Journal of the Computational Structural Engineering Institute of Korea (한국전산구조공학회논문집)

Computational Structural Engineering Institute of Korea (한국전산구조공학회)
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Computational Analysis of Geometrically Exact Shell Elements Using Multipatch IsoGeometric Analysis

다중 패치 등기하해석을 이용한 기하학적으로 엄밀한 쉘의 전산해석

  • Min-Geun Kim (Department of Mechanical and Automobile Engineering, Seoul National University of Science & Technology) ;
  • Yeoul Song (Department of Industrial Machinery DX, Korea Institute of Machinery & Materials) ;
  • Hanmin Lee (Department of Industrial Machinery DX, Korea Institute of Machinery & Materials) ;
  • Jaeseung Kim (Department of Industrial Machinery DX, Korea Institute of Machinery & Materials)
  • 김민근 (서울과학기술대학교 기계.자동차공학과) ;
  • 송여울 (한국기계연구원 산업기계DX연구실) ;
  • 이한민 (한국기계연구원 산업기계DX연구실) ;
  • 김재승 (한국기계연구원 산업기계DX연구실)
  • Received : 2024.07.12
  • Accepted : 2024.08.27
  • Published : 2024.10.31
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Abstract

In this paper, a multipatch isogeometric analysis method is developed for a multi-connected NURB patch model and applied to geometrically exact shell element analysis. When connecting different NURBS patches, isogeometric analysis may become inaccurate due to the density of control point meshes and discontinuity between patches. To solve this problem, Nitsche's method is applied to the isogeometric analysis method to ensure the compatibility of the displacement and traction between two patches by using a potential function defined as the product of the displacement difference and traction of the two patches. The final derived governing equation is formed as a symmetric stiffness matrix from this potential function. Since the added system matrices from the compatibility boundary conditions are calculated as a boundary integral between patches, the computational cost does not increase significantly. For the positive definiteness of the system equation, appropriate stability parameters are calculated through generalized eigenvalue analysis, and the stability parameters and solution accuracy are analyzed according to the density of the integration meshes between the two patches. This multipatch isogeometric analysis method is applied to geometrically exact shell elements considering first-order shear deformation, and it is confirmed that by using Nitsche's method in this shell analysis with multiple connected patches results in improved stress continuity as well as displacement continuity between patches.

본 논문에서는 다중 연결 NURBS 패치 모델에 대한 등기하해석방법을 제시하고 이를 기하학적으로 엄밀한 쉘의 해석에 적용하였다. 서로 다른 NURBS 패치를 연결할 떼 조정점 망(control point meshes)의 밀도와 패치간의 불연속성으로 인해 등기하해석이 부정확해질 수 있다. 이러한 문제를 해결하기 위해 니셰(Nitsche) 방법을 등기하해석법에 적용하여 두 패치 사이의 변위와 견인력(traction)의 정합성(compatibility)을 확보하였고, 최종 유도된 해석 방정식이 대칭성을 유지하도록 하였다. 추가되는 경계 조건은 패치간 경계의 적분으로 표현되기 때문에 계산비용이 크게 증가되지 않는다. 시스템 방정식이 양정 행렬(positive definite matrix)이 되도록 안정성 매개변수(stability parameters)를 도입하였으며 일반화된 고유치 해석을 통해 두 패치사이의 조정점 밀도에 따른 안정성 매개변수의 값과 응력장의 해의 정확성을 분석하였다. 이 다중 패치 등기하해석법을 1차 전단변형을 고려한 기하학적으로 엄밀한 쉘요소의 해석에 적용하였으며, 니셰 방법을 사용함으로써 패치간의 변위 및 응력 연속성이 향상된 결과를 확인 할 수 있었다.

Keywords

Acknowledgement

본 연구는 2021년 정부(방위사업청)의 재원으로 국방기술진흥연구소의 지원을 받아 수행된 연구임(No. KRIT-CT-21-013).

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