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재생 커널법과 몬테 카를로 적분법을 이용한 극초음속 비행체의 Newtonian 공력 계수 계산
조민지,안미치코 한국전산유체공학회 2023 한국전산유체공학회지 Vol.28 No.4
This study proposes a method to calculate a high-precision approximation of the exact Newtonian aerodynamic coefficients for arbitrary shapes by combining the Reproducing Kernel Hilbert Space (RKHS) method and Monte-Carlo integration. The RKHS method was used to obtain the approximation function of hypersonic vehicle geometry from the structured grid points, and the Newtonian aerodynamic coefficients were calculated using Monte-Carlo integration. The effectiveness of the RKHS method was verified by applying it to simple shapes, and it was confirmed that the structured grid points could be well interpolated with random sampling points. The predicted value of the drag coefficient, obtained using Monte-Carlo integration on the sampling point data of the interpolated basic shapes, was evaluated by comparing it with the analytical solutions. Improvements in prediction accuracy were confirmed when compared with the results from the panel method. As an example application to arbitrary shapes, the present methods were examined for the Apollo command module shape, and it was confirmed that the calculated Newtonian aerodynamic coefficients had good accuracy when compared with the analytical solutions, even when considering flow at different angles of attack.
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안승호,하승현,조선호,Ahn, Seung-Ho,Ha, Seung-Hyun,Cho, Seonho 한국전산구조공학회 2014 한국전산구조공학회논문집 Vol.27 No.1
레벨셋 기법과 무요소법을 결합한 위상 및 형상 최적설계 기법을 개발하여 선형 탄성문제에 적용하였다. 설계민감도는 애드조인트법을 사용하여 효율적으로 구하였다. 해밀턴-자코비 방정식을 업-윈드 기법을 이용하여 수치적으로 풀었으며, 구조물의 경계는 레벨셋 함수를 이용하여 암시적으로 표현하였다. 구조물의 응답과 설계민감도를 얻기 위하여 암시적 함수를 사용하여 명시적 경계를 생성하였다. 재생 커널 기법에 기초하여 얻어진 전역 절점 기저함수를 사용하여 연속체 지배방정식의 변위장을 이산화하였다. 따라서 질점들을 연속체 영역의 어느 곳이든 위치시킬 수 있으며, 이는 통해 명시적 경계를 생성하는 것이 가능하며, 결과적으로 정확한 설계를 얻을 수 있다. 개발된 방법은 제한 조건이 있는 최적설계 문제에 대하여 라그랑지안 범함수를 정의한다. 이는 경계의 변화를 통하여 허용 부피 제한조건을 만족시키면서 컴플라이언스를 최소화한다. 최적설계 과정 동안 라그랑지안 범함수의 최적화조건을 만족시킴으로써 해밀턴-자코비 방정식을 풀기 위한 속도장을 얻는다. 기존의 형상 최적설계 기법에 비하여, 본 방법론은 위상과 형상의 변화를 쉽게 얻어낼 수 있다. Using the level set and the meshfree methods, we develop a topological shape optimization method applied to linear elasticity problems. Design gradients are computed using an efficient adjoint design sensitivity analysis(DSA) method. The boundaries are represented by an implicit moving boundary(IMB) embedded in the level set function obtainable from the "Hamilton-Jacobi type" equation with the "Up-wind scheme". Then, using the implicit function, explicit boundaries are generated to obtain the response and sensitivity of the structures. Global nodal shape function derived on a basis of the reproducing kernel(RK) method is employed to discretize the displacement field in the governing continuum equation. Thus, the material points can be located everywhere in the continuum domain, which enables to generate the explicit boundaries and leads to a precise design result. The developed method defines a Lagrangian functional for the constrained optimization. It minimizes the compliance, satisfying the constraint of allowable volume through the variations of boundary. During the optimization, the velocity to integrate the Hamilton-Jacobi equation is obtained from the optimality condition for the Lagrangian functional. Compared with the conventional shape optimization method, the developed one can easily represent the topological shape variations.
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A Study on the Forming of Tower Flange Parts for Wind Turbine
Kyu-Taek Han(한규택) 한국생산제조학회 2009 한국공작기계학회 추계학술대회논문집 Vol.2009 No.-
In recent years, a new family of computational methods has emerged. The so-called meshless or mesh-free methods have been investigated and used by many researchers for treating a large variety of engineering problems, involving usually large displacements as encountered for example in forming process simulations. The main advantage of meshless methods is the fact that the interpolation accuracy is not significantly affected by the nodal distribution. Nevertheless, a troublesome task in these techniques is the imposition of essential boundary conditions, as in general the Kronecker delta property is not satisfied. This paper focuses on the description and analysis of the reproducing kernel particle method (RKPM) and its application for simulating some metal forming processes, and analysis of the tower flanges parts for wind turbine.
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Topological Shape Optimization Using Level Set and Meshfree Methods
Seonho Cho(조선호),Seung-hyun Ha(하승현) 대한기계학회 2005 대한기계학회 춘추학술대회 Vol.2005 No.5
Using level set and meshfree methods, we develop a topological shape optimization method applied to linear elasticity problems. Necessary design gradients are computed using an efficient adjoint design sensitivity analysis (DSA) method. The boundaries are represented by an implicit moving boundary (IMB) embedded in the level set function obtainable from the “Hamilton-Jacobi type” equation with the “Up-wind scheme.” Then, using the implicit function, explicit boundaries are generated to obtain the response and sensitivity. Global nodal shape function derived on a basis of the reproducing kernel (RK) method is employed to discretize the displacement field in the governing continuum equation. Thus, the points can be located everywhere in the continuum domain, which enables to generate the explicit boundaries and leads to a precise design result. The developed method defines a Lagrangian function for the constrained optimization. It minimizes the compliance, satisfying the constraint of allowable volume through the variations of boundary. During the optimization, the velocity to integrate the Hamilton-Jacobi equation is obtained from the optimality condition for the Lagrangian function. Compared with the conventional shape optimization method, the developed one can easily represent the topological shape variations.
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A Study on the Forming of Tower Flange Parts for Wind Turbine
Kyu-Taek Han(한규택) 한국생산제조학회 2009 한국생산제조시스템학회 학술발표대회 논문집 Vol.2009 No.10
In recent years, a new family of computational methods has emerged. The so-called meshless or mesh-free methods have been investigated and used by many researchers for treating a large variety of engineering problems, involving usually large displacements as encountered for example in forming process simulations. The main advantage of meshless methods is the fact that the interpolation accuracy is not significantly affected by the nodal distribution. Nevertheless, a troublesome task in these techniques is the imposition of essential boundary conditions, as in general the Kronecker delta property is not satisfied. This paper focuses on the description and analysis of the reproducing kernel particle method (RKPM) and its application for simulating some metal forming processes, and analysis of the tower flanges parts for wind turbine.
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