Study on the Dynamic Analysis Based on the Reduced System

축소모델 기반 구조물의 동적해석 연구

  • 김현기 (한국항공우주연구원 항공사업단) ;
  • 조맹효 (서울대학교 기계항공공학부)
  • Published : 2008.10.30

Abstract

In this study, the reduced system for the dynamic analysis is proposed and the selection criterion of the primary degrees of freedom is presented considering the relation between natural frequency and external loading frequency. A well-constructed reduced system can assure the accurate representation of the dynamic behavior under arbitrary dynamic loads. For selecting the primary degrees of freedom of the reduced system, we employ the robust two-level condensation scheme of which the reliability has been proven through previous study. In the numerical examples, the reliability of the dynamic analysis based on the reduced system is demonstrated through comparing with those of global system.

잘 구축된 축소시스템은 동하중을 받는 구조물의 거동을 정확하게 계산할 수 있으며, 유한요소 기반 동적해석에서 문제가 될 수 있는 계산시간과 전산자원의 문제를 해결할 수 있다. 본 연구에서는 축소모델 기반 동적해석 알고리즘을 개발하였고, 동적 축소모델의 구축을 위한 주자유도 선정방법을 제안하였다. 이 과정에서 기존 연구에서 신뢰성이 검증된 2단계 축소기법을 사용하여 중요 자유도를 선정하고, IRS 방법에 의해 최종 축소모델을 구축하였다. 이를 임의의 동하중을 받는 수치예제에 적용하고 전체시스템의 동적해석 결과와 비교하여 제안 방법의 신뢰성을 검증하였다.

Keywords

References

  1. Cho, M., Kim, H. (2004) Element-based node selection method for reduction of eigenvalue problems, AIAA Journal, 42(8), pp.1677-1684 https://doi.org/10.2514/1.5407
  2. Guyan, R.J. (1965) Reduction of stiffness and mass matrices, AIAA Journal, 3(2), p.380 https://doi.org/10.2514/3.2874
  3. Henshell, R.D., Ong, J.H. (1975) Automatic masters from eigenvalues economization. Journal of Earthquake Engineering and Structural Dynamics, 3, pp.375-383 https://doi.org/10.1002/eqe.4290030408
  4. Kidder, R.L.(1973) Reduction of structural frequency equations. AIAA Journal, 11(6), p.892 https://doi.org/10.2514/3.6852
  5. Kim, H., Cho, M. (2006) Two-level scheme for selection of degrees of freedom and semi-analytic sensitivity based on the reduced system, Computer Methods in Applied Mechanics and Engineering, 195(33-36), pp.4244-4268 https://doi.org/10.1016/j.cma.2005.08.004
  6. Kim, K.O., Choi, Y.J. (2000) Energy method for selection of degrees of freedom in condensation, AIAA Journal, 38, pp.1253-1259 https://doi.org/10.2514/2.1095
  7. Matta, K.W. (1987) Selection of degrees of freedom for dynamic analysis, Journal of pressure vessel technology, 109(1), pp.65-69 https://doi.org/10.1115/1.3264857
  8. O'Callahan, J. (1989) A procedure for an improved reduced system(IRS) model, Proceedings of the 7th international modal analysis conference, Union college, Schenectady. NY. pp.17-21
  9. Shah, V.N., Raymund, M. (1982) Analytical selection of masters for the reduced eigenvalue problem, International Journal for Numerical Methods in Engineering, 18, pp.89-98 https://doi.org/10.1002/nme.1620180108
  10. Zhang, D.W., Li, S. (1995) Succession-level approximate reduction(SAR) technique for structural dynamic model, Analysis conference(Nashville,TN), Union college press, Schenectady, NY, pp.435-441