self-exploration. It turned out that the combined algorithm provided the best shape among the three algorithms with no more than 100 cases of CFD calculation.

The Genetic Programing is known as a model identification method, but convergence gets worse under many variables condition. In this report, we report about the method based on Genetic Programing and compatible with many variables.

In sheet metal forming, area above trimmed line is called “earing”. The reduction of the earing directly affects the material reduction, and then it is important to determine the optimal blank shape minimizing the earing. In addition, it is well known that blank holder force (BHF) has a direct influence on the product quality. A high BHF causes tearing, while a low BHF leads to wrinkling. Therefore, it is important to determine an appropriate BHF through sheet metal forming. Recently, variable BHF (VBHF) approach which BHF varies through the punch stroke has received a lot of attention, and the validity is discussed. This approach can control the material flow into the die, and the product quality is then improved. In this study, optimal blank shape minimizing the earing under tearing/wrinkling design constraints is determined with the VBHF. Numerical simulation in sheet metal forming is so intensive that a sequential approximate optimization (SAO) using the radial basis function (RBF) network is adopted to explore the optimum solution.

This paper applies structural optimization to design an effective frame layout and component sizes of bus superstructure under strength requirements of bending, torsion, and natural frequency of the bus body with considerations of rollover safety according to European regulation, ECE-R66. The bus configuration is first determined by iterative topology optimizations for 4 geometric design variables, i.e., pillar, side, roof and floor structures, via finite element analysis. The objective of the optimization problem is to minimize the bus body weight subjected to the predefined upper bound displacement constraints of structural parts under each loading condition. The obtained bus frame design from topology optimization meets the required stiffness while its structural weight is 2.5% reduced from that of the baseline model. Size optimization is employed to adapt thicknesses of the bus structure so as to account for bus crashworthiness under dynamic rollover. To accelerate the optimization process, all constraints are applied based on equivalent static linear analyses with an adjustment accounting for the effects from material and geometric nonlinearity under rollover condition. The final design of bus structure possesses all strength requirements including rollover safety while the weight of bus structure is minimized. Diagonal members of roof and floor structures are proved to significantly affect bending and torsion stiffness with relatively small weight penalties while redistribution of structural mass provides bus design with improved energy absorption performance under bus rollover.

This paper presents a topology optimization method for a permanent magnet synchronous motor (PMSM), considering the nonlinear ferromagnetic material property. Based on the density approach, we propose an interpolation model using the relationship between the magnetic field intensity and the magnetic flux density. Since the appropriate value of the penalty parameter of the density approach is unclear when dealing with the nonlinear ferromagnetic material, we conducted a numerical experiment to determin the valid range of the penalty parameter. We clarified that the optimized configurations are independent of the penalty parameter settings and free from gray-scales. Additional numerical experiments are conducted to investigate the usefulness of the proposed method by solving a torque maximization problem for the design of PMSM.

生産システムは外的要因としての需要変動によって利益が最大（最適）かどうか決まるオープンシステムと言える。効率やコストは需要を考慮しないクローズなシステム指標である。変動する需要に対して生産能力、安全在庫、生産量を制御変数とし最適化指標（評価関数）はコストや効率ではなく利益とする。本研究は機会損失による売り上げへの影響や各種コスト要因を考慮し利益を評価関数とする生産システムをモデル化する最適制御問題として捉える。従来、安全在庫は統計的に欠品許容率から算出され、生産タクトタイムは試行錯誤の経験値から求められ、生産能力は平均需要に応じてコスト削減の対象として経営されてきた。個別にはトレードオフに関係にあるが本研究による手法は全体の指標である利益を評価関数とする最適化手法である。

This paper describes a level set-based topology optimization method for steady state Navier-Stokes flow. In this method, turbulence flow is also considered during optimization processes. For steady state fluid mechanics, RANS (Reynolds Averaged Navier-Stokes) model is one of famous model for analyzing turbulence flow and is applied to solve fluid field such as velocity and pressure in proposed method. It is also important for turbulence flow to consider wall law in boundary of optmized structure. We utilize immersed boundary method to treat wall low during optimization process. For Sensitivity analysis, topological sensitivity is applied in this method. The level set function updating scheme uses a reaction-dffusion equation. As a result, we can solve optimization problem with high Reynolds number flow. Example is shown in this paper. The effectiveness of this method is discussed.

