The engineering product development process in a collaborative design context can be viewed as: a network of linked decisions with interdependencies; problem decomposition of product design project and aggregation of sub-problems by multi-disciplinary or multi-talented teamwork; resource sharing and coordination process such as design objectives sharing, information exchanging with other team members, design conflicts detecting and resolving, and generating new ideas and design improvements. In this research, we propose a hybrid multi-agent architecture (ANetCoDE) for supporting such a distributed collaborative engineering design context. The agent architecture and network architecture of ANetCoDE are overviewed, autonomy-based network formation of agents with deliberative/reactive characteristics and local/remote distribution for the design agents are proposed, and multi-layered network architecture for facilitating the agent interactions is presented. Finally, a planar robot design with multidisciplinary design capabilities is demonstrated on the proposed ANetCoDE platform.

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In this research, we attempt to allow designers to share engineering resources and information such as geometric and non-geometric information on the networked design environment like Internet, Intranet, or WWW. For extending now standalone solid modeling process towards a distributed collaborative one, Solid Modeling Browser concept is proposed, which has been developed as a system module of ANetCoDE and a typical wrapper agent in ANetCoDE context. Based on multi-layered network architecture (interaction layer, coordination layer, communication layer, and transport layer), we realize the distribution of solid modeling process. The distribution and intelligent collaboration between heterogeneous engineering tools, for instance 3-D CAD system, are facilitated using KQML-CORBA integration, coordination mechanism and common interaction protocol. In addition, a wrapping concept for providing the interoperability between heterogeneous 3D-CAD systems is described. Finally, a network-centric solid modeling tool is proposed by combining the distributed computing technologies and multi-agent technologies.

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Design information sharing among diverse engineers and early performance evaluation are essential for the efficient design of electromechanical products. To address these issues we have proposed a methodology of rapid design and concurrent engineering using physical representation models based on mainly lumped parameter systems. To facilitate the practice of this method by designers, we have developed a tool that consists of the following three modules: 1. Design Information Editor, 2. Mathematical Simulation Engine, 3. Pre-processor for Design of Experiment (DOE). In this paper, feasibility of this tool is evaluated in the Hard Disk Drive (HDD) development processes including robust design and factorial effects analysis of the actuator parts, and advantages of this tool and effects to improve the design efficiency are reported.

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In the case that mechanical system is large or complicated, design of the system is often divided into design of its components and integrated from design resulted from the devided design level. Therefore designers have to integrate their components design into final design. However, in this stage, it can be seen some conflicts and it is important to resolve these conflict to make shorten the leadtime of design process and make profit. Recently, we can widly use computers in various design stages and we can decrease the number of times of time-consuming real experiments using analytical software. It can be seen the situation that offices of designers are apart from each other and the same situation for computers and analytical software in the offices. In this research, we proposed the collaboration design method that resolve the conflict among designs connecting the computers using networks. In our previous paper, we have proposed the design evaluation method using Data Envelopment Analysis and calculation method of compromise design. We have confirmed that it is effective to offer compromise information in the stage of components design. In this paper, we have improved our proposed that can offer the direction for compromise design and confirmed the effectiveness of the proposed method through some numerical examples.

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As design and manufacturing enterprises become increasingly globalized, human, physical and computational resources supporting corporate operations are increasingly dispersed geographically. Such situations require the development of product design support systems that exploit information network technology to enable the sharing of design resources and facilitate design processes, with widely separated individuals and groups acting in collaboration. This paper proposes a collaboration system that integrates product design information and the specific design goals held by each participating designer across the distributed network. The design information for such cooperative product design projects is managed using network agents that have two main features. First is an ability to clarify the wide range of design information required by separated designers, based on consistency management techniques. Second is the evaluation of design alternatives, based on optimization techniques, that assists the creation of successful product models. By using these agents, a team of geographically dispersed designers can collaboratively construct an optimal product design model and effectively find global optimum design solutions.

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This paper discusses an advanced collaborative system to support creative design efforts that depend on interactive communication among a number of designers. The process of collaboration, a requirement of practically any project involving more than one person, is often difficult. However, increasingly sophisticated customer requirements impel companies to develop increasingly advanced products to maintain market share, placing further importance on creative design collaboration. Collaboration is based on interactive communication, which can be divided into cooperative and oppositional interactions. The effective resolution of oppositional interactions is crucial to successful collaboration. Equally important, however, is the preservation of fresh ideas and inventive solutions that often develop as creative conflicts are resolved. This paper discusses analytical methods and solutions applicable to oppositional interactions during creative collaboration.

