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

Computational Structural Engineering Institute of Korea (한국전산구조공학회)
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The Energy Conserving Algorithm of the System Acted by an Exponential Impact Force

지수형 충격력을 받는 시스템의 에너지보존 알고리듬

  • 윤성호 (금오공과대학교 기계공학부)
  • Published : 2003.09.01
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Abstract

This paper aims at investigating the exact dynamic response of the system undergoing a exponential impact force from the viewpoints of conservations of momentum and energy. The midpoint method applied in the Newmark's family algorithm is found to be identical to the case of the application of the trapezoidal method which provides conservations of momentum and energy. For the linear impact force the mid point, the trapezoidal and the (n+1) point method exactly meet the conservation characteristics independent of the size of integration interval. On the other hand, constants for the dynamic motion resulting from the nonlinear impact are underestimated or overestimated by these method mentioned above. To overcome this indispensible error, the Simpson 1/3 method as one of multi step methods whose advantages is to use longer time interval with the same number of evaluation functions is adopted for the exact conservations of momentum and energy. Moreover, the suggested method is expected to expand the similar algorithm for the general dynamic motion including finite rotations.

본 연구에서는 지수형 함수로 표현된 비선형 충격력을 받는 시스템의 동적 응답 정밀도를 향상시키고자 선형 충격력의 경우와 비교ㆍ검토하였다. Newmark 계열의 중앙법 알고리듬이 사다리꼴법과 같이 충격력이 없는 경우 모멘텀과 에너지 보존을 성립하도록 유도되었다. 중앙법, 사다리꼴법, 시간구간 종점 평가법((n+1)점 방법)을 선형 충격력에 적용하면 적분간격의 크기에 상관없이 보존성질을 만족하나, 비선형 충격력의 경우 모멘텀과 에너지 보존 상수값이 과소 또는 과대평가 되어졌다. 이러한 오차를 제거하고자 시간간격을 늘리면서 평가함수의 개수를 최소로 하는 다단계 방법중의 하나인 Simpson 1/3법을 사용하여 보존상수값의 정밀도를 향상시켰다. 아울러 유한회전을 포함한 유한운동을 해석할 때에도 제안된 알고리듬이 확정ㆍ적용될 가능성을 보여주고 있다.

Keywords

References

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