Computational Structural Engineering (전산구조공학)

Computational Structural Engineering Institute of Korea (한국전산구조공학회)
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Development of 4-node Plate Bending Element using Nonconforming Displacement Modes

비적합 변위모드를 이용한 4절점 평판휨요소의 개발

  • 박용명 (포항산업과학연구원 강재이용기술부문 공학박사) ;
  • 최창근 (한구과학기술연구원 토목공학과)
  • Published : 1997.06.01
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Abstract

A 4-node element for efficient finite element analysis of plate bending is presented in this paper. This element is formulated based on Mindlin plate theory to take account of shear deformation. To overcome the overestimation of shear stiffness in thin Mindlin plate element, especially in the lower order element, five nonconforming displacement modes are added to the original displacement fields. The proposed nonconforming element does not possess spurious zero-energy mode and does not show shear locking phenomena in very thin plate even for distorted mesh shapes. It was recognized from benchmark numerical tests that the displacement converges to the analytical solutions rapidly and the stress distributions are very smooth. The element also provides good results for the case of high aspect ratio.

본 논문에서는 평판 구조물의 효율적인 해석을 위한 4절점 평판휨 요소를 개발하였다. 이 요소는 전단변형을 고려하기 위해 Mindlin평판이론에 의하여 유도하였다. 평판휨 문제에서 4절점요소와 같은 저차의 등매개변수 Mindlin평판요소는 전단강성을 실제보다 강하게 평가하기 때문에 얇은 평판에서는 요소의 기능을 발휘하지 못한다. 이러한 문제점을 극복하기 위해 4절점 요소에 5개의 비적합변위모드를 추가함으로써 개선된 결과를 얻을 수 있었으며, 개발된 요소는 유사영에너지모드를 발생시키지 않는다. 아주 얇은 평판에서도 요소의 형상과 무관하게 전단구속현상을 극복하였으며, 예제 해석으로부터 변위의 신속한 수렴성과 단면력의 분포가 양호한 결과를 얻을 수 있었다. 또한 요소형상비가 매우 큰 경우에도 좋은 결과를 얻을 수 있었다.

Keywords

References

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