Transactions of the Korean Society of Mechanical Engineers A (대한기계학회논문집A)

The Korean Society of Mechanical Engineers (대한기계학회)
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Study on the Local Refinement in Spline Finite Element Method by Using Hierarchical B-spline

계층적 B-스플라인을 이용한 스플라인 유한요소법의 국부 세분화에 관한 연구

  • Hah, Zoo-Hwan (School of Mechanical, Aerospace and Systems Engineering, Division of Mechanical Engineering, KAIST) ;
  • Kim, Hyun-Jung (School of Mechanical, Aerospace and Systems Engineering, Division of Mechanical Engineering, KAIST) ;
  • Youn, Sung-Kie (School of Mechanical, Aerospace and Systems Engineering, Division of Mechanical Engineering, KAIST)
  • Received : 2010.02.22
  • Accepted : 2010.06.14
  • Published : 2010.08.01
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Abstract

A new local refinement scheme for spline finite element method has been proposed; this scheme involves the use of hierarchical B-spline. NURBS has been widely used in CAD; however, the local refinement of NURBS is difficult due to its tensor-product property. In this study, we attempted to use hierarchical B-splines as local refinement strategy in spline FEM. The regions of high gradients are overlapped by hierarchically-created local meshes. Knot vectors and control points in local meshes are extracted from global meshes, and they are refined using specific schemes. Proper compatibility conditions are imposed between global and local meshes. The effectiveness of the proposed method is verified on the basis of numerical results. Further, it is shown that by using a proposed local refinement scheme, the accuracy of the solution can be improved and it could be higher than that of the solution of a conventional spline FEM with relatively lower degrees of freedom.

본 연구에서는 NURBS 의 국부 세분화 방법 중 하나인 계층적 B-스플라인을 이용해 스플라인 유한요소법의 국부 세분화를 수행하는 방법을 제안한다. 세분화가 필요한 영역에 전역 격자로부터 계층적으로 생성된 국소 격자를 중첩시켜 국부 세분화를 수행한다. 국소 격자의 매듭 벡터와 제어점은 전역 격자로부터 추출된 후 세분화 되는 과정을 거친다. 생성된 국소 격자에 적절한 연속성 조건을 부여 함으로써 전역 격자와 국소 격자의 연속성을 유지 한다. 제안된 방법을 이용해 수치 예제의 해석을 수행하였다. 이를 통해 기존 NURBS 기반 스플라인 유한요소법에 비해 제안된 방법의 효율성을 검증하였다.

Keywords

References

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