This article presents the use of optimization technology in aerospace engineering. The optimization has been the key technology since the first Right brothers' Flyer, and must have the important role in the development the future Spaceplane which will take off horizontally, climb to the space-station, and make a landing horizontally.

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In this paper, a simultaneous design method for systems with variable inertial term is proposed. Because conventional control methods can hardly deal with the system due to the variable inertial term, a noninteracting control is applied to linearize the system. In addition, to insure the reliability of the imperfectly linearized system, evaluation methods in H_2 and H_∝ are determined. Through the linearization method and the evaluation methods, conventional linear control methods can be applied to the system. The property of this structure system concerns the control performance so that the simultaneous design method of structure and control is employed to design the controlled system. This design method is applied to an example of a system with variable inertial term, and it is confirmed that the method can design the controller and improve the control performance.

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In this paper, we deal with solving optimal design problems of a new type active suspension and its control system based on a modified genetic algorithm. The problems aim to pursue the improvement of vibration isolation performance to the limit. We consider simultaneously to optimize a state feedback gain vector of the control system and structural parameters of the suspension, i.e., stiffness of a spring and damping coefficient of a dash pod. As for active suspension of a 1/4 passenger car model, we do to optimize a feedback control gain vector and structural parameters simultaneously. Then, we show to be able to design an active suspension by which a vehicle body hardly receives the influence of road disturbance.

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In this paper, we study an inverse kinematic problem in which trajectories of walking robot toes are generated under the condition of minimum walking energy. Under spatial constraints such as obstacle avoidance, mathematical optimization method is used for the optimization of several parameters which describe the trajectory function of toe. The calculation of optimum trajectory takes much time, therefore it is difficult to control for walking robot in real time. In this study we use a neural network controller. Data of optimum trajectory obtained by using the mathematical optimization is used for learning of the neural network. Under spatial constraints such as an obstacle, the optimum trajectories of toes are generated by the neural network controller and the controlling values of joint angles are successfully obtained.

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We consider an integrated design problem of structural and control systems for a class of lossless systems. For such class of control object we show that the maximum stability margin for the normalized coprime factorization becomes 1/√<2>. With this result the H_∞ controller proposed by McFarlane and Glover can be obtained explicitly. We show that an integrated design of the structural and control system for the closed-loop system can be approximately cast as LMI.

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This paper describes a new multiobjective GA named Adaptive Range Multiobjective GA (ARMOGA). Adaptive Range GA (ARGA) has been extended to multiobjective optimization problems. It helps GAs to handle a large search space that requires continuous sampling. ARGA has two characteristics : de-coding based on Gaussian random number and adaptive search space renewed at a certain interval. The resulting AEMOGA is compared with the conventional MOGA by using test problems. The results confirm that ARMOGA consistently finds better solutions than the conventional MOGA.

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Mixed-integer linear programming (MILP) can be used for a variety of optimization problems. However, it is limited to relatively small-scale problems, because its computation time increases dramatically with the number of integer variables. Decomposition methods have been presented to derive good feasible solutions of MILP problems. The objective of this paper is to propose a strategy for partitioning variables in using a decomposition method presented by the authors. The strategy proposed here is to decompose an original MILP problem into the smallest MILP subproblems, each of which has a single integer variable, and enables one to assume the values of part of integer variables efficiently to obtain a reduced MILP master problem. A single-period operational planning problem of a simplified heat supply system is investigated analytically to show the meaning and validity of the strategy. A multi-period operational planning problem of a practical heat supply system is also investigated numerically to show the validity and effectiveness of the decomposition method into which the strategy is incorporated.

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The authors are aiming to establish the method that vehicle frontal structure and occupant restraint system are designed simultaneously for the vehicle frontal collision with a balance between structural lightening and occupant safety. In this study, the deceleration waveform on vehicle collision was focused because it can be considered as an interface function between the design of frontal structure and the design of occupant restraint system. By treating the deceleration waveform as a parameter, its effectivity analysis was conducted for occupant injury and the design of occupant restraint system using the Statistical Design Support System, and a correlation among those was considered.

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In this paper, we introduce a improved perturbation analysis of eigenvalue for structural-acoustic coupled system. Two years ago, we gave the derivation of perturbation series from a standard symmetric eigenvalue, this time we give it from a non-symmetric eigenvalue problem. The coefficients of the perturbation series will be more compact because it is unnecessary to calculate the part from non-symmetric problem into symmetric one. We confirm the adequacy through some numerical examples.

