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SON HAI LE,강신성,TRIET MINH PHAM,이경훈 한국산업응용수학회 2021 Journal of the Korean Society for Industrial and A Vol.25 No.4
This study formulates a new geometric parameterization scheme to effectively address numerical analysis subject to the variation of the fiber radius of a square unit cell. In particular, the proposed mesh-morphing approach may lead to a parameterized weak form whose bilinear and linear forms are affine in the geometric parameter of interest, i.e. the fiber radius. As a result, we may certify the reduced basis analysis of a square unit cell model for any parameters in a predetermined parameter domain with a rigorous a posteriori error bound. To demonstrate the utility of the proposed geometric parameterization, we consider a two- dimensional, steady-state heat conduction analysis dependent on two parameters: a fiber radius and a thermal conductivity. For rapid yet rigorous a posteriori error evaluation, we estimate a lower bound of a coercivity constant via the min-θ method as well as the successive constraint method. Compared to the corresponding finite element analysis, the constructed reduced basis analysis may yield nearly the same solution at a computational speed about 29 times faster on average. In conclusion, the proposed geometric parameterization scheme is conducive for accurate yet efficient reduced basis analysis.
정적응축 축소기저요소법을 사용한 고압 수소저장용기의 신뢰성 기반 최적설계
강다영(Dayoung Kang),Minh Triet Pham,이경훈(Kyunghoon Lee) 대한기계학회 2022 大韓機械學會論文集A Vol.46 No.2
본 논문은 수소충전소용 압력용기에 대한 신뢰성 기반 중량최소설계를 수행하여 안전하고 경제적인 수소유통체계 구축에 기여하고자 한다. 확률론적 최적설계를 위한 목적함수로 용기 중량, 설계변수로 반지름과 두께, 구속조건으로 부피와 최대허용응력을 고려하였다. 불확실한 운용조건에 의한 내부압력 변동은 정규분포를 따르는 확률변수로 표현하였다. 최대응력은 정적응축 축소기저요소법에 기반한 선형 정탄성 해석을 통해 기존 유한요소법에 비해 신속하고 정확하게 도출하였다. 이를 위해 용기를 세 개의 컴포넌트로 분할한 후 반지름, 두께, 내부압력에 대해 매개변수화된 선형 정탄성 해석모형을 구축하였다. 신뢰성 기반 최적화 결과 기존 용량 대비 중량을 35.7% 감소하면서 목표 신뢰도를 99% 만족하는 최적설계안을 효율적으로 도출하였다. We conducted a reliability-based weight minimization of a storage vessel for hydrogen refueling stations aimed at achieving a safe and economical hydrogen transportation system. We formulated a probabilistic design optimization problem by setting the weight to an objective function and using the radius and thickness as design variables. The volume and maximum allowable stress of the vessel were considered as constraints. The uncertain internal pressure due to varying operational conditions was expressed as a Gaussian random variable. We evaluated the stress via a linear elastostatic analysis using a static condensation reduced basis element method that is rapid yet accurate compared to the conventional finite element method. For this analysis, we divided a vessel into three components and constructed a linear elastostatic model parameterized in radius, thickness, and internal pressure. Owing to the reliability-based design optimization, we lowered the weight by 35.7% while achieving 99% of the target reliability.
Dayoung Kang(강다영),Minh Triet Pham,Kyunghoon Lee(이경훈) 대한기계학회 2022 대한기계학회 춘추학술대회 Vol.2022 No.5
In this study, we perform a design optimization to minimize the weight of a hydrogen vessel under the uncertainty of an operating condition. We set a weight to an objective function by adopting radius and thickness as design variables. In terms of constraints, we set the volume and maximum allowable stress to deterministic equality and probabilistic inequality constraints, respectively. We solve linear elastostatic problems using a component-based reduced basis method to evaluate the maximum stress and thus attained accurate solutions rapidly as compared with using the finite element method. To apply a component-based approach, we divide a vessel model into three simple components and create a linear elastostatic model using geometric and physical parameters. After performing reliability-based design optimization, we achieved a lightweight vessel with target reliability. Moreover, owing to the computational efficiency of the reduced basis solution, we reduced the time to required to achieve an optimal design by realizing efficient simulations.