Journal of the Earthquake Engineering Society of Korea (한국지진공학회논문집)

Earthquake Engineering Society of Korea (한국지진공학회)
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Efficient Vector Superposition Method for Dynamic Analysis of Structures

구조물의 동적해석을 위한 효율적인 벡터중첩법

  • 김병완 (한국과학기술원 건설 및 환경공학과) ;
  • 정형조 (세종대학교 토목환경공학과) ;
  • 김운학 (국립한경대학교 토목공학과) ;
  • 이인원 (한국과학기술원 건설 및 환경공학과)
  • Published : 2003.06.01
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Abstract

Modified Lanczos vector superposition method is proposed for efficient dynamic analysis of structures, The proposed method is based on the modified Lanczos algorithm that generates stiffness-orthonormal Lanczos vectors. The proposed Lanczos vector superposition method has the same accuracy and efficiency as the conventional Lonczos vector superposition method in the analysis of structures under single input loads. On the other hand, the proposed method is more efficient than the conventional method in the analysis of structures under multi-input loads. The effectiveness of the proposed method is verified by analyzing two numerical examples.

본 논문에서는 구조물의 효율적인 동적해석을 위한 수정된 Lanczos 벡터중첩법을 제안하였다. 제안방법은 강성행렬에 직교하는 Lanczos 벡터를 생성하는 수정된 Lanczos 알고리즘에 기초하고 있다. 단일입력하중을 받는 구조물의 해석에 있어서 제안한 Lanczos 벡터중첩법은 기존의 Lanczos 벡터중첩법과 동일한 정확도와 효율성을 갖는 반면 다중입력하중을 받는 구조물의 경우 제안방법이 기존의 방법보다 더욱 효율적이다. 수치예제를 통해 제안방법의 효율성을 검증하였다.

Keywords

References

  1. Wilson, E. L., Yuan, M. W., and Dickens, J. M., “Dynamic analysis by direct superposition of Ritz vectors,” Earthquake Engineering and Structural Dynamics, Vol. 10, 1982, pp. 813-821. https://doi.org/10.1002/eqe.4290100606
  2. Bayo, E. P. and Wilson, E. L., “Use of Ritz vectors in wave propagation and foundation response,” Earthquake Engineering and Structural Dynamics, Vol. 12, 1984, pp. 499-505. https://doi.org/10.1002/eqe.4290120406
  3. Wilson, E. L., “A new method of dynamic analysis for linear and nonlinear systems,” Finite Elements in Analysis and Design, Vol. 1, 1985, pp. 21-23. https://doi.org/10.1016/0168-874X(85)90004-6
  4. Leger, P. and Wilson, E. L., “Generation of load dependent Ritz transformation vectors in structural dynamics,” Engineering Computations, Vol. 4, 1987, pp. 309-318. https://doi.org/10.1108/eb023709
  5. Leger, P., “Load dependent subspace reduction methods for structural dynamic computations,” Computers and Structures, Vol. 29, No. 6, 1988, pp. 993-999. https://doi.org/10.1016/0045-7949(88)90325-2
  6. Ibrahimbegovic, A., Chen, H. C., Wilson, E. L., and Taylor, R. L., “Ritz method for dynamic analysis of large discrete linear systems with non-proportional damping,” Earthquake Engineering and Structural Dynamics, Vol. 19, 1990, pp. 877-89. https://doi.org/10.1002/eqe.4290190608
  7. Mehai, L., Paultre, P., and Leger, P., “Efficiency of modal analysis to compute the seismic response of damfoundation systems with non-proportional damping,” Engineering Computations, Vol. 12, 1995, pp. 333-342. https://doi.org/10.1108/02644409510799622
  8. Nour-Omid, B. and Clough, R. W., “Dynamic analysis of structures using Lanczos co-ordinates,” Earthquake Engineering and Structural Dynamics, Vol. 12, 1984, pp. 565-577. https://doi.org/10.1002/eqe.4290120410
  9. Lanczos, C., “An iteration method for the solution of the eigenvalue problem of linear differential and integral operators,” Journal of Research of the National Bureau of Standards, Vol. 45, No. 4, 1950, pp. 255-282. https://doi.org/10.6028/jres.045.026
  10. Nour-Omid, B. and Clough, R. W., “Block Lanczos method for dynamic analysis of structures,” Earthquake Engineering and Structural Dynamics, Vol. 13, 1985, pp. 271-275. https://doi.org/10.1002/eqe.4290130210
  11. Nour-Omid, B. and Regelbrugge, M. E., “Lanczos method for dynamic analysis of damped structural systems,” Earthquake Engineering and Structural Dynamics, Vol. 18, 1989, pp. 1091-1104. https://doi.org/10.1002/eqe.4290180802
  12. Chen, H. C. and Taylor, R. L., “Solution of viscously damped linear systems using a set of load-dependent vectors,” Earthquake Engineering and Structural Dynamics, Vol. 19, 1990, pp. 653-65. https://doi.org/10.1002/eqe.4290190503
  13. Pan, T. C. and Li, J., “Dynamic vehicle element method for transient response of coupled vehicle-structure systems,” ASCE Journal of Structural Engineering, Vol. 128, No. 2, 2002, pp. 214-223. https://doi.org/10.1061/(ASCE)0733-9445(2002)128:2(214)
  14. Park, K. S., Jung, H. J., and Lee, I. W., “A comparative study on aseismic performances of base isolation systems for multi-span continuous bridge,” Engineering Structures, Vol. 24, 2002, pp. 1001-1013. https://doi.org/10.1016/S0141-0296(02)00020-2