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The features and outline of "Theory of Inventive Problem Solving (TRIZ)" initially developed by Altshuller and "Engineering Design, Systematic Approach (P&B Method)"systemized Pahl & Beitz are briefly described in concept design stage. The former is effective to support thinking for new ideas, the latter offers a design frame and process to follow by designers. TRIZ is a theory which consists of inventive principles, rules and techniques by investigating huge amount of patents and extracting the principles its. Following P&B Method the beginners even carry out a comparatively good design. In the paper we present an idea about a method how to fuse and make good use of their features.

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This paper proposes case-based design aid using similarity between design cases. First, design cases and design modification cases are described by physical quantities and their calculations to represent physical phenomena and terms to explain them. Then, a quantity dimension space defined by nine fundamental and supplementary quantities in SI is introduced and similarity between physical quantities is mathematically defined in the space. Also, similarity between terms is defined by combining literal similarity and cooccurrence statistics. Finally, similarity between design (modification) cases is defined based on quantity- and term-similarities. By using design case similarity, designers can retrieve and consult the similar or relevant cases to a new design problem. Also, design modification knowledge such as "which physical quantity or design parameter should be modified to solve specific trouble" can be extracted by analyzing recorded design modification cases. The proposed methods are implemented as a Lisp program and examined through some examples.

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We propose a new concept of CAD/CAM/CAE-Integrated system that works on the common graphical data. And it has the function of process design for molding by the use of Topology (Meaning is different from the idiomatic expression in custom CAD). We use the special area coordinate system for the parametric space to define the surface that is different form the custom boorean CAD system, and we can define circler patch without trim. And adding to it, it has no error in the connection between surfaces. This system reduce the quantity of the graphic data to 1/100 of custom CAD, and this feature of topology-CAD is very useful for the Revolution on Web of Production Technology.

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This paper proposes a stereolithography method in which photopolymer resin is exposed to ultraviolet ray through grayscale mask to control light intensity pattern. Since 2-D density pattern of the grayscale gradation is transferred to the curing thickness pattern, the fabricated object can have smoothly curved or patterned surface without steps which inevitably appear in case of conventional layer-by-layer stereolithography. A ultraviolet light source, photopolymer resin and mask material for grayscale mask stereolithography are discussed, and post-curing in the water for less distortion is proposed. One of the possible applications of the grayscale mask stereolithography is fabrication of optical lenses. This paper shows fabrication examples of prism lens and spherical lens array using grayscale pattern calculated from the target surface pattern, and quasi-relief using usual photograph film as a mask.

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In order to develop design support system from initial design stage to detail design stage, Topdown Oriented Design Method is assumed to be available. The authors developed Topdown Oriented Design System, in which the design model is expressed by the concepts of "Entity, Attribute and Relation Model" . One of the important purposes of the Topdown Oriented Design System is to describe design processes in computer system. It is valuable if the design support system can evaluate the design processes of designers and informs the designers of the unsuitable results of design process. In this paper, the authors suggest the frameworks of the evaluation methods for the design process by using QFD, Quantification Theory III, DSM and ISM in Topdown Oriented Design System.

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Product development is a complicated activity which consists of a lot of tasks related with each other. Therefore, designing not only the product, but also the design process is very important. However, traditional project management or simulation tools are not suitable to deal with the complicated design process which includes coupled design tasks. In this paper, a new process simulation model is proposed based on DSM (Design Structure Matrix) and DiFS (Design Information Flow Simulation), in order to support the analysis and improvement of the design process. The proposed method can simulate the progress of the complicated design process in detail, and verify the effectiveness of process improvement strategies.

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Recently, because of the importance of the production with considering the product life cycle and the dynamic change in manufecturing paradigm from the current mass production to the sustainable production, a modular design attracts attention very much. One module of a product has the interface functionally connected to other modules on a structure, and so the interface of the modules is key concept in modular design. In this paper, authors propose the modular design supporting system based on a management of the product's joint information. The new design methodology for the modular design that generates the joint information stepwise is proposed by this system. In order to support the modular design with considering the product life cycle, this methodology shows one design scenario for the modularization by arrangement of the flows of a product design and a modular design.