Microscopic traffic simulations are useful for solving various traffic-related problems, e.g. traffic jam and accidents, local as well as global environmental and energy problems and so on. An origin-destination (OD) matrix is a typical representation form of traffic demands that is required for simulation. In this study, we propose an indirect method to estimate the OD matrix using a traffic simulator as an internal model. The method mainly consists of the following two processes: the process of the simulation from assumed OD matrix and the process of updating the matrix. Until the estimated matrix becomes converged, these processes are iterated. Though observed ink traffic volume is required to run this method, the number of the data is limited and it describes the characteristics of not network but each single link. Then, we introduce macroscopic fundamental diagram into the proposed method to deal with this problem. We discuss the accuracy and the characteristics of the proposed method.

This paper deals with a shallow flow channel design for minimizing dissipation energy. In the flow channel design, we prepare a quasi three-dimensional flow model which simplify the 3D-RANS (Reynolds Averaged Navier-Stokes) equations regarding the flow channel height as a parameter. Then, the flow channel is designed using topology optimization where the design variable is the channel height. In topology optimization the design update scheme is based on a time-dependent diffusion equation using a design sensitivity which is calculated by a discrete adjoint approach.

This paper describes about the method for detecting chain elongation.,the chain system is widely used for power transmission device. Commonly,It is known that if the chain enlongates ,the position of the chain-rollers in the sprocket tooth move to tooth tip. And the most papers show that if the chain have a uniformity enlongation over the whole length, all chain-roller in the sprocket tooth move the same amount. On this time , we look into the structural feature of the chain , and we verify the videograph of the camera fixed at position of specific tooth on the sprocket, so we can elucidate the next two characteristics. (1)if the chain enlongetes, the link enlongates on every other link. (2) if the chain enlongetes,on the sproket the tooth that chain-roller is on the pitch circle exists certainly. With these as assumption, we verify the engagement condition of chain-roller and sprocket tooth in the geometrical techniques with CAD. As a result, we confirm that if the chain enlongetes, the different of engagement hight between the neighboring chain-rollers and this different correlates with the elongation amount. We develope the enlongation amount measuring method, and verified the effect of this method with the experiment.

Until now, we have considered structure of large generators by parametric optimization for weight saving and stiffness improvement. But the improvement effect was often small because substantial structural modification is generally difficult by parametric optimization. So we're studying the most suitable reinforcement structure of generators using topology optimization which is non-parametric optimization. We analyzed by three patterns of geometric constraints and found the most suitable reinforcement structure in the respective conditions. We proved efficacy of topology optimization in frame design of large generators.

Recently composite materials reinforced with fibers such as carbon and glass fibers have been more and more used for light-weight structural components in various industrial fields such as aerospace, automobile and so forth. Although there are several sophisticated and practical processing techniques for manufacturing fiber reinforced composite materials, promise and possibility of additive manufacturing of those materials like CFRP (carbon fiber reinforced plastics) are indispensable because such newcomers of material and structural processing obviously allow design methodologies widen beyond their conventional design and optimization approaches. Topology optimization designs are very attractive for additive manufacturing product designs. However, this well-proofed method still seems not to be perfect in case that one tries to apply it to fiber reinforced composite materials design, in which one should take into consideration their orthotropic and graded material and physical properties. In this preliminary report, the present author tries to raise awareness of this issue and also attempts to formulate an extension or a generalization of the existing density-based topology optimization scheme, that is, SIMP (Solid Isotropic Material with Penalization) method.