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In current product design and manufacturing environments that depend upon optimization techniques, numerous product criteria such as cost, performances, qualities, reliability, environmental impact, and product life cycle factors, must be all be considered in order to obtain the most preferable design solution. During such optimization processes, a key point that enables present design solution limitations to be broken through is to make use of wider feasible design regions, which include superior solutions. Collaborative optimization is the most promising strategy for achieving this broadening of design regions. In this paper, first, the merits of collaborative optimization are explained, and next, the difficulties of collaborative optimization are described. Then, collaborative optimization for product design and manufacturing is discussed from the following three collaboration viewpoints : (1) Collaboration in which decision-makers of different divisions having different requirements and knowledge cooperatively evolve solutions concerning product design and manufacturing, (2) Collaboration in which different groups and/or enterprises having competitive relationships consider collaborative projects, and (3) Collaboration in which experts are integrated into the optimization process, using mobile-agents operating in networked computing environments. Finally, current perspectives and the future outlook concerning these kinds of collaborative optimization are discussed.

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If the buckling mode of the main side members can be kept in a good mode, it is possible to get a stead deceleration characteristic, and to reduce the weight. In this study, the authors proposed a new mode controlling approach to control the buckling mode of the side member. The results of the optimized design given by the new approach showed that not only can this new design method reduce the weight of the side member at the geometric design step, but also it can improve the basic characteristic of the energy absorbing behavior of side member.

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A large-scale machine system often has a general hierarchical structure. For hierarchical structures, optimization is difficult because many local optima exist in the hierarchical optimization problem, however genetic algorithms that have a hierarchical genotype can be applied to treat such problems directly. Relations between the structural components are analyzed and this information used to divide the hierarchical structure. Dividing large-scale problems into sub-problems that can be solved using parallel processed GAs increases the efficiency of the optimization search. The optimization of the large-scale system then becomes possible due to information sharing concerning Pareto optimum solutions for the sub-problems.

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Nowadays one of the largest bottlenecks against the optimization of expensively time-consuming analyses, such as CFD problems and crash analyses, should be the number of iterations to optimize. So far many researches have been performed to reduce the number of iterations to optimize with some techniques, such as RSM approximation method and Orthogonal Arrays DOE. On the other hand, this paper tries to show an application example of VCM approximation method for CFD problem not to reduce the number of iterations but to decrease the total elapsed time. The difference between the efficiency of VCM applied case and the one of not-applied case is obvious. This VCM approximation method can be one of the most effective techniques to optimize some large analyses.

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In this technical paper, a example of MDO (Multi-Disciplinary Optimization) technology and its application are presented. MDO is the most effective solution or framework for the successive concurrent engineering and could be a true collaborative engineering environment. In this paper, MDO focused not on a particular design area but on whole design process of development cycle. The example problem employed in this paper is an optimization problem of molding injection and structural analysis with TIMON and NASTRAN.

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This paper proposes an efficient design optimization algorithm for the multidisciplinary design optimization of link mechanisms. Since the design problem of link mechanisms is multidisciplinary and mini-max type under time-dependence of link motion, the algorithm is composed of non-hierarchic coupled system decomposition, which consists of the iteration of partial optimization of divided subproblems and coordination of such partial solutions, and mini-max relaxation. Further, successive quadratic programming (SQP) is used as a mathematical programming technique by inheriting Hessian approximation of Lagrangian function across its iterative executions. After the multidisciplinary design problem of a link mechanism used in hydraulic shovels is formulated, its design optimization with the proposed method is demonstrated. The numerical results show more than about four times of speed-up and robust performance as compared with a conventional optimization method.

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This paper describes unified and efficient new optimum design methods for plane frame structures with nonlinear materials. The structural analysis problem with material nonlinearity is formulated as the total complementary energy minimization problem subject to equilibrium equations, and the necessary conditions for nonlinear analysis problem are derived. Then the primal optimum design problem is reformulated considering both the primal design constraints and the necessary conditions for analysis problem. Furthermore the unknown member end forces for each member elements and the displacements at the free nodes are also dealt with as the design variables in addition to the primal sizing and configuration variables. The reformulated optimum design problem is solved efficiently by using the gradient projection method. The advantages, rigorousness, efficiency and reliability of the proposed optimum design method are demonstrated by comparing the results obtained by the dual method in which the behavior sensitivities are used.

