The deterministic topology optimization (TO) has become one of the better-known optimization approaches in the engineering design of structures. However, its approximation errors have placed several restrictions on designers as it does not consider inherent uncertainties such as loads, geometrical dimensions, and materials in structures. To remedy this issue, the TO methods were incorporated with reliable design with highly martials involved under uncertainties for structural/mechanical problems. In the current reliability-based topology optimization (RBTO) procedures under multi-source uncertainties, dynamic mean value (DMV) was applied for evaluating the probabilistic constraints. For this aim, a sequential TO and reliability analysis (STORA) was proposed for application in various TO methods. The TO loop coupled bisection method as inverse topology layout applied in reliability loop that the DMV was utilized for evaluating the probabilistic constraint using sufficient descent condition. In the current RBTO model based on STORA, different TO methods named moving iso-surface threshold (MIST), evolutionary structural optimization (ESO), Level-set, and solid isotropic material with penalization (SIMP) are discussed for various problems with continuous design domains. The comparative results are discussed for different TO methods basis bisection approach for TO and RBTO solutions. The results demonstrated that the stable results provided by DMV and different optimal shapes between inverse TO-based bisection and RBTO solutions are captured. The proposed RBTO method using STORA provides safe optimum shapes for almost TO methods with uncertainties in material properties and loads.
Citation: Yiqing Shi, Mahmoud Alfouneh, Chao Yuan. Sequential topology optimization and reliability analysis using bisection: Level-set vs MIST, SIMP and ESO methods with multi-source uncertainties[J]. AIMS Mathematics, 2025, 10(6): 14392-14433. doi: 10.3934/math.2025648
The deterministic topology optimization (TO) has become one of the better-known optimization approaches in the engineering design of structures. However, its approximation errors have placed several restrictions on designers as it does not consider inherent uncertainties such as loads, geometrical dimensions, and materials in structures. To remedy this issue, the TO methods were incorporated with reliable design with highly martials involved under uncertainties for structural/mechanical problems. In the current reliability-based topology optimization (RBTO) procedures under multi-source uncertainties, dynamic mean value (DMV) was applied for evaluating the probabilistic constraints. For this aim, a sequential TO and reliability analysis (STORA) was proposed for application in various TO methods. The TO loop coupled bisection method as inverse topology layout applied in reliability loop that the DMV was utilized for evaluating the probabilistic constraint using sufficient descent condition. In the current RBTO model based on STORA, different TO methods named moving iso-surface threshold (MIST), evolutionary structural optimization (ESO), Level-set, and solid isotropic material with penalization (SIMP) are discussed for various problems with continuous design domains. The comparative results are discussed for different TO methods basis bisection approach for TO and RBTO solutions. The results demonstrated that the stable results provided by DMV and different optimal shapes between inverse TO-based bisection and RBTO solutions are captured. The proposed RBTO method using STORA provides safe optimum shapes for almost TO methods with uncertainties in material properties and loads.
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Figures(25) / Tables(5)
Yiqing Shi, Mahmoud Alfouneh, Chao Yuan. Sequential topology optimization and reliability analysis using bisection: Level-set vs MIST, SIMP and ESO methods with multi-source uncertainties[J]. AIMS Mathematics, 2025, 10(6): 14392-14433. doi: 10.3934/math.2025648
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