DOI QR코드

DOI QR Code

The Cholesky rank-one update/downdate algorithm for static reanalysis with modifications of support constraints

  • Liu, Haifeng (School of Mathematics and Statistics, Xi'an Jiaotong University) ;
  • Zhu, Jihua (School of Software Engineering, Xi'an Jiaotong University) ;
  • Li, Mingming (Network Center, Jilin University)
  • 투고 : 2016.04.22
  • 심사 : 2016.12.22
  • 발행 : 2017.05.10

초록

Structural reanalysis is frequently utilized to reduce the computational cost so that the process of design or optimization can be accelerated. The supports can be regarded as the design variables and may be modified in various types of structural optimization problems. The location, number, and type of supports can make a great impact on the performance of the structure. This paper presents a unified method for structural static reanalysis with imposition or relaxation of some support constraints. The information from the initial analysis has been fully utilized and the computational time can be significantly reduced. Numerical examples are used to validate the effectiveness of the proposed method.

키워드

과제정보

연구 과제 주관 기관 : Natural Science Foundation of China

참고문헌

  1. Abu Kasim, A.M. and Topping, B.H.V. (1987), "Static reanalysis: a review", J. Struct. Eng., ASCE, 113(5), 1029-1045. https://doi.org/10.1061/(ASCE)0733-9445(1987)113:5(1029)
  2. Davis, T.A. (2006), Direct Methods for Sparse Linear Systems, SIAM, Philadephia, PA, USA.
  3. Gao, H.H., Zhu, J.H., Zhang, W.H. and Zhou, Y. (2015), "An improved adaptive constraint aggregation for integrated layout and topology optimization", Comput. Meth. Appl. M., 289, 387-408. https://doi.org/10.1016/j.cma.2015.02.022
  4. Gill, P.E., Golub, G.H., Murray, W. and Saunders, M.A. (1974), "Methods for modifying matrix factorizations", Math. Comput., 28(126), 505-535. https://doi.org/10.1090/S0025-5718-1974-0343558-6
  5. Golub, G.H. and Van Loan, C.F. (2013), Matrix Computations, 4th Edition, The Johns Hopkins University Press, Baltimore, MD, USA.
  6. Hassan, M.R.A., Azid, I.A., Ramasamy, M., Kadesan J., Seetharamu, K.N., Kwan, A.S.K. and Arunasalam P. (2010), "Mass optimization of four bar linkage using genetic algorithms with dual bending and buckling constraints", Struct. Eng. Mech., 35(1), 83-98. https://doi.org/10.12989/sem.2010.35.1.083
  7. Kirsch, U. (2008), Reanalysis of Structures, Springer, Dordrecht, Netherlands.
  8. Kozikowska, A. (2011), "Topological classes of statically determinate beams with arbitrary number of supports", J. Theor. Appl. Mech., 49(4), 1079-1100.
  9. Leu, L.J. and Tsou, C.H. (2000), "Application of a reduction method for reanalysis to nonlinear dynamic analysis of framed structures", Comput. Mech., 26(5), 497-505. https://doi.org/10.1007/s004660000200
  10. Liu, H.F. and Yue, S.G. (2014), "An efficient method to structural static reanalysis with deleting support constraints", Struct. Eng. Mech., 52(6), 1121-1134. https://doi.org/10.12989/sem.2014.52.6.1121
  11. Liu, H.F., Wu, B.S., and Li, Z.G. (2012), "An efficient approach to structural static reanalysis with added support constraints", Struct. Eng. Mech., 43(3), 273-285. https://doi.org/10.12989/sem.2012.43.3.273
  12. Liu, H.F., Wu, B.S., Li, Z.G. and Zheng, S.P. (2014), "Structural static reanalysis for modification of supports", Struct. Multidisc. Optim., 50(3), 425-435. https://doi.org/10.1007/s00158-014-1063-5
  13. Olhoff, N. and Taylor, J.E. (1983), "On structural optimization", J. Appl. Mech., ASME, 50(4), 1139-1151. https://doi.org/10.1115/1.3167196
  14. Sun, W.Y. and Yuan, Y.X. (2006), Optimization Theory and Methods: Nonlinear Programming, Springer, New York, NY, USA.
  15. Takezawa, A., Nishiwaki, S., Izui, K. and Yoshimura, M. (2006), "Structural optimization using function-oriented elements to support conceptual designs", J. Mech. Des., ASME, 128(4), 689-700. https://doi.org/10.1115/1.2198257
  16. Terdalkar, S.S. and Rencis, J.J. (2006), "Graphically driven interactive finite element stress reanalysis for machine elements in the early design stage", Finite. Elem. Anal. Des., 42(10), 884-899. https://doi.org/10.1016/j.finel.2006.01.009
  17. Xia, Q. and Shi, T.L. (2016), "Topology optimization of compliant mechanism and its support through a level set method", Comput. Meth. Appl. M., 305, 359-375. https://doi.org/10.1016/j.cma.2016.03.017
  18. Xia, Q., Wang, M.Y. and Shi, T.L. (2014), "A level set method for shape and topology optimization of both structure and support of continuum structures", Comput. Meth. Appl. M., 272, 340-353. https://doi.org/10.1016/j.cma.2014.01.014
  19. Zhu, J.H. and Zhang, W.H. (2010), "Integrated layout design of supports and structures", Comput. Meth. Appl. M., 199(9-12), 557-56. https://doi.org/10.1016/j.cma.2009.10.011

피인용 문헌

  1. High-order quasi-conforming triangular Reissner-Mindlin plate element pp.0264-4401, 2018, https://doi.org/10.1108/EC-11-2017-0446
  2. Predictions of the maximum plate end stresses of imperfect FRP strengthened RC beams: study and analysis vol.9, pp.4, 2017, https://doi.org/10.12989/amr.2020.9.4.265