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This paper proposes a simultaneous optimization method for both module combination and module attributes of multiple products. Simultaneous design of multiple products, which is called product variety design etc., becomes an important strategy in manufacturing. Toward rationalization of such practice, we configure an optimization method. The optimization method hybridizes a genetic algorithm, a mixed-integer programming method with a branch-and-bound technique, and a constrained nonlinear programming method, i.e., a successive quadratic programming method. In its optimization process, the first optimizes the combinatorial pattern of module commonality and similarity among different products, the second optimizes the directions of similarity on scale-based variety, and the third optimizes the continuous module attributes under the others. Finally it is applied to simultaneous design of multiple airplanes.

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In recent years, 3D-CAD spreads through the design of home electronics, machine apparatus, etc. quickly, and the effect is taken out to an improvement of the development process. However, the present condition is that it is not fully utilized by development of the manufacture equipment with exclusive function in the small-scale group. It is because 3D-CAD is not necessarily suitable as the expression method of design in the conceptual and embodiment design process. Then, in this paper, present data analysis of a manufacture equipment of custom-made article was performed paying attention to the expression method of design. Furthermore, since it was adapted for the actual design process and the validity was proved, it reports.

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Most methods of assemblability evaluation are based on the experiences in shop floors. They do not provide generic rationale of the evaluation results. We believe assemblability of mechanical parts depends on their behavior while they are being mated. This paper proposes an assemblability evaluation method that analyzes the state of parts in the mating process based on the assembly model. The state of parts is represented by a set of contacts which one part has with other parts. Mating process can be described by the series of these contact states. In each contact state, parts in contact form a mechanism. By simulating possible behavior of the mechanism the transition from the contact states to the other contact states is analyzed. The result will be a good basis for assemblability evaluation. A prototype system is in development using solid modeling system and kinematics analysis software.

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User maintenance increases customer satisfaction and decreases total maintenance cost. Furthermore, appropriate maintenance work extends product life-cycle. Some products, however, are too much complicated for users to disassemble/assemble for maintenance work. Therefore, user maintenance support tool is very helpful in those cases. The paper describes a web-based fishing reel maintenance system to support user level maintenance. The system covers two phases of maintenance, or corrective maintenance and preventive maintenance, using intuitive manipulation on 3D objects.

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Order Management System (OMS) in Distribution Centers (DCs) has important effects on the levels of flexibility, customer service, and inventory cost. It deals with the order and material exchanges between DC and its partners. Development of appropriate user interfaces for OMS leads to effective communication with partners and efficient order management. The paper reviews the requirements for the user interface. In order to meet the requirements, a system architecture for OMS is proposed. It is composed of seven subsystems, as following: (1) system for material ordering from customers; (2) system for material dispatching to customers; (3) system for material ordering to suppliers; (4) system for material dispatching from suppliers; (5) demand forecasting system; (6) inventory-order state monitoring system; (7) decision making system. The paper describes the necessary features for user interfaces of each subsystem and demonstrates several sample user interfaces. The engine software behind the user interfaces is explained too.

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Collaboration consists mainly of two tasks; one is each partner's task which is done by the individual, the other is communication with each other. Both of them are very important for the smooth collaboration. From the viewpoint, the collaboration support system should be a coalition between the operation support and the communication support. We have developed the 3D shape evaluation support system in virtual space and the embodied virtual communication system for the analysis by synthesis. The fusion of two system is necessary for the collaboration support system for 3D shape evaluation in virtual space. From the viewpoint of communication, the talkers tend to prefer the situation in which they can share embodied interaction by observing their interaction of avatars including themselves in the same virtual space. However, the motion images including themselves would discourage them from the shape evaluation. In this paper, the influence of difference of the point of view on the shape evaluation in virtual space is investigated using the proposed system by the sensory evaluation of paired comparison and the questionnaire analysis. The subjects can see their actions by translucent avatars or see only their forearms' motions. It is found that the subjects prefer the point of view from which they can see only their forearms' motion for the shape evaluation in virtual space.

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Speech driven embodied interaction systems called "InterRobot" as physical media and "InterActor" as electronic media are developed for supporting human interaction and communicaion by generating the coherently related communicative motions to speech input. Talkers can share the context of communication by mutual embodied entrainment via "InterRobot" and "InterActor". In this paper, the effectiveness of the proposed hierarchical interaction model for "InterRobot" and "InterActor" is confirmed by comparing with single stage model. Actual applications of "InterRobot" and "InterActor" to human interface are also demonstrated for developing a new embodied communication industry.

