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

Computational Structural Engineering Institute of Korea (한국전산구조공학회)
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Single Level Adaptive hp-Refinement using Integrals of Legendre Shape Function

적분형 르장드르 형상함수를 이용한 단일 수준 적응적 hp-체눈 세분화

  • 조준형 (한국전력공사 전력연구원 녹색성장연구소) ;
  • 유효진 (영남대학교 건설시스템공학과) ;
  • 우광성 (영남대학교 건설시스템공학과)
  • Received : 2010.04.29
  • Accepted : 2010.05.25
  • Published : 2010.06.30
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Abstract

The basic theory and application of new adaptive finite element algorithm have been proposed in this study including the adaptive hp-refinement strategy, and the effective method for constructing hp-approximation. The hp-adaptive finite element concept needs the integrals of Legendre shape function, nonuniform p-distribution, and suitable constraint of continuity in conjunction with irregular node connection. The continuity of hp-adaptive mesh is an important problem at the common boundary of element interface. To solve this problem, the constraint of continuity has been enforced at the common boundary using the connectivity mapping matrix. The effective method for constructing of the proposed algorithm has been developed by using hierarchical nature of the integrals of Legendre shape function. To verify the proposed algorithm, the problem of simple cantilever beam has been solved by the conventional h-refinement and p-refinement as well as the proposed hp-refinement. The result obtained by hp-refinement approach shows more rapid convergence rate than those by h-refinement and p-refinement schemes. It it noted that the proposed algorithm may be implemented efficiently in practice.

적응적 hp-세분화 기법과 그 기법의 효과적인 구성방법을 포함한 새로운 적응적 유한요소 알고리즘의 기초이론 및 적용이 이 연구를 통해 제시되었다. 적응적 hp-세분화 기초의 유한요소기법은 적분형 르장드르 형상함수와 요소별로 불균등한차수의 분배 및 비정형적인 절점연결과 관련된 연속조건을 만족시킬 수 있는 제약조건을 필요로 한다. 따라서 요소간의 접합부분에서 적응적 hp-유한요소망의 연속성이 중요한 문제로 대두된다. 이러한 문제를 요소경계에 연속성 제약조건을 절점연결 사상행렬을 적용하여 해결하였다. 또한, 적분형 르장드르 형상함수의 계층성질을 이용하여 제시된 알고리즘의 효율적 정식화 방안을 제시하였다. 간단한 캔틸레버문제가 h-세분화, p-세분화 그리고 hp-세분화 방법에 의해 계산되었다. hp-세분화의 결과는 다른 방식의 세분화에 비해 보다 빠른 수렴성을 보여 주는 것이 확인되었다. 그러므로 제시된 hp-세분화 알고리즘은 실제문제에 효율적으로 적용될 수 있을 것으로 생각된다.

Keywords

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