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Applying the basis vector method to complicated shape optimization problem is examined that it is effective things. But, when actually calculating shape optimization problem or in real optimization system development, many application problems exist yet. In this paper, a flexible basis vector method is applied to the optimization of 3D structure. And examined some problems such as : how to control inside substructures when the boundary shape is changed; how to check the independence of basis vector to each other; and the re-meshing problem when the shape variable is changed. Then proposed calculation algorithm, respectively. In the numerical example, and optimization problem of structure is calculated, the result verify out validity of present methods.

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Finite Element Analysis is widely recognised as a useful design tool in every product development scene for predicting various characteristics of predetermined structures. On the other hand, requirement for easy-to-use shape optimization procedure for achieving design objectives is becoming higher. Although basis vector method is a typical shape optimization procedure, it requires cost and knowledge to prepare several basis vector models before the analysis is made. In this study, an easy 3D shape optimization method for FEM solid element model is proposed. It does not depend on basis vector method, but combines our custom simple program with MSC/NASTRAN numerical value optimizer which is widely adopted for product development.

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In the case of the engine mounting design, the decoupled layout is very important for the isolations of engine vibration and shock torque. On the other hand, the optimum layout is difficult to select many parameters such as mounting position, cushion rubber spring rate, etc. So, the Genetic Algorithm so called GA is newly applied for the stiffness matrix calculation and the many parameters optimization. The MPOD, stands for Most Probable Optimal Design based on the Holographic Neural Network, is also tried to compare the accuracy against GA. The optimized results by GA were well matched with the theoretical calculation, which needs the special vibration analysis technique and also takes over two weeks. But, it takes only one hour, and the inexperienced engineers can easily obtain the optimized result. By the confirmation test of FEM, the engine lateral vibration level at 25Hz dropped below 1/5 and its effects were significant.

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Suspension design is one of many important disciplines required to develop automobiles. Since a suspension system has strong non-linearities and many design variables, it is difficult to design. In this paper, the authors discuss the benefits of an optimization technique to design suspension systems and propose a design support system based on the concepts of optimization, Response Surface Methodology (RSM), and consideration of robust design techniques. A prototype of the design support system for automobile suspension design was developed. In this system, the suspension was analyzed and evaluated by the mechanical system simulation software ADAMS. The validity of the design support system was clarified through case studies by focusing on toe characteristics. The design technique using the proposed design support system is discussed.

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A discretized model to represent dynamic and flexible behavior of structural member is presented for the analysis and synthesis of compliant mechanisms, which utilize the flexibility to obtain its dynamic motion for prescribed performance. The flexible member is discretized into straight segments connected by three-dimensional virtual coil springs at nodes. The equation of motion is derived on the basis of Lagrange's equation of motion in terms of the generalized coordinates, that is, the Euler angles of the segments. The time-history analysis of the motion associated with sensitivity analysis with respect to design parameters is performed by Newmark β method. The change of the motion of flexible member is approximated in the first-order sense with respect to design parameters change through the sensitivity analysis. The governing equations to determine design parameters are derived so as to make the approximated motion equal to prescribed one. The solution of the design parameters is handled by the Moore-Penrose generalized inverse, since the governing equations are summarized in the form of linear simultaneous equations with rectangular matrix of coefficients.

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In this paper, an effective method for the topology optimization of 3D structures is presented. In this method, the structures are analyzed using the finite element method with PCG solver. The density approach is adopted as the topology optimization method. The optimality criteria method is used for solving the optimization problem, and the filtering method is used for preventing the checkerboards in the solution. The effectiveness of the present method is demonstrated by some numerical examples.

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Most rubber components usually suffer large deformation, thus one should consider finite deformation theories when designing rubber products such as tires. Although FEA is useful for computing nonlinear structural response in standard problems, it is more difficult to predict the undeformed original to-be-manufactured shape of a part corresponding to a design constraint involving a prescribed deformed shape under a given load. For example, one can use an optimization technique to predict the original shape in the sense of an inverse problem via successive iteration. As the another procedure to solve such inverse problems, Govindjee and Mihalic have proposed a new computational procedure to predict undeformed (to-be-manufactured) shapes for prescribed exterior deformed configurations, Cauchy traction and displacement boundary conditions. In this paper, we demonstrate applications of the inverse shape determination problem for a tire design. The proposed methodology enables us to predict an undeformed (to-be-manufactured) tire shape corresponding to the design constraint of a prescribed exterior deformed configuration. After reviewing the formulation of the inverse shape determination, some numerical examples illustrating the methodology in a tire design are presented.