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In design of products especially far public use such as automobile, and PC the requirements become widely spread. Thus, we should have to estimate pgoducts by using multi-objective optimization, and it should be estimated in scalar value. In such cases, Data Envelopment Analysis (DEA) works very well. In this study, we analyze the growth of frontier of products and try to estimate the future requirements for the product design. In order to demonstrate the proposed method, we apply it to the growth of Japanese Car for five years. From those results, we show the growth of the frontier for specific class of cars, and also we show the shifts of requirements by shifts of frontier for other specific class of cars.

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In this research, the description model by integrating the functional and geometrical information have been developed. In this system, the relationship the mechanisms having input event and output behavior is considered. The designers have designed the products by the combinations of multiple mechanisms. By the change of the combination input event, the mechanisms have different output behavior. This variety condition must be transmitted other designers because the products have not the behavior that a designer wants. In this paper, the method that many people know the condition of the mechanisms with input event and output behavior and that the correspondence management having the relationship input event and output behavior has been proposed.

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The life cycle of products is an increasingly important evaluative factor in successful product design optimization. However, the effective integration of life cycle issues into the product design process requires the inclusion of a number of factors that express product life cycle details in the optimization formulations. These factors are often hierarchical and have constraint conditions that until nowhave prevented their concurrent evaluation. In order to integrate life cycle factors in complex optimization problems, this paper proposes an optimization method based on consideration of hierarchical and constraint relationships, among the decision variables, which represent correlations between a number of decision-making factors. The complicated relationship between these design factors is graphically displayed and hierarchical genetic algorithms, whose genes incorporate the hierarchical structure of the design variables, are employed in the search for an optimal design solution. The proposed method can be effectively applied to the design of products that consider reuse and recycling factors, as it clarifies an optimal life cycle strategy.

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Recently, the design problems for machine products such as machine tools tend to have a large number of evaluative characteristics, and are almost always multi-objective. In such cases, the optimization problem systems often yield a large number of unsatisfactory local optimum solutions due to complexities in the cooperative and conflicting relationships among the design characteristics. Most design optimization methods seldom succeed in finding an ideal optimum solution. In order to overcome this problem, this paper proposes a design optimization method for large-scale problems based on decomposition and hierarchical ordering of characteristics, focusing on the interrelationships among design characteristics. This method begins by carefully examining the characteristics and decomposing each one into as simple sub-characteristics as possible. Next, based on these examinations, all the characteristics are hierarchically ordered and grouped into a number of basic optimization units (BOU). Then, feasible design solutions are searched for using an effective strategy and the system problem is gradually optimized, starting with lower BOU hierarchies and proceeding sequentially to the upper hierarchies. In this paper, this method is applied to the design problem for a simple machine product.

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As the need for the company designers to consider product lifecycle has arose, the number of design criteria and variables has mushroomed. In addition, due to the diversification of users' requests and the rapid changes in fashion, companies must reduce their product development cycle times to an absolute minimum. Consequently, companies now face a two-fold difficulty: design projects that can only be dealt with as large-scale optimization problems, and the need to shorten the development cycle to an absolute minimum. This paper proposes a concurrent criteria-ordering method for large-scale design optimization problems that not only yields an optimum criteria order for evaluation, but also shows how criteria groups can be optimized in parallel. This method consists of two optimizations. First, the input and output data for each criteria will be optimized. Then the order of criteria for evaluation will be optimized according to the optimized input and output data.

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A robust optimal design method for multistage expansion of energy supply systems based on the minimax regret criterion is proposed so that they are robust economically against the uncertainty in energy demands which increase stepwise with construction of buildings. Equipment capacities and utility contract demands as well as energy flow rates for each expansion period are determined to minimize the maximum regret in the levelized annual total cost and satisfy all the possible energy demands for the overall planning period. This optimization problem is formulated as a kind of multilevel linear programming problem, and its solution is obtained by repeatedly evaluating upper and lower bounds for the optimal value of the maximum regret. Through a numerical case study on a cogeneration system, the relationship between the optimal equipment capacities and the number of years for expansion periods is clarified.

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Multilayer coatings are widely used to various optical parts, for example, multimode optical fibers, beam splitters, antireflection coatings and so on. In the design of optical multilayer coatings, refractive index and thickness of each layer must be determined in accordance with the specifications on spectral reflectance or transmittance. In this paper, sensitivities of the spectral reflectance for design parameters are considered at the optimization process to obtain robust design solutions. If an insensitive design is obtained, the manufacturing cost may be reduced. The thickness and the index of each layer, the incident angle and the wavelength of incident ray are treated as the design parameters. Our developed design system is used to solve the optimization problem. Some robust solutions are obtained by using our design system.

