DOI QR코드

DOI QR Code

An efficient approach to structural static reanalysis with added support constraints

  • Liu, Haifeng (Department of Mathematics, School of Mathematics and Statistics, Xi'an Jiaotong University) ;
  • Wu, Baisheng (Department of Mechanics and Engineering Science, School of Mathematics, Jilin University) ;
  • Li, Zhengguang (Department of Mechanics and Engineering Science, School of Mathematics, Jilin University)
  • Received : 2011.09.06
  • Accepted : 2012.06.01
  • Published : 2012.08.10

Abstract

Structural reanalysis is frequently used to reduce the computational cost during the process of design or optimization. The supports can be regarded as the design variables in various types of structural optimization problems. The location, number, and type of supports may be varied in order to yield a more effective design. The paper is focused on structural static reanalysis problem with added supports where some node displacements along axes of the global coordinate system are specified. A new approach is proposed and exact solutions can be provided by the approach. Thus, it belongs to the direct reanalysis methods. The information from the initial analysis has been fully exploited. Numerical examples show that the exact results can be achieved and the computational time can be significantly reduced by the proposed method.

Keywords

Acknowledgement

Supported by : National Natural Science Foundation of China

References

  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. Akesson, B. and Olhoff, N. (1988), "Minimum stiffness of optimally located supports for maximum value of beam eigenfrequencies", J. Sound. Vib., 120(3), 457-463. https://doi.org/10.1016/S0022-460X(88)80218-9
  3. Akgun, M.A., Garcelon, J.H. and Haftka, R.T. (2001), "Fast exact linear and non-linear structural reanalysis and the Sherman-Morrison-Woodbury formulas", Int. J. Numer. Meth. Eng., 50(7), 1587-1606. https://doi.org/10.1002/nme.87
  4. Golub, G.H. and Van Loan, C.F. (1996), Matrix Computations, 3rd Edition, The Johns Hopkins University Press, Baltimore, London.
  5. 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
  6. Kirsch, U. (2008), Reanalysis of Structures, Springer, Dordrecht.
  7. 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
  8. Li, Z.G. and Wu, B.S. (2007), "A preconditioned conjugate gradient approach to structural reanalysis for general layout modifications", Int. J. Numer. Meth.. Eng., 70(5), 505-522. https://doi.org/10.1002/nme.1889
  9. Liu, C.H., Cheng, I., Tsai, A.C., Wang, L.J. and Hsu, J.Y. (2010), "Using multiple point constraints in finite element analysis of two dimensional contact problems", Struct. Eng. Mech., 36(1), 95-110. https://doi.org/10.12989/sem.2010.36.1.095
  10. 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
  11. Sherman, J. and Morrison, W.J. (1949), "Adjustment of an inverse matrix corresponding to changes in the elements of a given column or a given row of the original matrix", Ann. Math. Stat., 20(4), 621.
  12. Sun, W.Y. and Yuan, Y.X. (2006), Optimization Theory and Methods, Springer, New York.
  13. 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
  14. Tanskanen, P. (2006), "A multiobjective and fixed elements based modification of the evolutionary structural optimization method", Comput. Meth. Appl. M., 196(1-3), 76-90. https://doi.org/10.1016/j.cma.2006.01.010
  15. 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
  16. Wang, B.P. and Chen, J.L. (1996), "Application of genetic algorithm for the support location optimization of beams", Comput. Struct., 58(4), 797-800. https://doi.org/10.1016/0045-7949(95)00184-I
  17. Wang, D., Jiang, J.S. and Zhang, W.H. (2004), "Optimization of support positions to maximize the fundamental frequency of structures", Int. J. Numer. Meth. Eng., 61(10), 1584-1602. https://doi.org/10.1002/nme.1124
  18. Woodbury, M. (1950), "Inverting modified matrices", Memorandum Report 42. Statistical Research Group, Princeton University, Princeton.
  19. Zhu, J.H. and Zhang, W.H. (2010), "Integrated layout design of supports and structures", Comput. Meth. Appl. M., 199(9-12), 557-569. https://doi.org/10.1016/j.cma.2009.10.011

Cited by

  1. An efficient method to structural static reanalysis with deleting support constraints vol.52, pp.6, 2014, https://doi.org/10.12989/sem.2014.52.6.1121
  2. Preconditioned Conjugate Gradient Method for Static Reanalysis with Modifications of Supports vol.141, pp.2, 2015, https://doi.org/10.1061/(ASCE)EM.1943-7889.0000832
  3. Reanalysis of Modified Structures by Adding or Removing Substructures vol.2018, pp.1687-8094, 2018, https://doi.org/10.1155/2018/3084078
  4. The Cholesky rank-one update/downdate algorithm for static reanalysis with modifications of support constraints vol.62, pp.3, 2012, https://doi.org/10.12989/sem.2017.62.3.297