기하학적 보존을 만족하는 최소제곱법을 활용한 무격자 구조해석 기법 개발
Development of Meshless Method Using Least-Squares Method with Geometric Conservation Law for Structural Dynamic Analysis
0
조회
0
다운로드
0
인용
0
참고문헌
키워드
초록
본 논문은 코시 모멘텀(Cauchy’s Momentum) 방정식을 이산화하기 위해 GC-LSM(Geometric Conservative Least Squares Method)을 사용한 새로운 Meshless 방법을 제시한다. FEM(Finite Element Method) 방법이 구조해석에 널리 사용되고 있지만 무격자 기법은 격자를 이동해야 할 때 장점이 많기 때문에 개발되었다. 본 작업은 무격자 기반의 FSI(Fluid-Structure Interaction) 프로그램을 개발하기 위한 기틀을 다지는 단계이다. 본 논문에서는 Cauchy’s Momentum 방정식을 GC-LSM을 사용하여 강형식 형태로 이산화하였고, 시간 적분을 위해 New Mark Beta 방법을 사용하였다. 개발된 기법은 1D, 2D 및 3D 벤치마킹 문제에서 검증했으며, 정적 해석 및 동적 해석 결과가 해석해와 비교시 매우 정확한 결과를 보여준다.
Abstract
A meshless technique using the geometric conservation least-squares method (GC-LSM) was devised to discretize the governing equation of linear elasticity. Although the finite-element method is widely used for structural analysis, a meshless method was developed because of its advantages in a moving grid system. This work is the preliminary phase for developing a fully meshless-based fluid-structure interaction solver. In this study, Cauchy’s momentum equation was discretized in strong form using GC-LSM for the structural domain, and the Newmark beta method was used for time integration. The solver was validated in 1D, 2D, and 3D benchmarking problems. Static and dynamic results were obtained. The results are more accurate than those of analytic solutions.
참고문헌 (12)
- Dolbow, J., "An Introduction to Programming the Meshless Element Free Galerkin Method", Arch. Comput. Methods Eng, 5, pp.27~241 (1998)
- Gordnier, R. E., "Computation of the Aeroelastic Response of a Flexible Delta Wing at High Angles of Attack", J. Fluids & Struct, 19, pp.785~800 (2004)
- Huh, J. Y, "New Least Squares Method with Geometric Conservation Law(GC-LSM)for Compressible Flow Computation in Meshless Method", Comput. & Fluids, 172, pp.122~146 (2018)
- Intel, M. K. L., "Intel Math Kernel Library, Developer Reference", ~ (2020)
- Katz, A., "A Comparison of Various Meshless Schemes Within a Unified Algorithm", 47th AIAA Aerospace Sciences Meeting Including The New Horizons Forum and Aerospace Exposition (2009)
- Mase, G. T., "Continuum Mechanics for Engineers", pp.398~ (1999), CRC press
- Mavriplis, D. J., "Revisiting the Least-Squares Procedure for Gradient Reconstruction on Unstructured Meshes", AIAA 16th Computational Fluid Dynamics Conference, pp.2003~3986 (2003)
- Newmark, N. M., "A Method of Computation for Dynamic", J. Eng. Mech. Div, 85(3), pp.67~94 (1959)
- Nguyen, V. P., "Meshless Methods : A Rreview and Computer Implementation Aspects", Math & Comput. Simul, 79, pp.763~813 (2008)
- CFD Vision 2030 Study: A Path to Revolutionary Computational Aerosciences, "Slotnick, J. P.", NASA, 20~, pp.No. NF1676L-18332 (2014)
- Timoshenko, S. P., "Theory of Elasticity", pp.23~ (1970), McGraw Hill
- Xia, G. H., "A 3D Implicit Unstructured-Grid finite Volume Method for Structural Dynamics", Comput. Mech, 40, pp.299~312 (2007)