The present study minimizes the number of layers of wing shaped plates fabricated by laminated composite (CFRP) under aeroelastic constraint which keeps stable flutter speed. The finite element analysis for the aeroelastic characteristics requires considerable calculation effort. Therefore, the response surface method (RSM) is utilized to reduce the computational time for optimization where an approximate expression uses bending rigidity of composite plates as input and flutter speed as output. Then, the distributed genetic algorithm (DGA) is employed as an optimizer to minimize the numbers of layers of composite plates by designing fiber orientation angles. The optimized wing model shows weight reduction and enough flutter speed in less computational time than without RSM.

The morphing wing changes the geometrical shape seamlessly and continuously to improve the aerodynamic performance. Several studies have been conducted with variety of approaches. This study focuses on obtaining the optimum airfoil shape for the morphing wing using the corrugated structures arranged in the rear side of the airfoil. For numerical efficiency, SAO (sequential approximate optimization) method using RBF (radial basis function) network is adopted. The airfoil shape is modeled by using nonuniform rational basis spline (NURBS) curves and the passing points are adopted as design variables. Through numerical examples, the validity of the optimization method is demonstrated.

A wing that can be deformed the geometrical shape seamlessly and continuously to improve aerodynamic performance of wing is called a morphing wing. A compliant mechanism has been proposed as the internal structure of the wing to achieve the desirable deformation. Most previous studies have adopted the ground structure approach to obtain the internal structural configuration of the morphing devices. We consider to adopt the level set-based topology optimization method to improve the structural feature of the morphing wing. Then, we begin with the problem formulation to minimize the difference between the ideal given deformed shape and the deformation of the obtained compliant configuration. This manuscript gives current status of the study by illustrating some simple numerical examples.

三次元的な複雑形状をプレス加工する場合，除荷後のスプリングバックを考慮した形状予測が難しい．所望の形状を得るため，実験的アプローチを用いて金型やワークの形状を調整する場合，破断を考慮に入れつつ最適形状を得るのに数多くの試作が必要となる．そこで，スプリングバックを良く再現できる吉田-上森モデルを用いたプレス加工解析にFLD(Forming Limit Diagram)による破断評価を適用しつつ，メッシュモーフィングによる最適化を行った．この結果，対象となる評価領域を分割しそれぞれで最適化することで加工後形状が良好な精度となる初期開口形状を得た．

The purpose of this study is to obtain an optimum structure by using the optimum design method of multi-layer films under the target specifications to reflect the near-infrared light range and transmit the visible light range. We propose a method to achieve the spectral characteristics of the target specification in a wide wavelength range by combining sub-structures to high reflection of light. Generally antireflection films used in solar panels are designed for controlling only the normal incident light. In this study, a sub-structure to control the oblique incident light at a particular angle is formulated and applied to design of multilayered structure. It works not only for vertical incident light but also for oblique incident light. Furthermore the film structure is designed for controlling more wide range of oblique incident angle by laminating the resulting sub-structures. Finally multilayer films that achieved the transmission of light in the visible region and high reflection in the near infrared region for wide-angle incident light are obtained.

In deep drawing, a low blank holder force (BHF) will cause wrinkling, while a high BHF will lead to tearing. Therefore it is important to determine an appropriate BHF through drawing. Recently, variable BHF (VBHF) which varies through the punch stroke is an attractive approach in the industries. In this study, it is purpose of leading optimum VBHF trajectory that applies on segmented blank holders. The objective is taken as the minimization of the deviation of whole thickness. In general, numerical simulation on sheet metal forming is so expensive that a sequential approximate optimization (SAO) using the radial basis function (RBF) network is adopted. Regarding the optimum solution, numerical simulation is compared to experiment.

Analysis technology of FEM is a very versatile numerical analysis. Recently these Analysis technology's accuracy is enhanced, in the field of structural analysis and metal processing have received a great benefit. Simulate with FEM, The introduction of the FEM analysis process and simulate with FEM, it has become possible to reduce the cost of the prototyping. But Current state, often error between the actual workpiece and the analysis results is increased. In this paper, propose a reasonable shape optimization using the FEM and RBF network.

