• Transactions of the Korean Society of Mechanical Engineers A
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• v.25 no.9
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• pp.1444-1451
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• 2001

The evolutionary structural optimization(ESO) method has been under continuous development since 1992. The bidirectional evolutionary structural optimization(BESO) method is made of additive and removal procedure. The BESO method is very useful to search the global optimum and to reduce the computational time. This paper presents the ranked bidirectional evolutionary structural optimization(R-BESO) method which adds elements based on a rank, and the performance indicator which can estimate a fully stressed model. The R-BESO method can obtain the optimum design using less iteration number than iteration number of the BESO.

• Structural Engineering and Mechanics
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• v.27 no.1
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• pp.49-61
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• 2007

This paper presents a modified and improved bi-directional evolutionary structural optimization (BESO) method for topology optimization. A sensitivity filter which has been used in other optimization methods is introduced into BESO so that the design solutions become mesh-independent. To improve the convergence of the optimization process, the sensitivity number considers its historical information. Numerical examples show the effectiveness of the modified BESO method in obtaining convergent and mesh-independent solutions. A study of the effects of various BESO parameters on the solution is then conducted to determine the appropriate values for these parameters.

• Structural Engineering and Mechanics
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• v.72 no.2
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• pp.181-190
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• 2019

Topology optimization of structures seeking the best distribution of mass in a design space to improve the structural performance and reduce the weight of a structure is one of the most comprehensive issues in the field of structural optimization. In addition to structures stiffness as the most common objective function, frequency optimization is of great importance in variety of applications too. In this paper, an efficient multi-objective Bi-directional Evolutionary Structural Optimization (BESO) method is developed for topology optimization of frequency and stiffness in continuum structures simultaneously. A software package including a Matlab code and Abaqus FE solver has been created for the numerical implementation of multi-objective BESO utilizing the weighted function method. At the same time, by considering the weaknesses of the optimized structure in single-objective optimizations for stiffness or frequency problems, slight modifications have been done on the numerical algorithm of developed multi-objective BESO in order to overcome challenges due to artificial localized modes, checker boarding and geometrical symmetry constraint during the progressive iterations of optimization. Numerical results show that the proposed Multiobjective BESO method is efficient and optimal solutions can be obtained for continuum structures based on an existent finite element model of the structures.

• Structural Engineering and Mechanics
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• v.86 no.4
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• pp.473-486
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• 2023

Nowadays, urban centers are increasingly vertical, making architects and engineers look for more efficient tools to analyze the effects of wind on tall buildings. Topology optimization can be used as an efficient tool for the design of bracing systems. Therefore, this work obtained the wind loads that act in the CAARC building, following the Brazilian standard NBR 6123/1988 and using Computational Fluid Dynamics. Four loading situations were considered, using the SIMP and BESO methods to optimize two-dimensional structures. A comparison between the SIMP and BESO methods is presented, showing the differences in the geometry of the solution found by both methods, the percentage variation in the objective function values and the dimensionless processing time. The solutions obtained through the loads obtained by the Brazilian standard are also compared with the numerical solutions obtained by CFD. The results show that the BESO method presented more rigid structures compared to the SIMP method. The bracing structures obtained with the SIMP method always present similar patterns in the distribution and quantity of bars, in contrast to the BESO method where no characteristic topology pattern was observed. It was concluded that even though the structures obtained by the BESO method presented greater stiffness, the SIMP method was less susceptible to the methodology used for the determination of wind loads. Additionally, it was evident the great potential that the combination topology optimization and computational wind engineering have in the design of bracing systems of high functional and aesthetic standards.

• Proceedings of the KSME Conference
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• 2001.06a
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• pp.752-757
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• 2001

To reduce stress concentration around the intersection between a spherical pressure vessel and a cylindrical nozzle under various load conditions using less material, the optimization for the distribution of reinforcement has researched. The ranked bidirectional evolutionary structural optimization(R-BESO) method is developed recently, which adds elements based on a rank, and the performance indicator which can estimate a fully stressed model. The R-BESO method can obtain the optimum design using less iteration number than iteration number of the BESO. In this paper, the optimized intersection shape is sought using R-BESO method for a flush and a protruding nozzle. The considered load cases are a radial compression, torque and shear force.

