Layout Optimization Method Research Articles

212 耐衝突部材のトポロジー最適設計

In this paper, we propose a topology optimization method of a structural members for crash-safety by using density approach. This method is based on the generalized layout optimization method and design variable is a virtual isotropic material whose properties are functions of the element density. Because of the finite element configuration, the optimal configuration tend to have checkerboard patterns and the gray scale density in this approach. For this reason, we applied the gravity control function for design of structural members for crash-worthiness as a filtering method. Moreover we also applied the parallel computing to reduce the calculation time. Several numerical examples are shown to verify the present method.

An investigation into the use of spatial coordinates for the genetic algorithm based solution of the fixture layout optimization problem

The fixture layout optimization problem is highly modal. It has been shown that layout optimization methods that use the genetic algorithm (GA) are effective at finding high quality solutions. To date, such methods have used FEA node numbers to represent the locations of fixture elements. This paper presents a new GA based optimization method that uses spatial coordinates to represent the locations of fixture elements. This method integrates a number of important GA concepts such as real encoding, increased mutation, and sharing. Test results show that the new method provides higher quality solutions with substantially less numbers of generations than the old method. These results also show that the use of increased mutation and sharing significantly improves the performance of the new method.

An investigation of the effectiveness of fixture layout optimization methods

Deriving the optimal layout of fixture elements is critical to minimizing the impact of fixture–workpiece deformation on machined feature error. Various optimization methods for solving this problem have been reported. Unfortunately no investigation has been executed to compare their relative performance. This paper presents the methodology and results of an extensive investigation into the relative effectiveness of the main elements of these competing methods. All methods were tested over a broad range of conditions. Performance measures that were tracked included solution quality, solution repeatability, and computation time. The results of this investigation show that the best overall performance is provided by optimization methods that use both the genetic algorithm and continuous interpolation for the distribution of boundary conditions.

Facility layout optimization using simulation and genetic algorithms

Traditionally, the objective of a facility layout problem has been to minimize the material handling cost of the manufacturing system. While it is important to reduce the amount of material handling, the traditional methods do not address the actual time at which the material is transported. In today's short cycle time production environments, the timing of material movement may have a bigger impact on the productivity of the system than its cost. In this paper, a facility layout optimization technique is presented that takes into consideration the dynamic characteristics and operational constraints of the system as a whole, and is able to solve the facility layout design problem based on a system's performance measures, such as the cycle time and productivity. Each layout solution is presented in the form of a string that is suitable for analysis by a genetic algorithm technique. These solutions are then translated into simulation models by a specially designed automated simulation model generator. Genetic algorithms are used to optimize the layout for manufacturing effectiveness while simulation serves as a system performance evaluation tool. Combined with a statistical comparison technique to reduce the simulation burden, the test results demonstrate that the proposed approach overcomes the limitations of traditional layout optimization methods and is capable of finding optimal or near optimal solutions.

Optimization of 2-D structures subjected to nonlinear deformations using the homogenization method

The generalized layout optimization method is applied to nonlinear problems. The algorithm was originally invented by Bendsoe and Kikuchi (1988), where an admissible design domain is assumed to be composed of periodic microstructures with tiny cavities; the sizes and the rotational angle of the cavities are defined as design variables which are optimized to minimize the applied work. The macroscoic material tensor of the porous material is calculated by the homogenization method for the sensitivity analysis. In order to apply it to nonlinear problems, we present a 2-D database of the material tensor calculated by the elasto-plastic homogenization method and an interpolation technique of the database for the practical computation. Several numerical examples of 2-D structures and a thin shell are shown to demonstrate the effectiveness of our algorithms. The algorithm is also extended to the finite deformation problems, and a practical optimized design is exhibited.

Optimization of 2-D structures subjected to nonlinear deformations using the homogenization method

The generalized layout optimization method is applied to nonlinear problems. The algorithm was originally invented by Bendsøe and Kikuchi (1988), where an admissible design domain is assumed to be composed of periodic microstructures with tiny cavities; the sizes and the rotational angle of the cavities are defined as design variables which are optimized to minimize the applied work. The macroscoic material tensor of the porous material is calculated by the homogenization method for the sensitivity analysis. In order to apply it to nonlinear problems, we present a 2-D database of the material tensor calculated by the elasto-plastic homogenization method and an interpolation technique of the database for the practical computation. Several numerical examples of 2-D structures and a thin shell are shown to demonstrate the effectiveness of our algorithms. The algorithm is also extended to the finite deformation problems, and a practical optimized design is exhibited.