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This paper presents a numerical solution to boundary shape optimization problems of continua with respect to minimization problem of external work under a volume constraint taking into account material non-linearity and minimization problem of the time integration of squared error on the responded velocity and the prescribed velocity under a volume constraint taking into account geometrical non-linerity. Shape variation is described by using a one-parameter family of mappings defined in a domain where a continuum lies initially. The shape sensitivities are derived using the Lagrange multiplier method and the formula of the material derivative. A procedure to solve this problem using the traction method is presented, which one of the authors has proposed as an approach to solving domain optimization problems. The varidity of proposed method is verified by applying basic numerical examples.

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This paper investigates the structural optimization of plate wing for supersonic flutter. The optimization is performed to improve the critical dynamic pressure of the wing model by extending the Evolutionary Structural Optimization method. A delta wing with elastic plate is considered for the analysis model. The objective function is the difference between the variation of the first and second eigenfrequency in the vicinity of the critical dynamic pressure. Numerical results show that the critical dynamic pressure has been improved by the proposed optimization procedure.

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Algorithms based on Semi-Definite Programming (SDP) are proposed for the truss topology optimization problems for specified fundamental eigenvalue of free vibration and linear buckling load factor, and optimal topologies of trusses are computed by using the Semi-Definite Programming Algorithm (SDPA). It is well known that optimizing structures for specified minimum eigenvalue is difficult because of non-differentiability of the minimum eigenvalue for the cases of multimodal solutions. It is shown, in the examples, that the proposed algorithms are applicable to multimodal cases.

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Evolutionary Structural Optimization (ESO) method is one of the powerful and promising techniques for pursuing the optimal structural form. Although it is easy to carry out the calculation of ESO, there have been remained some weak points in its evolutionary process, by which inefficiency of calculation is caused or unreasonable solutions are generated. A new method through the usage of the contour lines is proposed in order to remove such defects of the usual ESO as well as to enable the structures to not only be scraped off but also grow up toward the final optimal structures. Some numerical examples clearly show the effectiveness of the proposed scheme.

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Present paper describes the use of a stochastic search procedure that is the bases of genetic algorithms (GAs), in developing near-optimal topologies of load-bearing truss structures. Many works have been already published until today on the structural optimization of truss topology using the genetic algorithms. In most cases these works express the truss topology as a combination of members, and existence of each member is directly connected to the genetic code. These methods, however, have a fatal weak point. Namely when the topology is made along these methods, they might include needless members or those which lies on the other members. In addition to these problems, generated structures are not always stable. These problems become more remarkable when freedom of the problem becomes large. We have already proposed a new method that resolves those problems by expressing the truss topology as a combination of triangles that are joined with each other. However, the length of chromosome tends to become long. This paper proposes brand-new implements for effective optimization. Detail of the proposed methodology is presented as well as the results of numerical examples that clearly show effectiveness and efficiency of the present method.

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In the process of optimization with a large nonlinear dynamic analysis, a large amount of computational cost is required to obtain the optimal design. A large portion of this cost can be avoided using Response Surface Model (RSM) by approximating the more costly analysis. Therefore, the optimization with RSM is studied by various approaches. Sequential Approximate Optimization (SAO) that allows RSM to be updated with new design points during optimization obtains final design better then the method of non updating RSM. But, the design is not always optimal design. In this paper, we propose a method that cross SAO's design and a good design of current process of optimization by the real type crossover model (RXM). RXM was referred crossover models of Real coded Genetic Algorithms, was developed. We applied a multimodal parameter problem and a nonlinear dynamic analysis problem, obtained good results.

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In the process of optimal design for nonlinear problem, the sensitivity analysis techniques can be used easily by Response Surface Model (RSM). But RSM can't be applied to the problems that have folded response, whose differential coefficient is not continuity, or those that have plural peaks. In this paper, we present a technique to approximate the folded response by RSM using Moving Least Squares method. And we also present an effective method for searching the optimum solutions.

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In this paper, the compact thermal modeling by using the Response Surface Methodology (RSM) is proposed. It is known that the compact model ing in the thermal simulation can reduce the calculation cost for a system model. But our original GA-based technique to develop a thermal compact model takes a considerable CPU time, because it includes thermal simulation processes in the optimazation process. To separate the thermal simulation processes from the optimazation process, we employ the RSM for our new compact modeling technique. We applied this technique to develop a simple compact model, and confirm that it can save the CPU time keeping its accuracy to some extent.