• Journal of Mechanical Science and Technology
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• v.14 no.9
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• pp.913-919
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• 2000

The purpose of this study was to develop a new element removal method for ESO (Evolutionary Structural Optimization), which is one of the topology optimization methods. ESO starts with the maximum allowable design space and the optimal topology emerges by a process of removal of lowly stressed elements. The element removal ratio of ESO is fixed throughout topology optimization at 1 or 2%. BESO (bidirectional ESO) starts with either the least number of elements connecting the loads to the supports, or an initial design domain that fits within the maximum allowable domain, and the optimal topology evolves by adding or subtracting elements. But the convergence rate of BESO is also very slow. In this paper, a new element removal method for ESO was developed for improvement of the convergence rate. Then it was applied to the same problems as those in papers published previously. From the results, it was verified that the convergence rate was significantly improved compared with ESO as well as BESO.

• Journal of the Korean Society of Manufacturing Technology Engineers
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• v.19 no.6
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• pp.826-833
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• 2010

Electric-thermal-structural actuated compliant mechanisms are mechanisms onto which electric voltage drop is applied as input instead of force. This mechanism is based on thermal expansion of material while being heated. Compliant mechanisms are designed subjected to electric charge input using BESO(bi-directional evolutionary structural optimization) method. Reliability-based topology optimization (RBTO) is applied to the topology design of actuators. performance measure approach (PMA), which has probabilistic constraints that are formulated in terms of the reliability index, is adopted to evaluate the probabilistic constraints. In this study, BESO method is used to obtain optimal topology of compliant mechanisms from initial design domain. PMA approach is used to evaluate reliability index. The procedure has been tested in numerical applications and compared with the results obtained by other methods to validate these approaches.

• Structural Engineering and Mechanics
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• v.34 no.5
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• pp.581-595
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• 2010

This paper presents topology optimization of geometrically and materially nonlinear structures using a bi-directional evolutionary optimization (BESO) method. To maximum the stiffness of nonlinear structures under prescribed design load, the complementary work is selected as the objective function of the optimization. An optimal design can be obtained by gradually removing inefficient material and adding efficient ones. The proposed method can be applied to a series of geometrically and/or materially nonlinear structures. The results show considerable differences in topologies and stiffness of the optimal designs for linear and nonlinear structures. It is found that the optimal designs for nonlinear structures are much stiffer than those for linear structures when large design loads (which result in significantly nonlinear deformations) are applied.

• Journal of the Korean Society of Manufacturing Technology Engineers
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• v.20 no.4
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• pp.412-418
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• 2011

Reliability-based Topology optimization(RBTO) is to get an optimal design satisfying uncertainties of design variables. Although RBTO based on homogenization and density distribution method has been done, RBTO based on BESO has not been reported yet. This study presents a reliability-based topology optimization(RBTO) using bi-directional evolutionary structural optimization(BESO). Topology optimization is formulated as volume minimization problem with probabilistic displacement constraint. Young's modulus, external load and thickness are considered as uncertain variables. In order to compute reliability index, four methods, i.e., RIA, PMA, SLSV and ADL(adaptive-loop), are used. Reliability-based topology optimization design process is conducted to obtain optimal topology satisfying allowable displacement and target reliability index with the above four methods, and then each result is compared with respect to numerical stability and computing time. The results of this study show that the RBTO based on BESO using the four methods can effectively be applied for topology optimization. And it was confirmed that DLSV and ADL had better numerical efficiency than SLSV. ADL and SLSV had better time cost than DLSV. Consequently, ADL method showed the best time efficiency and good numerical stability.

• Journal of the Korean Society of Manufacturing Technology Engineers
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• v.19 no.5
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• pp.691-697
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• 2010

Reliability-based topology optimization (RBTO) is to get an optimal topology satisfying uncertainties of design variables. In this study, reliability-based topology optimization method is applied to the inner reinforcement of vehicle's hood based on BESO. A multi-objective topology optimization technique was implemented to obtain optimal topology of the inner reinforcement of the hood. considering the static stiffness of bending and torsion as well as natural frequency. Performance measure approach (PMA), which has probabilistic constraints that are formulated in terms of the reliability index, is adopted to evaluate the probabilistic constraints. To evaluate the obtained optimal topology by RBTO, it is compared with that of DTO of the inner reinforcement of the hood. It is found that the more suitable topology is obtained through RBTO than DTO even though the final volume of RBTO is a little bit larger than that of DTO. From the result, multiobjective optimization technique based on the BESO can be applied very effectively in topology optimization for vehicle's hood reinforcement considering the static stiffness of bending and torsion as well as natural frequency.