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This paper studies the structural optimization with robustness for buckling of FRP laminated circular cylindrical shells. For this purpose, the buckling equation under axial compression is derived based on the classical lamination theory, and a multi-objective optimization problem is defined by taking a critical buckling load and a sensitivity of the buckling load as objective functions, and the bucking load and the sensitivity would be maximized and minimized simultaneously, respectively, by optimizing the fiber angle of the shell. In optimization, a multi object genetic algorithms are employed to solve the optimization problem. In numerical calculations, the pareto optimal solutions are obtained for the present problem, and the applicability of the GA employed here is also studied from numerical results obtained.

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In this paper, we will develop prediction system of accident of the system by using radius basis function network (RBFN). In monitering the machine, although it is connected on line, it is sometimes difficult to store or transfer all data that it corrects. In stochastic way of doing diagnosis, they need continuous data to find mean value and standard deviation. Beside that it has no meaning when data has two steady states. However, in our system, we can express situation of steady states even if they have more than two steady states. By using actucal data, we will show the effectiveness of the proposed method.

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This study deals with a principal component analysis about limit state functions for structural systems reliability assessment. Although it is pointed out that the measure must be important such as directional cosine of limit state functions on standardized space, we can discuss about characteristics both variances and covariance of limit state functions from other view points. It is proposed that the problem can be solved by using the method of principal component analysis of covariance matrix of limit state functions according to reliability indices. This approach can be explained about the important measure considered as geometry of members of structural system.

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The reliability-based optimum laminate construction of a laminated composite plate subject to in-plane loads is addressed by adopting lamination parameters as design variables. The reliability of each ply failure is evaluated by the first order reliability method, where the material properties and applied loads are treated as random variables. The first ply failure criterion is adopted as the plate failure. Then, the system is modeled as a series system consisting of each ply failure. The system reliability is approximated by Ditlevsen's bounds. The lamination parameters have been used as intermediate design variables for deterministic optimization. Because the structural response can be described by a smooth function in terms of the small number of the lamination parameters. In this study, the lamination parameters are applied to the two types of reliability-based optimization. The effectiveness of using the lamination parameters is demonstrated through numerical calculations.

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There are many studies on setting a critical line for prediction of slope failure caused by rainfall. The focus of these studies lies in the determination of the boundary between dangerous region and safety region with single criteria. However, because of the complexity of nature, it is almost impossible to distinguish complicated slope failure with them. In this study, we use rain data both on failure rain and un-failure rain and made up the data with two dimensions: short term estimation as hourly rainfall and long term estimation as effective rainfall. We compare the results with conventional Critical Line and showed the effectiveness of the proposed method.

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This paper proposes an aspiration level approach to multi-objective method of using GDEA (Generalized Data Envelopment Analysis) and GA (Genetic Algorithms). Moreover, through numerical examples, we show that several Pareto optimal solutions closest to a aspiration level of decision makers can be listed up, as candidates of a final decision making solution, by the proposed method.

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Dramatic progress of computer technology enables us to introduce accurate control system to practical design of structure cheaper and easier.In such situation the way thinking control system as a part of structure may bring a chance to design innovative structual system. And such structual system should be highly efficient. In this paper we consider sinple two dimensional truss structure and linear actuator to design new structure system. As objective function for optimization we take total mass and displacement of load points and total displasement of structure. We use two optimization methods togeter to optimize the structure here. First one is genetic argoritm and second method SQP. As a result we could find out some good structual system. We succeed to design structures lighter weights and smaller displacements. This means we can have a big potential to have innovative truss structual design.

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We study an recursive approach to optimal design of structural system. In this study, two processes dealing with geometrical constraint are discussed; that is, one is initial degeneration process and the other is shape transformation process. It is shown that these processes can also be performed in a recursive manner. Example optimal designs are conducted and the results show the practicability of the proposed recursive optimization approach.

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In this study, a model of Genetic Algorithms (Gas) on the computational grids is discussed through the numerical experiments. The proposed system is a master worker model. In this system, a master site reserves the information of the best searching point of a worker site in a queue when the master checks the calculation progress of the workers. At the same time, the master site sends the other information of the searching point that is derived in the worker site to the other worker site. By this operation, the searching information is transferred to every worker site. The proposed system can solve the problems on the computational grids; the sudden halt of the site and network. These characteristics of the proposed system are confirmed and discussed through the numerical experiments.