In design of make-to-order products, fast estimate of design parameters corresponding to customer requests through interactive communication between customer and designers is required. To realize fast estimate design, we are constructing analysis led customer co-design system, which can evaluate the product performance and specification in short time, utilizing a machine learning technology. As a vehicle product of customer co-design system, we try to apply for estimate design of centrifugal compressor. Engineer considers estimate design of product specification corresponding to customer demands. We developed a specification predicting technology to provide a design specification faster time for engineers. The design specification predicting program shows the result of rotation speed and number of impeller in 32 seconds.

A fast first-order optimization method is presented for the quasi-static elastoplastic analysis of large-scale truss structures. The incremental problem is formulated as an unconstrained nonsmooth convex optimization problem. An accelerated proximal gradient method is adopted for solving this unconstrained optimization problem efficiently. The most expensive computation of this method consists of some matrix-vector products, and the method is free from numerical solution of a system of linear equations.

A new method of geometrically nonlinear analysis of large-scale framed structures are proposed in this paper by using accelerated-gradient-method (AGM). AGM has attracted attention in recent years as an effective method for large-scale unconstrained single-objective optimization problem especially in the field of machine learning. A geometrically nonlinear analysis can be formulated as a total potential energy minimization problem. In this study, AGM is adopted for solving the total potential energy minimization problem efficiently in order to solve a geometrically nonlinear analysis at higher speed.

To design accurately, the uncertainty of design variables or design parameters should be considered. The methods considering uncertainty are classified into three methods, using safety factor, design method based on reliability and design method based on robustness. In this paper, the design method based on robustness is focused. The past robust design methods have the problem that it is difficult to show the design has enough robust. Then, this paper proposes a optimization method for obtaining the robust design using evolutionary computation. Through some numerical example, the validity of proposed method is shown.

In the last several decades, periodic structures such as photonic and phononic crystals have attracted much attention of researchers and engineers, because these materials have various special properties such as full bandgaps. The full bandgap is defined as a “frequency range in which waves cannot propagate in any direction”. It is expected that the distinguished property can realise advanced wave devices such as photonic crystal laser, cloaking etc. To design such sophisticated devices, it is required to establish a method for controling full bandgaps of periodic structures. We have already developed a stable algorithm of the topology optimisation for 2D square/hexagonal lattice structures. The main scope of this paper is to develop an algorithm which accelerates the topology optimisation for periodic structures.

This paper proposes a new approach for wind tunnel testing, which bases on multi-objective design exploration. This approach bases on wind tunnel tests for design objective function evaluation and uses a multi-objective design optimization method to define wind tunnel test conditions. In this paper, the proposed approach is applied to a design optimization problem of a plasma actuator applied to a NACA0015 airfoil model. Analysis of the objective function values and the design parameter values of the obtained non-dominated solutions shows the present approach enables efficient research based on wind tunnel testing for understanding aerodynamic phenomena.

本手法は従来の最適化手法の基本概念である「最小化」とは異なる「満足化」の概念に基礎を置く手法であり、集合(セット)をベースにして多目的性能を同時実現する多設計変数解範囲を求める手法である。設計の基本構造である目標性能、影響因子（設計変数）および両者の関係のもとで成立する手法であり、機械・構造系のみならず電子、制御等他分野への適用も可能である。本報告では、手法の考え方や実際の手順、および多くの目的と影響因子で構成される設計問題への適用例と結果について述べる。

Hydroelectric power generation is a highly stable renewable energy power, and it is necessary to optimize hydro turbine to meet each specification. In order to enhance hydraulic performance, multi objective design optimization was carried out by using Computational Fluid Dynamics(CFD). The optimization algorithm employs Particle Swarm Optimization(PSO). To increase the degrees of freedom of shape, blade shape of runner is defined by NURBS curve. As a result, it was confirmed that an optimized runner with more uniform runner outlet flow has better performance than conventional runner.

