• 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 the Korean Society of Manufacturing Technology Engineers
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• v.19 no.5
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• pp.589-595
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• 2010

This paper presents a reliability-based shape optimization (RBSO) using the evolutionary structural optimization (ESO). An actual design involves uncertain conditions such as material property, operational load, poisson's ratio and dimensional variation. The deterministic optimization (DO) is obtained without considering of uncertainties related to the uncertainty parameters. However, the RBSO can consider the uncertainty variables because it has the probabilistic constraints. In order to determine whether the probabilistic constraint is satisfied or not, simulation techniques and approximation methods are developed. In this paper, the reliability-based shape design optimization method is proposed by utilization the reliability index approach (RIA), performance measure approach (PMA), single-loop single-vector (SLSV), adaptive-loop (ADL) are adopted to evaluate the probabilistic constraint. In order to apply the ESO method to the RBSO, a sensitivity number is defined as the change of strain energy in the displacement constraint. Numerical examples are presented to compare the DO with the RBSO. The results of design example show that the RBSO model is more reliable than deterministic optimization.

• Journal of the Korean Society of Manufacturing Technology Engineers
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• v.19 no.4
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• pp.469-475
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• 2010

The objective of this study is to integrate reliability analysis into shape optimization problem using the evolutionary structural optimization (ESO) in the application example. Reliability-based shape optimization is formulated as volume minimization problem with probabilistic stress constraint under minimization max. von Mises stress and allow stress. Young's modulus, external load and thickness are considered as uncertain variables. In order to compute reliability index, four methods, i.e., reliability index approach (RIA), performance measure approach (PMA), single-loop singlevector (SLSV) and adaptive-loop (ADL), are used. Reliability-based shape optimization design process is conducted to obtain optimal shape satisfying max. von Mises stress and reliability index constraints with the above four methods, and then each result is compared with respect to numerical stability and computing time.