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This paper presents a new method to determine optimum topologies for truss structre by using affinet transformation. Our basic idea is to obtain optimum topology in complex design domain from optimum topology obtained in simple design domain by using affine transformation. We define simple design domain and optimum design problem. We calculate optimum topology in the simple design domain. For determination of optimum topology we use Genetic Algorithms. We call this optimum topology as basic optimum topology. Then we apply affine transformation to basic optimum topology, and can obtain some optimum topologies. To compare with those topologies, we calculate optimum topologies directly in the same design domain after coordinate transformation. We show that strain energy between orthogonal and nonorthogonal coordinate system is conserved under a certain condition by affine transformation, and our proposed method are simple and faster to get the optimum topology.

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This paper presents fundamental contents of a general-purpose genetic algorithm (GA) Workbench under development. We consider for the workbench to be more versatile by adopting superior GA operations peculiar local rules different to each problem. The local rules work effectively to accelerate convergence of GA operations. The bench is developing on the viewpoints of 1) being available for many kinds of GA operations, 2) being a platform-independent and 3) making the bench so as to be black box by adopting object-oriented language C++. Consequently the bench will become possible to apply to various kinds of optimization problems.

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The optimal design problems of trusses can be classified into three problems, size, topology and layout in weight minimization problems. All of these classified problems are solved by using the algorithm reported in here. Size problems already are reported efficiency to optimize by using index alpha of FSD. The algorithm is applicable to topology optimization problems by adding node movements as genes. Moreover, the solutions can be obtained with sufficient accuracy to various kinds of optimal problems by the general-purpose optimization tool GA Workbench, which is under development. In this report two examples are shown 2-dimentional trusses by GA Workbench.

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This paper proposes an optimum design problem of structural and control systems, taking a 1-link flexible arm as an example. This object is modeled by finite element method, and an output feedback H_∞ controller is designed using H_∞ control theory. The objective functions of structual system and control one are structual weight and H_∞ norm of transfer function from disturbance input to controlled output, respectively. Design variables are cross sectional areas of flexible arm. This design problem becomes a multi-purpose objective one. By transforming it into a single-purpose problem, optimum solutions are obtained. In this approach, we adopt the simplex method for solving this nonlinear problem. As the result, the optimum form of flexible arm is such that tapers off. Through the numerical examination we show the validity of the optimum design.

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[in Japanese]

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Stiffener layout patterns are studied in this paper to acquire the maximal natural frequency for a plate by applying a growing and branching rule just like tree branch model. The stiffener starts from seeds, positions of which are specified in advance, and grows in the direction depending on the sensitivity of natural frequency with respect to the cross sectional area of the stiffener. The update increase of cross sectional area is proportional to the sensitivity value. When the cross sectional area reaches a specified threshold value, the stiffener will branch off or degenerate. Simulation of some numerical examples are implemented to prove the validity and effectiveness of the proposal method, and optimal patterns of stiffener layout for some kinds of support conditions are demonstrated.

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A smart structure is composed of the piezoelectric film sensors and actuators in order to reduce the structural vibration. H_2 controller is designed with the reduced order model of the smart structure which is obtained by finite element and modal analyses. The control force is applied by the piezoelectric film actuator and the feedback signals are detected by the piezoelectric film sensor and the accelerometers in the system. The vibration response is suppressed by the modal control and the displacement control in which the shape of the piezoelectric actuator is appropriately designed for the enhanced control performance. Efficient optimization algorithm based on a two-step procedure is employed in the simultaneous optimization of piezoelectric shape and H_2 control system. It is verified by some applications that the enhanced performance for the vibration suppression can be achieved by the presented optimum design.

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Despite a recent need for the improvement of train crashworthiness, few design methods have been proposed. To establish it, we tried to introduce the concept of "Crushable body structure" to the design of train bodies in the past reports. There a train car with crushable zone was modeled by nonlinear spring and mass systems. Here we adopted a closer nonlinear spring and mass model to the real structure, and propose a method to determine the optimized structure of the train. We also considered an optimization problem by using the same model. Then we solve the problem by two different optimization methods and find strengths of nonlinear spring in the crushable zones as to minimize the maximum decelerations evaluated in the center of the gravity of the train. We use 1-car train model and 2-cars train model to compare the results. In several numerical examples, it is seen impact decelerations were reduced, and passenger zones could be maintained enough spaces not to injure passengers by the proposed method.

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