• International Journal of CAD/CAM
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• v.7 no.1
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• pp.61-69
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• 2007

The objective of this work is to integrate reliability analysis into topology optimization problems. We introduce the reliability constraint in the topology optimization formulation, and the new model is called Reliability-Based Topology Optimization (RBTO). The application of the RBTO model gives a different topology relative to the classical topology optimization that should be deterministic. When comparing the structures resulting from the deterministic topology optimization and from the RBTO model, the RBTO model yields structures that are more reliable than the deterministic ones (for the same weight). Several applications show the importance of this integration.

• 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.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.30 no.8 s.251
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• pp.889-896
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• 2006

The concept of reliability has been applied to the topology optimization based on a reliability index approach or a performance measure approach. Since these approaches, called double-loop single vector approach, require the nested optimization problem to obtain the most probable point in the probabilistic design domain, the time for the entire process makes the practical use infeasible. In this work, new reliability-based topology optimization method is proposed by utilizing single-loop single-vector approach, which approximates searching the most probable point analytically, to reduce the time cost. The results of design examples show that the proposed method provides efficiency curtailing the time for the optimization process and accuracy satisfying the specified reliability.

• Journal of Mechanical Science and Technology
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• v.20 no.4
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• pp.494-504
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• 2006

This research proposes a reliability-based topology optimization (RBTO) using the finite element method. RBTO is a topology optimization based on probabilistic (or reliability) constraints. Young's modulus, thickness, and loading are considered as the uncertain variables and RBTO is applied to static and eigenvalue problems. The RBTO problems are formulated and a sensitivity analysis is performed. In order to compute probability constraints, two methods-RIA and PMA-are used. Several examples show the effectiveness of the proposed method by comparing the classical safety factor method.

• 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.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.

• Journal of the Korean Society of Manufacturing Technology Engineers
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• v.19 no.4
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• pp.529-538
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• 2010

This paper presents a reliability-based topology optimization (RBTO) based on bidirectional evolutionary structural optimization (BESO). In design of a structure, uncertain conditions such as material property, operational load and dimensional variation should be considered. Deterministic topology optimization (DTO) is performed without considering the uncertainties related to the design variables. However, the RBTO can consider the uncertainty variables because it can deal with the probabilistic constraints. The reliability index approach (RIA) and the performance measure approach (PMA) are adopted to evaluate the probabilistic constraints in this study. In order to apply the BESO to the RBTO, sensitivity number for each element is defined as the change in the reliability index of the structure due to removal of each element. Smoothing scheme is also used to eliminate checkerboard patterns in topology optimization. The limit state indicates the margin of safety between the resistance (constraints) and the load of structures. The limit State function expresses to evaluate reliability index from finite element analysis. Numerical examples are presented to compare each optimal topology obtained from RBTO and DTO each other. It is verified that the RBTO based on BESO can be effectively performed from the results.

• Journal of the Korean Society of Manufacturing Technology Engineers
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• v.19 no.2
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• pp.224-229
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• 2010

This paper presents a reliability-based topology optimization (RBTO) using bi-directional evolutionary structural optimization (BESO). An actual design involves uncertain conditions such as material property, operational load and dimensional variation. Deterministic topology optimization (DTO) is obtained without considering of uncertainties related to the uncertainty parameters. However, the RBTO can consider the uncertainty variables because it has the probabilistic constraints. In this paper, the reliability index approach (RIA) is adopted to evaluate the probabilistic constraint. RBTO based on BESO starting from various design domains produces a similar optimal topology each other. Numerical examples are presented to compare the DTO with the RBTO.

• Transactions of the Korean Society of Machine Tool Engineers
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• v.17 no.6
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• pp.77-82
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• 2008

This paper presents a Reliability-Based Topology Optimization(RBTO) using the Evolutionary Structural Optimization(ESO). An actual design involves some uncertain conditions such as material property, operational load and dimensional variation. The Deterministic Topology Optimization(DTO) is obtained without considering the uncertainties related to the uncertainty parameters. However, the RBTO can consider the uncertainty variables because it has the probabilistic constraints. In order to determine whether the probabilistic constraints are satisfied or not, simulation techniques and approximation methods are developed. In this paper, the reliability index approach(RIA) is adopted to evaluate the probabilistic constraints. In order to apply the ESO method to the RBTO, sensitivity number is defined as the change in the reliability index due to the removal of the ith element. Numerical examples are presented to compare the DTO with the RBTO.

• Transactions of the Korean Society of Automotive Engineers
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• v.12 no.2
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• pp.123-130
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• 2004

The automobile suspension system is composed of parts that affect performances of a vehicle such as ride quality, handling characteristics, straight performance and steering effort, etc. Moreover, by using the finite element analysis the cost for the initial design step can be decreased. In the design of a suspension system, usually system vibration and structural rigidity must be considered simultaneously to satisfy dynamic and static requirements simultaneously. In this paper, we consider the weight reduction and the increase of the first eigen-frequency of a suspension part, the upper control arm, especially using topology optimization and size optimization. Firstly, we obtain the initial design to maximize the first eigen-frequency using topology optimization. Then, we apply the multi-objective parameter optimization method to satisfy both the weight reduction and the increase of the first eigen-frequency. The design variables are varying during the optimization process for the multi-objective. Therefore, we can obtain the deterministic values of the design variables not only to satisfy the terms of variation limits but also to optimize the two design objectives at the same time. Finally, we have executed reliability based optimal design on the upper control arm using the Monte-Carlo method with importance sampling method for the optimal design result with 98％ reliability.