An optimization approach employing Kriging-based response surface method and Multi-Objective Genetic Algorithm in the design of MCHX with a wavy fin is presented. New CFD-based prediction models for the Colburn factor (j) and friction factor (f) of wavy fins based on 671 results obtained from the CFD simulations are generated by Kriging response surface method. The new models agree better with CFD results than prediction models derived by multiple regression method, which describes 100% of the points within 5% of CFD j factor data and 95.7% of the points for f factor. Design optimization for MCHXs in refrigeration cycles are also performed using MOGA and Kriging models. It was observed that Pareto fronts of objective functions such as pressure drop, LMTD, power consumption, and HX weight are identified by searching optimum solutions in the entire design space without ending with local solutions

Recently, many efficient Multi-Objective Evolutionary Algorithms (MOEAs) for Constrained Multi-Objective Optimization Problems (CMOPs) have been proposed. For evaluating their performance, the C-DTLZ functions and Real-World-Like Problems (RWLPs) are frequently used in the previous work. In this paper, however, we point out that almost all of them have some critical problems. A part of the C-DTLZ functions has only one constraint, and the experimental results in this paper show that an MOEA without constraint handling techniques can obtain well-approximated nondominated feasible solutions on them. We also show that MOEAs can easily find feasible solutions on widely used RWLPs which are considered as “MOEA-hard” problems, and it is seldom that an infeasible solution violates multiple constraints simultaneously. Thus, benchmark problems for CMOPs and the performance of MOEAs reported in the previous work need a careful reconsideration.

This study evaluates the effect of crossover operators in many-objective evolutionary algorithms (MOEAs). We consider NSGA-III , ε-MOEA, MOEA/D and IBEA as major MOEAs. In each MOEA, we apply SBX, DE, SPX, PCX and UNDX as crossover operators. Test problems are DTLZ2 and DTLZ3. In this study, Generational Distance (GD) metric is used to evaluate not only the convergence performance of finally obtained pareto optimal set but also the running convergence performance. When we change the number of objective functions for each test problem, we investigate the difference in the convergence performance among crossover operators in each MOEA. As a result, we can confirm that the effective crossover operator is changed by both the problem property and the number of objectives.

The pseudoelastic characteristic of Shape Memory Alloy (SMA) material can be used to absorb energy as the corresponding hysteretic loop of this kind of material. In this study, we deal with a truss structure having shape memory alloy wires as well as ordinary elastic wires. This kind of truss structure has the capabilities of vibration absorption and isolation because of this conspicuous characteristic of SMA wire. Since SMA wires in slack or small strain condition cannot play a significant role in energy absorption, such SMA wires can be replaceable to ordinary wires from this point of view. On the basis of this consideration, we are able to suppress the number of SMA wires of the truss structure with due consideration to the effect of vibration isolation and absorption. We combine the two kinds of wires in the truss structure in order to obtain the solution of configuration considering both of the effects of absorption and isolation of vibration under the constraint condition of the number of SMA wires.

The purpose of this study is to generate the gait of two-legged robot by using optimization method. Stepping points are determined optimally under the conditions of maximizing walking speed and minimizing energy for walking. The gait generation problem is reduced to a multi-objective combinatorial optimization problem solved by using genetic algorithm. Orbits of toes and hip between stepping points are generated by means of parametric modeling. The stable walking patterns are obtained under the condition of the maximizing walking speed and the minimizing energy consumption. The Pareto front of the multi-objective optimization for the each robot specification is visualized by the NSGA-II. The proposed method can generate an optimum walking gait under the constraints on the stable walking.

Simulation-Based Design is the design process having both ways of the product quality improvement and cost reduction by introducing a simulation considered the specification uncertainty in a concept design. The advantage of this design process is able to decrease numbers that a design process starts over and to advance to the detail design phase as robust. Usually, it is difficult to define definite values of the specification because there is much uncertain information in a conceptual design. Therefore, I institute a simulation looking out over all design processes as 1DCAE. Moreover, the value arranging in ranges and sensitivities are calculated by the concept that is called Uncertainly Quantification (UQ), using the Taguchi Method as UQ in this study. As a result, optimized solutions of sizes, layouts and the combination of functions are derived.

