SQP법을 이용한 고층 강골조 구조물의 최적설계에 관한 연구

신수미(Shin Su-Mi),박성수(Park Sung-Soo) 대한건축학회 2003 大韓建築學會論文集 : 構造系 Vol.19 No.5

The objective of this paper is to present formulation solving structural optimization problems for all planar frameworks using SQP(Sequential Quadratic Programming) Method. Key aspects in the code development involved the treatment of lower and upper bounds on the variables and on the solution of the QP subproblems. The importance of cost scaling in conjunction with SQP methods is explained here for the first time. The SQP method has attractions: the starting point can be handled in addition to the inequalities, and the method can be proved to converge under certain assumptions. This paper presents SQP problems for optimal design of steel structural frameworks. The lateral drift is an important factor for the serviceability and may have a harmful influence on the safety in highrise buildings. Engineers would put limitations on the drift according to structural design codes or their experience. Because of the characteristics of the problem, they control it not quantitatively, by a trial-error approach. SQP is developed for discrete optimization of tall steel framework subject to lateral drift constraint. The objective function considered is total weight of the structure. Special features of proposed method include discrete design variables, the standard steel sections provided by AISC manual, and an open format for prescribing constraint.

SQP법을 이용한 최적선형개발에 대한 연구

최희종(Hee-Jong Choi),이경우(Gyoung-Woo Lee),김상훈(Sang-Hoon Kim),김호(Ho Kim) 한국항해항만학회 2005 한국항해항만학회 학술대회논문집 Vol.1 No.-

본 연구에서는 최적화기법과 전산유체역학의 기술을 이용하여 저항의 관점에서 최적의 형상을 가지는 선형을 개발하는 알고리즘을 개발하였다. 최적화기법으로는 SQP(sequential Quadratic programming)을 사용하였으며, 목적함수인 저항을 구하기 위하여 먼저 조파저항은 비선형자유수면수면경계조건을 고려한 선체주위 포텐셜유동을 계산할 수 있는 수치해석기법인 상방향패널이동법을 사용하였고, 선체에 미치는 전저항을 구하기 위하여 ITTC 1957년 모형선-실선상관곡선을 이용하였다. 선형최적화 과정 중의 선체의 변경이나 계산 격자의 생성은 NURBS(Non-Uniform Rational B-Spline)기법을 사용하여 구현하였다. 이와 같은 방법을 사용하여 개발된 선형최적화 기법의 타당성을 검증하기 위하여 선형이 비교적 잘 알려진 선형인 Wigley선형과 Series 60(CB=0.6)선형에 대하여 설계속도 Fn=0.316에서 선형최적화를 위한 수치해석을 수행하고 그 결과를 초기선형과 서로 비교하였다. This paper presents the method for developing an optimum hull form with minimum wave resistance using SQP(sequential quadratic programming) as an optimization technique. The wave resistance is evaluated by a Rankine source panel method with non-linear free surface conditions and the ITTC 1957 friction line is used to predict the frictional resistance coefficient. The geometry of the hull surface is represented and modified using NURBS(Non-Uniform Rational B-Spline) surface patches. To verity the validity of the developed program the numerical calculations for Wigley hull and Series 60(CB=0.6) hull had been performed and the results obtained after the numerical calculation had been compared with the original hulls.

SQP법을 이용한 최적선형개발에 대한 연구

최희종(Hee-Jong Choi),이경우(Gyoung-Woo Lee),윤순동(Soon-Dong Yun) 한국항해항만학회 2006 한국항해항만학회지 Vol.30 No.10