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This paper presents a unified and efficient new optimum design method for nonlinear plane frame structures with box sections. In the primary design problem, the design variables are the upper and lower flange plate thicknesses of box sections of all member elements and the stress and displacement constraints are dealt with as behavior constraints. The primary optimum design problem is reformulated considering both the primary design constraints and the necessary conditions for analysis problem which are derived from the analysis problem expressed as the total complementary energy minimization problem. The reformulated optimum design problem is solved efficiently by using the gradient projection method. In the optimization process, the complementary energy sensitivity with respect to primary design variables is used, however the calculation of behavior sensitivity with respect to primary design variables is not necessary. The rigorousness, efficiency and reliability of the proposed method are demonstrated by comparing the results obtained by the dual method in which the behavior sensitivities are used.

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Computer Aided Engineering (CAE) is widely utilized in automotive industries since its performance has been improved in ten years. CAE makes it possible to quantitatively estimate a variety of automotive performance, and to propose an alternative idea to improve it. Most automotive designers, however, cannot directly use CAE due to sophisticated operations require ring specific skills. In order to overcome this problem, a new concept of CAE, First Order Analysis (FOA), is proposed. In this paper, we discuss two optimization methods utilized in FOA. That is, first, the topology optimization method using beams is described. Second, the shape optimization based on the response surface method is explained. Finally, some prototypes of software are presented to confirm the methods presented here

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Recent years, financial difficulties led engineers to look for not only the efficiency of the function of a product but also the cost of its development. In order to reduce the time for the development, engineers in each discipline have to develop and improve their objectives collaboratively. Sometimes, they have to cooperate with those who have no knowledge at all for their own disciplines. Collaborative designs have been studied to solve these negotiations will be done successfully. However, in the most cases of real designs, manager of each discipline does not want to give up his or her own objectives to stress on the other objectives. In order to carry out these negotiations smoothly, we need some sort of evaluation criteria which will show efficiency of the product considering the designs by each division and if possible, considering the products of the competitive company, too. In this study, we use data Envelopment Analysis (DEA) to calculate the efficiency of the design and showed every decision maker the directions of the development of the design. We will call here these kinds of systems as supervisor systems and implemented these systems in computer networks that every decision maker can use conveniently. Through simple numerical examples, we showed the effectiveness of the proposed method.

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A new method for solving optimization problems is proposed in terms of a dynamical system. This method aims for compatibility, which has often been problem in solutions, between two requirements : searching with a high probability for the most likely candidates of the optimal points, and searching quickly in the region. The proposed dynamical system realizes setting vlues of the visiting-weight and speed of the orbits to the system, with an assumption of ergodicity, by values of long-time limit. High values can be set for the visiting-weight to areas where the objective function takes low (high) values. Further, independently, a high-value can be set for the speed of the orbits. Consequently, the two requirements can be satisfied. Accordingly, a trade-off between a searching-weight and a searching-speed does not exist. In a numerical simulation assuming an objective function, validity within a finite time for the system formulated with the long-time limit was confirmed.

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The present study employs and electric resistance change method for identifications of delamination cracks. For the method, appropriate number of electrodes to identify delaminations is investigated, and the diagnostic tool for the inverse problems to identify the delamination crack location and size from the electric resistance changes is discussed. FEM analyses are conducted to obtain electric resistance changes due to delamination crack creations with three-electrode, four-electrode and five-electrode type specimens. Using the artificial neural networks (ANNs), the required number of electrodes for identifications of delamination cracks location and size from the electric resistance changes is investigated. By comparisons of the estimations with the ANNs and with the response surfaces (RS), a better diagnostic tool is discussed in detail. As a result, the five-electrode type specimen is shown to be better for the identifications, and the RS using quadratic polynomials is a better tool than ANNs for identifications of delamination crack location and size using electric resistance change.

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The methodology of the sportswear design is not yet established. The sportswear is required of the better functions than those of the usual apparels, and its design must always be done with the expressions synergic between the Basic Design (body elements, functions) and the Visual Design (esthetic element, decoration). Especially the former i.e. Body elements, is the basic element of the design, and on its treatment depends the levels of the sportswears. Thus, the way to design purposively, is to analyse a human body anatomically, and to find the joint between the human body and the design. Here as an exemple, the extensibility and the dermatome structure of the skin will be demonstrated. These functions have the deep relations with the motor function, basic function of the sportswear, and will derive the structural principle of the apparel pattern which is its apropriate expression measure.