Optimal Layout of Damping Material Using Homogenization Method.

This paper shows an optimal layout algorithm of a damping material which is affixed on a vibrating surface of a structural component. This method is based on the generalized layout optimization method(1) where a prescribed amount of material is distributed in a design space so that an objective function may be minimum. The complex elastic moduli are employed to express the visco-elastic behaviours of a damping material under periodic loads. Two different objective functions are employed in numerical examples. One is dynamic mean compliance, which is useful in reducing the displacement at the loading points. The other is square product of the nodal displacement vector, which is effective to reduce the overall dynamic response of the structure. It is shown that both of the results show good convergence and give reasonable layout.

Optimal Design of a Shell Structure Subjected to a Plastic Deformation.

In previous reports, an optimization method for a two-dimensional structure subjected to a plastic deformation was presented and some numerical examples were shown to demonstrate the validity of the algorithm. The algorithms is based on the generalized layout optimization method presented by Bends■e and Kikuchi, where an admissible design domain is assumed to be composed of microstructures with cavities and the cavity size and the rotational angle of the microstructures are design valuables. In this study, the method is applied to a thin shell based on the layered approach subjected to a plastic deformation, For the sensitivity analysis, two-dimensional data base of macroscopic elasto-plastic material tensor which was calculated by the homogenization method is adapted to the in-plane stiffness of each layer. Several numerical examples are shown to validate the present method. The algorithm is also adapted to finite deformation problems. The effectiveness of this method is shown by a numerical example.

Development of shape-topology optimization method for air duct layout (Part 1: Survey on two-dimensional design problems) Tohru Komoriya (Subaru Research Center Co., Ltd.)

Development of shape-topology optimization method for air duct layout (Part 1: Survey on two-dimensional design problems) Tohru Komoriya (Subaru Research Center Co., Ltd.)

Optimal Design of a Two-Dimensional Structure Subjected to a Plastic Deformation. 1st Report. Formulation.

We presented an algorithm for shape and topology optimization of two-dimensional structures subjected to a plastic deformation. This algorithm is based on the generalized layout optimization method proposed by Bens φe and Kikuchi in 1988, where a prescribed amount of material is distributed in a given domain so that the work done by applied loads may be minimized. In the present algorithm, a given domain is assumed to be composed of microstructures with a regular triangular cavity, and the rotation angles and cavity sizes of the microstructure are taken as design variables. A material database of microstructures taking into consideration in the effect of plastification for various design variables is made to enable an elastoplastic analysis and a sensitivity analysis of porous material. The accuracy of the elastoplastic analysis using the database is confirmed through a numerical example.

Optimal Material Distribution of a Frame Structur Subjected to a Plastic Deformation. 1st Report. Optimization Algorithm.

An optimization algorithm of a frame structure subjected to a plastic deformation is presented in this paper. This method is based on the generalized layout optimization method proposed by Bendsφe and Kikuchi in 1988, where a solid-cavity composite material is distributed in an admissible domain and cavity size is determined so that it becomes large in the area where strain energy is small. In the present algorithm, a material is distributed inside frame members so that the external work done by prescribed loads may become minimum. As a result, some regions inside frame members may be hollow while others may be solid.

Optimal Material Distribution of a Frame Structure Subjected to a Plastic Deformation. 2nd Report. Verification of the Algorithm with Numerical Examples.

An optimization algorithm of a frame structure subjected to a plastic deformation was presented in the previous report. It is based on the generalized layout optimization method proposed by BendsΦe and Kikuchi in 1988, where a solid-cavity cmposite material is distributed in an admissible domain and cavity size is determined so that it becomes large in the area where the strain energy is small. In this report, the present algorithm is verified by several numerical examples in which it is shown that the object function is highly improved by the optimization and converges rapidly. The optimization algorithm including the effect of shear deformations is also discussed for frame structures with fairly short members and a numerical example is shown.