본 연구에서는 최적화기법과 전산유체역학의 기술을 이용하여 저항의 관점에서 최적의 형상을 가지는 선형을 개발하는 알고리즘을 개발하였다. 최적화기법으로는 SQP(sequential quadratic programming)을 사용하였으며, 목적함수인 저항을 구하기 위하여 먼저 조파저항은 비선형자유수변경계조건을 고려한 선체주위 포텐셜유동을 계산할 수 있는 수치해석기법인 상 방향 패널이동법을 사용하였고, 선체에 미치는 전 저항을 구하기 위하여 ITTC 1957년 모형선←실션상관곡선을 이용하였다 선형최적화 과정 중의 선체의 변경이나 계산 격자의 생성은 NURBS(Non-Uniform Rational B-Spline) 기법을 사용하여 구현하였다. 이와 같은 방법을 사용하여 개발된 선형최적화 기법의 타당성을 검증하기 위하여 선형이 비교적 잘 알려진 선형인 Wigley선형과 Series 6O (CB=0.6)선형에 대하여 설계속도 Fn=0.316에서 선형최적화를 위한 수치 해석을 수행하고 그 결과를 초기선형과 서로 비교하였다. This paper presents the method for developing an optimum hull form with minimum wave resistance using SQP(sequential quadratic programming) as an optimization technique. The wave resistance is evaluated by a Rankine source panel method with non-linear free surface conditions and the ITTC 1957 friction line is used to predict the frictional resistance coefficient. The geometry of the hull surface is represented and modified using NURBS(Non-Uniform Rational B-Sptine) surface patches. To verity the validity of the developed program the numerical calculations for Wigley hull and Series 60(CB=O.6) hull have been performed and the results obtained by the numerical calculations have been compared with the original hulls.

반복이차계획법을 이용한 엔드플레이트 접합의 실제적 최적설계

윤성덕,윤성기 대한건축학회지회연합회 2007 대한건축학회지회연합회 학술발표대회논문집 Vol.2007 No.1

The optimum value of members consisting of end-plated connection were searched by using theoretical optimum, SQP method, and practical optimum. They were the theoretical and practical optimum value by bolt size, and the optimum value of cost function. The structure designer determines the member of end-plated connection. The SQP method is verified by investigating reliability of convergence and the structure designer can use directly the practical optimum value of this program. If we input the material property such as strength of bolt and plate and beam size, it is expected that this program is the excellent optimum design program that is searched the optimum value as concerns all end-plated conncetion.

반복이차계획법을 이용한 엔드플레이트 접합의 실제적 최적설계

윤성기(Yoon Sung-Kee),이치형(Lee Chy-Hyoung),윤성덕(Yun Sung-Duck) 대한건축학회 2008 大韓建築學會論文集 : 構造系 Vol.24 No.8

The optimum values of members consisting of end-plated connection are searched by using theoretical optimum, SQP method, and practical optimum. These values are obtained as the theoretical and practical optimum values by bolt size, and the optimum value of cost function. The SQP method is verified by investigating reliability of convergence and the structure engineer can use directly the practical optimum value of this program when he designed the end-plated connection. If the material property such as strength of bolt and plate and beam size are given as a input data, it is expected that this program is the excellent optimum design program that is searched the optimum value as concerns all end-plated connection.

고속 Ro-Pax선형의 조파저항성능 향상을 위한 최적 선형설계에 관한 연구

박동우(Dong-Woo Park),최희종(Hee-Jong Choi) 한국항해항만학회 2012 한국항해항만학회지 Vol.36 No.10

최적화기법과 선형변환 자동화기법을 도입하여 고속 중형 Ro-Pax선박의 조파저항성능을 향상시킬 수 있는 선형설계방법에 대하여 연구하였다. 최적화기법으로는 SQP(sequential quadratic programming)을 적용하였으며, 선형변환 자동화기법으로는 NURBS(Non-Uniform Rational B-Spline)기법을 적용하였다. 목적함수인 선박의 조파저항성능을 예측하기 위하여 비선형 자유수면 경계조건과 선체의 침하량을 고려한 비점성 유동 해석 기법인 패널법을 적용하였다. 기준선형에 대하여 선형최적화를 수행하였으며 그 결과로 도출된 최적선형에 대하여 모형선을 제작하여 모형시험을 수행하였다. 기준선형과 최적선형에 대한 수치해석을 수행하여 얻은 결과와 최적선형에 대한 모형시험을 수행하여 얻은 결과를 서로 비교하였다. A hull form design technique to enhance the wave-making resistance performance for a medium size high speed Ro-Pax ship was studied introducing an optimization method and an automatic hull form modification method. SQP(sequential quadratic programming) was applied as the optimization algorithm and the geometry of hull surface was represented and modified using the NURBS(Non-Uniform Rational B-Spline). The wave-making resistance performance as an objective function in the optimization procedure was evaluated using the Rankine source panel method in which nonlinearity of the free surface boundary conditions and the trim and sinkage of the ship was fully taken into account. Using the Ro-Pax ship as a base hull, the hull-form optimization method was applied to obtain the hull shape that produced the lower wave-making resistance. To verify the validity of the hull-form optimization method, the numerical results was compared with the model test results.