Mixed-integer programming (MIP) is a key-technology for the optimization of relevant business processes such as supply chain network design. Many practical aspects like demand variations often require the solution of a sequence of very similar MIPs, in which two consecutive problems share most of their data. Using a state-of-the-art MIP solver for every model in the sequence, branching information from previous models is usually lost and needs to be reinitialized during an expensive strong-branching procedure. In this paper, we investigate the benefits of transferring branching information from previous runs when sequences of similar models are solved. Computational experiments confirm that the proposed method effectively reduces the overall solving time on a set of instances from both MIPLIB2003 and real-world scenarios

There are a lot of studies on Robust Design. Mainly, they had two objective functions such as maximizing their behavior and minimizing influence of behavior against perturbation of design variables and/or design parameters. Conceptually, these ideas are meaningful for real use of the results. However, in its formulation, they mainly use first order of Taylor expansion to estimate influence against perturbation. In that sense, they optimize behavior and its sensitivity. But, we have pointed out these formulation are wrong in the last study, and think about robustness of the solution by carrying out optimization assuming worst case. In this study, we would like to treat trade-off between behavior and amount of perturbation.

Ant Colony Optimization (ACO) was inspired by a behavior of ant swarm intelligence. In this study, the principal stress vector was introduced in Ant Colony Topology Optimization (ACTO). Generally, Topology Optimization has applied the volume constraint as a termination condition, and has optimized a mean compliance. On the other hand, as a product design, a weight minimization with the local stress constraint is the most important object to attain it. Moreover, in a mechanical structural design, usually, a weight minimization is performed under the maintaining stiffness through checking the flow of forces (principal stress vector). However, topology optimization for a weight minimization with the local stress constraint is difficult, since the optimization problem has many local optimal solutions. In order to overcome the difficulty, we propose the ACTO method by considering the flow direction of the principal stress as a route, since ACO is a suitable optimization algorithm for route generation like a travel salesman problem.

本研究は，所与の大変形経路のもとで構造の塑性散逸エネルギーを最大化するトポロジー最適化手法の開発を目的とする．経路依存問題のため，要求される感度解析は過去の変形履歴の影響を考慮した特殊な微分操作となる．ここでは，移動硬化を考慮できる異方性モデルへ発展させる上での数値解析上の優位性を踏まえ，超弾性構成則および塑性中間配置を参照する諸量を用いて構成モデルを記述する．これをもとに，構成方程式およびリターンマッピング式を参照して，経路依存型の感度解析アルゴリズムを新たに定式化する．

The present study proposes a density-based topology optimization applying the coupled thermo-elastic analysis in order to consider the effect of the both structural analysis and heat conductivity analysis simultaneously. In this study, heat conduction equation is derived from the law of energy conservation and equation of motion, and the displacement and temperature fields are simultaneously solved by employing the generalized degree of freedoms. For topology optimization, material parameters (Young's modulus, thermal expansion coefficient, and heat conductivity etc.) are relaxed by the RAMP approach. The proposed method is verified by a series of numerical examples with the linear thermo-elasticity.

本研究は，均質化法に基づく非線形マルチスケール解析の適用を前提に，材料微視組織（ミクロ構造）の最適トポロジーを決定することでマクロ構造のエネルギー吸収性能を最大にする問題を取り扱う．ミクロ構造は２相複合材料で，いずれの相もvon Misesの等方性弾塑性構成則でモデル化した．本研究では既往の研究[1]で提案された感度導出法を分離型マルチスケール解析法に導入し，低コスト・高精度の新しいマルチスケールトポロジー最適化の枠組みを提案する．

We have been investigating topology optimisation methods with the boundary element method (BEM) and the level set method for wave problems. In this paper, we propose a method for meshing three dielectric materials by using two level set functions and voxels, which is essential to the topology optimisation method, for two-dimensional electromagnetic problems with the BEM. We also verified the accuracy of topological derivative in three domain problem.