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

  • 제27권3호
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  • Pages.183-189
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  • 2014
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  • 1229-3059(pISSN)
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  • 2287-2302(eISSN)
한국전산구조공학회 (Computational Structural Engineering Institute of Korea)
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다면체 유한요소의 형상함수 개발에 관한 연구

A Study on the Development of Shape Functions of Polyhedral Finite Elements

  • 김현규 (서울과학기술대학교 기계자동차공학과)
  • Kim, Hyun-Gyu (Department of Mechanical and Automotive Engineering, Seoul National University of Science and Technology)
  • 투고 : 2014.04.02
  • 심사 : 2014.05.21
  • 발행 : 2014.06.30
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초록

본 연구에서는 다면체 요소의 개발을 위하여 Wachspress 좌표계와 이동최소자승 근사를 기반으로하는 형상함수와 수치적분 방법을 제시하고 있다. 사면체 요소를 사면체 영역으로 분할하여 형상함수가 구성이 되고 이 영역을 사용한 일관성있는 수치적분이 수행되게 된다. 다면체 요소 면에서 Wachspress 좌표계를 사용하고 요소 내부에서 라플라스 방정식을 적용하여 이동최소자승 근사의 가중함수를 정의하게 된다. 본 연구에서 개발되는 다면체 요소의 형상함수와 수치적분 방법은 일반적인 유한요소와 유사한 특성을 갖게 되는데 수치 예제를 통하여 유효성을 보여주었다.

In this paper, a polyhedral element is presented to solve three-dimensional problems by developing shape functions based on Wachspress coordinates and moving least square approximation. A subdivision of polyhedrons into tetrahedral domains is performed for the construction of shape functions of polyhedral elements, and numerical integration of the weak form is carried out consistently over the tetrahedral domains. The weight functions for moving least square approximation are defined by solving Laplace equation with boundary values based on Wachspress coordinates on polyhedral element faces. Polyhedral elements presented in this paper have similar properties to conventional finite element regarding the continuity, the completeness, the node-element connectivity and the inter-element compatibility. Numerical examples show the effectiveness of the present method for solving three-dimensional problems using polyhedral elements.

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참고문헌

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피인용 문헌

  1. Periodic Mesh Generation for Composite Structures using Polyhedral Finite Elements vol.27, pp.4, 2014, https://doi.org/10.7734/COSEIK.2014.27.4.239