T-Stub로 접합된 보-기둥 접합부 부재의 최적설계에 관한 연구

신수미,박성수 대한건축학회지회연합회 2006 대한건축학회지회연합회 학술발표대회논문집 Vol.2 No.1

In this study, the optimum design is performed with the restrained condition such as the size and number of bolt, the thickness of plate, the length of beam member about beam-to-column connections with T-stub in steel structures. After optimum design is executed, values of minimum objective function are as follow : Total cost of T-stub Connection are decreased than ordinary connection design. Thus we got to have a conclusion that this program is efficiency enough.

Optimal Active-Control & Development of Optimization Algorithm for Reduction of Drag in Flow Problems(3) -Construction of the Formulation for True Newton Method and Application to Viscous Drag Reduction of Three-Dimensional Flow

박재형,Bark, Jai-Hyeong Computational Structural Engineering Institute of 2007 한국전산구조공학회논문집 Vol.20 No.6

저자는 기존의 연구에서 대용량-비선형성을 가지는 유체의 최적화를 수행하기 위해 몇 가지 강력한 방법들을 제시한 바 있다. 즉, 최적화 과정에서 수렴성을 높이기 위해 step by step기법을 사용하였고, 또한 수렴속도를 높이기 위하여 최적화이터레이션 과정에서 얻어지는 민감도정보를 이용하여 시스템 평형방정식의 해석을 위한 좋은 초기치를 제공하는 방법과, 평형방정식을 구속조건으로 사용하는 동시기법(simultaneous technique)에서 착안하여 해석과 최적화 수렴 판정치를 조작하는 방법을 제시한 바 있다. 그러나 그들 기법은 기본적으로 유사뉴턴법에 기본을 두고 있다. 현재까지 최적화에서 SQP기법을 사용할 때는 정확한 헤시안 매트릭스의 유도가 매우 까다롭고 힘들기 때문에 유사뉴턴법을 사용하고 있는 실정이다. 그러나 3차원 문제와 같이 더욱 큰 용량의 문제를 위해서는 진정한 의미에서의 뉴턴법, 트루 뉴턴법(true Newton method)을 사용할 필요가 있다. 본 연구에서는 트루 뉴턴법을 사용하기 위해 헤시안 매트릭스의 정확치를 얻는 과정을 유도하고 이를 기본으로 트루 뉴턴법을 이용한 최적화 루틴을 만들었다. 그리고 이를 3차원 문제에 적용하여 그 효과를 검증하였다. We have developed several methods for the optimization problem having large-scale and highly nonlinear system. First, step by step method in optimization process was employed to improve the convergence. In addition, techniques of furnishing good initial guesses for analysis using sensitivity information acquired from optimization iteration, and of manipulating analysis/optimization convergency criterion motivated from simultaneous technique were used. We applied them to flow control problem and verified their efficiency and robustness. However, they are based on quasi-Newton method that approximate the Hessian matrix using exact first derivatives. However solution of the Navier-Stokes equations are very cost, so we want to improve the efficiency of the optimization algorithm as much as possible. Thus we develop a true Newton method that uses exact Hessian matrix. And we apply that to the three-dimensional problem of flow around a sphere. This problem is certainly intractable with existing methods for optimal flow control. However, we can attack such problems with the methods that we developed previously and true Newton method.

에너지법을 이용한 정정 트러스의 최적화 정식 개발

박재형 牧園大學校 建築·都市硏究센터 2001 建築·都市環境硏究 Vol.9 No.-

The aim of this paper is to present a new formulation which can significantly reduce computing time in solving structural optimization problems. Conventional approaches need to solve the system equations(Ku=P) to get displacements at each iteration during optimization processes, and furthermore require to perform the very complicated sensitivity analysis. These formidable task have made optimization techniques, until recently, out of the reach. Commonly-available computers have not been powerful enough to warrant such an approach. Herein, we develop and present an efficient formulation to solve this problem. based on the energy method to get displacements. The examples demonstrate that the formulation is extremely effective for optimal design of statically determinate trusses.

T-Stub으로 접합된 보-기둥 접합부의 최적설계에 관한 연구

신수미 대한건설환경학회 2005 건설환경연구 Vol.4 No.1