Structural optimization of guyed trusses

HERE is a strong trend in the design of skeletal structures to, wherever practical, make increasing use of tensioned cables. One of the best examples of the convergence of structural efficiency to a best design can probably be found when studying the evolution of the configurations of power transmission towers. From the early days of cantilever truss structures these have now evolved to the much lighter rope type in which two separate vertical cable-stayed lattice struts support the power conductors through suspension from a cross rope. Apart from the savings in material, significant savings in transportation cost can also be obtained especially since erection often has to occur in remote areas. Although the cable-stayed structures are easy to analyze, the determination of a best or least weight design can be complex due to the variety of design variables available. These are, typically, configuration, geometry, member sizing, and prestraining. The optimization of a configuration is complex and is best accomplished manually, perhaps with the aid of layout optimization methods. On the contrary, geometric and prestrain optimization and sizing can be treated by direct sensitivity analysis of a chosen topology. This paper describes the sizing and prestrain optimization of guyed trusses. For the nonlinear analysis the total Lagrangian method is used in combination with the pure Newton method and adaptive arc-length procedures. Because of the lack of stiffness of a cable structure in its undeformed state, soft spring elements are used to stabilize the structure temporarily during the load stepping phase. The choice of prestrain instead of prestress variables is justified by both the simplicity of inclusion of prestrain in the sensitivity analysis and by the independence of the prestrain quantity with respect to the sequence of pretensioning of the structure. The prestraining of a member can also simply be seen as the lack of fit of a member in a fixed geometry and can, in practice, be accomplished by specifying member lengths to create a predetermined lack of fit or by specifying turns of a turnbuckle included in the member. For the optimization process, two optimization methods are used, namely, the sequential quadratic programming (SQP) method IDESIGN (PLBA) authored by Arora1 and the successive approximation method (SAM) algorithm of Snyman and Stander2 and Stander et al.3 Using two methods gives optima in which greater confidence can be placed. Additionally, some idea of the degree of difficulty of the newly formulated optimization problems is gained. Five examples are given to demonstrate the analysis and optimization methodology. The optimization of example structures subjected to second-order effects show that unexpected results can be obtained. A number of papers,48 related to the general topic of the sensitivity analysis and optimization of structures with nonlinear geometric

Optimization of a frame structure subjected to a plastic deformation

An optimization method for a frame structure subjected to a plastic deformation is proposed in this paper. The method is based on the generalized layout optimization method proposed by Bendsoe and Kikuchi in 1988, where the solid-cavity composite material is distributed in the admissible domain and the cavity size is determined so that it becomes large in the area where the strain energy is small. Elasto-plastic analysis based on the homogenization method is carried out to obtain the nonlinear average stress-strain relations of a porous material first. Then the optimization algorithm of a frame structure is derived by taking plastification into account. Finally in order to demonstrate the effectiveness of the present algorithm, several numerical examples are illustrated.

A Method for the Shape and Topology Optimization of Mechanical Structures by Using Genetic Algorithm. Layout Optimization Method by Adoption of Removal and Addition parameters of Elements as Chromosomes.

This paper presents a method for the shape and topology optimization (i. e., layout optimization)of mechanical structures by using a genetic algorithm. It may be difficult or not always possible to obtain the global optima for layout optimization problems by using the traditional gradient-based algorithms. The generic algorithm is known to be an excellent means to obtain the global optima for the problems. The algorithm, however, usually requires a large number of generations and individuals for the final layouts to be obtained certainly. We propose a method in which the behaviors of layouts are pursued for the optimum layout by selecting the layouts of the mechanical structures as individuals instead of the finite elements, and by adopting removal and addition parameters of elements as chromosomes. The efficiency and reliability of the method are demonstrated with various experiments for finite-element models of two-dimensional continuums and for minimum weight problems.

Optimization method for mount layout and mount specifications of vehicle sub-frame

The purpose of this study is to develop an optimization method for designing the mount (vibration insulator) system of a vehicle sub-frame (engine cradle), using modal analysis and sensitivity analysis in general viscous damping. Designers have to balance the contradictory performances (ride comfort, driving stability and driveability). Hereby for the performance of idle vibration, the design parameters (mount layout, stiffness damping) are optimized with an elastic body model, considering frequency dependence of mount characteristics. Furthermore, it is proved by experiments that the proposed method is effective in the early design stage.

Interactive Layout Optimization of Trusses

A method is presented for performing practical layout optimization of trusses subjected to arbitrary multiple-loading conditions using interactive computer graphics. Design constraints are allowable tensile and compressive stresses based on the American Institute of Steel Construction specification as well as user-specified displacement constraints and lower and upper bounds on design variables. The layout optimization is based on changing certain key dimensions of the truss and performing optimization for each layout by taking advantage of the interactive environment of computers with graphic facilities. In contrast to formal shape optimization procedures that are computationally expensive and may produce non-practical designs, this synergic man-machine approach is an effective method for practical layout optimization of trusses.