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A new multi-objective design approach is proposed for handling many different objective functions in the design problem of laminated composite plates. First, a number of various vibration and buckling eigenvalues are calculated for some discretized fiber angles of the plate by the Ritz method. These eigenvalues are taken to be the object functions. The second step is based on statistical treatment of the data. For each object function, the calculated eigenvalues for different fiber angles are normalized by the maximum value and then the deviated values are determined on the assumption that the eigenvalues are sujected to the Gaussian distribution with the standard deviation of 10 and average of 50. The optimal fiber angle, within the discretized values of fiber angles, is determined by examining the sum of the deviated values of all the object functions.

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The present paper shows an efficient optimization approach on composite structures for vibration where layer angles in addition to layer thicknesses are used as design variables. A high-quality approximation method of natural frequencies with respect to layer angle and layer thickness is proposed. First in the present paper, several approximate methods of natural frequencies after design variation are compared. Next an approximation method is then applied to a minimum weight design of cantilevered laminated plates under multiple frequency constraints. The validity of the present approach is verified through the numerical examples of laminated plates.

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In this study, the tunneling method is applied to the reliability analysis of a laminated composite plate subject to in-plane loads. In the first order reliability method (FORM), the structural reliability is evaluated as the minimum distance from the origin to the limit state surface in the standard normal distribution space. It is formulated as a nonlinear optimization problem. However, it is difficult to find the design point, when the limit state surface has several local minimum points such as a case of the laminated composite plate subject to the first ply failure. In order to find the global design point, the tunneling method is applied as one of global optimization methods. A new tunneling function suitable for the FORM is proposed to find the other design point which has a lower objective function value and satisfies the equality constraint. Through numerical calculations, the efficiency of the tunneling method is demonstrated.

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This paper studies the optimization of beam-type rahmen structures simply-supported at both edges by Genetic Algorithm. In optimization, maximum deflection or maximum principal stress of the structure subjected a concentrated force is minimized under the constraint condition, where total volume of the structure is kept to be constant, by selecting optimal beam members of the structure. The deflection or stress of the structure is evaluated by using the finite element program developed for two-dimensional elasticity in this study, and optimal design solutions are obtained from numerical calculations by using the genetic algorithm employing binary coding, reproduction, crossover and mutation.

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Stacking sequence optimization is an important problem in composite laminate design. It is efficient to use lamination parameters as design parameters. We have discovered the fractal structure of design space represented with out-of-plane lamination parameters. We also have proposed a novel approach named Fractal-branch and Bound Method which depends on the fractal structure. This method can find exact optimal solution deterministicly. This method is limited to the bending problem. This paper extended this method to solve multi-objective problem on out-of-plane lamination parameters.

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Recently, optimization becomes more important in various fields. The structural optimization by using genetic algorithms has been developed and applied to various kinds of products such as cathode-ray tubes, laser beam machines and cellular mobile telephone flips. A new optimization system that works on personal computers is developed so that engineers can use the optimization technique easily. This optimization system can handle several optimization techniques such as P-GA, FSD, SA and RSM. Furthermore, it is applicable to multiple fields optimization, for example, structural analyses, thermal analyses, vibration analyses and control analyses. This paper presents applications of the optimization system to structural optimization of products such as a three-dimensional laser beam machine, a cellular mobile telephone flip and a stator of a wind turbine generator Moreover, each optimization result of P-GA, FSD, SA and RSM is examined and discussed in detail, and a guideline to choose an optimization technique corresponding to optimization problems is proposed.

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The axial crushing behavior of a triangulated cylindrical shell constructed by one set of helical strips and circles lying on the surface, is simulated by the finite element method. This paper also discusses the affection to the crushing characteristic of the angle and the number of the helix as well as the division along the axis direction of the cylinder. Based on the numerical analyses, minimum problem of the axial crushing force of triangulated cylindrical shells are solved by using the crashworthiness maximization technique for tubular structures which combined the techniques of design-of-experiment, response surface approximation as well as usual mathematical programming. Moreover, the behavior of the triangulated cylinders when subjected simultaneously to crushing and twisting forces is studied.

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