DOI QR코드

DOI QR Code

Perturbation Based Stochastic Finite Element Analysis of the Structural Systems with Composite Sections under Earthquake Forces

  • Cavdar, Ozlem (Karadeniz Technical University, Department of Civil Engineering) ;
  • Bayraktar, Alemdar (Karadeniz Technical University, Department of Civil Engineering) ;
  • Cavdar, Ahmet (Karadeniz Technical University, Department of Civil Engineering) ;
  • Adanur, Suleyman (Karadeniz Technical University, Department of Civil Engineering)
  • 투고 : 2006.03.06
  • 심사 : 2008.03.07
  • 발행 : 2008.04.25

초록

This paper demonstrates an application of the perturbation based stochastic finite element method (SFEM) for predicting the performance of structural systems made of composite sections with random material properties. The composite member consists of materials in contact each of which can surround a finite number of inclusions. The perturbation based stochastic finite element analysis can provide probabilistic behavior of a structure, only the first two moments of random variables need to be known, and should therefore be suitable as an alternative to Monte Carlo simulation (MCS) for realizing structural analysis. A summary of stiffness matrix formulation of composite systems and perturbation based stochastic finite element dynamic analysis formulation of structural systems made of composite sections is given. Two numerical examples are presented to illustrate the method. During stochastic analysis, displacements and sectional forces of composite systems are obtained from perturbation and Monte Carlo methods by changing elastic modulus as random variable. The results imply that perturbation based SFEM method gives close results to MCS method and it can be used instead of MCS method, especially, if computational cost is taken into consideration.

키워드

참고문헌

  1. Antonio, C. C. and Hoffbauer, L. N. (2007), "Uncertainty analysis based on sensitivity applied to angle-ply composite structures", Reliability Engineering and System Safety, 92, 1353-1362. https://doi.org/10.1016/j.ress.2006.09.006
  2. Deodatis, G. (1991), "Weighted integral method I: stochastic stiffness matrix", J. Engng Mech. 117, 1851-1864. https://doi.org/10.1061/(ASCE)0733-9399(1991)117:8(1851)
  3. Ganesan, K. and Kowda, V. K. (2005), "Buckling of composite beam-columns with stochastic properties", Reinforced Plastics Compos, 24, 513-531. https://doi.org/10.1177/0731684405045017
  4. Ghanem, R. (1999), "Ingredients for a general purpose stochastic finite elements implementation", Comput. Methods Appl. Mech. Engrg. 168, 19-34. https://doi.org/10.1016/S0045-7825(98)00106-6
  5. Ghanem, R. G. and Spanos, P. D. (1991), "Spectral stochastic finite element formulation for reliability analysis", J. Engng Mech., ASCE, 10, 2351-2372.
  6. Kaminski, M. (2006), "On generalized stochastic perturbation-based finite element method", Commun. Numer. Meth. Engng. 22, 23-31.
  7. Kaminski, M. and Kleiber, M. (2000), "Perturbation based stochastic finite element method for homogenization of two-phase elastic composites", Comp Structures, 78, 811-826. https://doi.org/10.1016/S0045-7949(00)00116-4
  8. Kleiber, M. and Hien, T. (1992), The stochastic finite element method, John Wiley and Sons, New York, USA
  9. Lal, A., Singh, B. and Kumar, N. R. (2007), "Natural fequency of laminated composite plate resting on an elastic foundation with uncertain system properties", Struct Eng Mech, 27, 199-222. https://doi.org/10.12989/sem.2007.27.2.199
  10. Ngah, M. F. and Young, A. (2007), "Application of the spectral stochastic finite element method for performance prediction of composite structures", Composite Structures, 78, 447-456. https://doi.org/10.1016/j.compstruct.2005.11.009
  11. Papadopoulos, V. and Papadrakakis, M. (1997), "Stochastic finite element-based reliability analysis of space frames", Prob. Eng. Mech. 13, 53-65.
  12. PEER (Pacific Earthquake Engineering Research Centre), http://peer.berkeley.edu/smcat/data, 2007.
  13. Pilkey, W. D. (2002), "Analysis and Design of Elastic Beams-Computational Methods", Wiley, New York.
  14. Sapountzakis, E. J. (2004), "Dynamic analysis of composite steel-concrete structures with deformable connection", Computers and Structures, 82, 717-729. https://doi.org/10.1016/j.compstruc.2004.02.012
  15. Sapountzakis, E. J. and Mokos, V. G. (2007), "Vibration analysis of 3-D composite beam elements including warping and shear deformation effects", J Sound Vib, 306, 818-834. https://doi.org/10.1016/j.jsv.2007.06.021
  16. Sapountzakis, E. J. and Mokos, V. G. (2007), "3-D beam element of composite cross section including warping and shear deformation effects", Comput Struct, 85, 102-116. https://doi.org/10.1016/j.compstruc.2006.09.003
  17. Shinozuka, M. (1972), "Monte Carlo Simulation of structural dynamics", Computers Struct, 2, 865-874.
  18. Stefanou, G. and Papadrakakis, M. (2004), "Stochastic finite element analysis of shells with combined random material and geometric properties", Comput. Methods Appl Mech Eng, 193, 140-160.
  19. uake Engineering Research Centre), http://peer.berkeley.edu/smcat/data, 2007.
  20. Vellascoa, P. C. G., Andradeca, S. A. L., Silvab, J. G. S., Limaa, L. R. O. and Brito, O. (2006), "A parametric analysis of steel and composite portal frames with semi-rigid connections", Engineering Structures, 28, 543-556. https://doi.org/10.1016/j.engstruct.2005.09.010
  21. Wang, J. F. and Li, G .Q. (2007), "Testing of semi-rigid steel-concrete composite frames subjected to vertical loads", Eng Struct, 29, 1903-1916. https://doi.org/10.1016/j.engstruct.2006.10.014
  22. Yamazaki, F., Shinozuka, M. and Dasgupta, G. (1988), "Neumann expansion for stochastic finite element analysis", J. Eng. Mech., 114, 1335-1354. https://doi.org/10.1061/(ASCE)0733-9399(1988)114:8(1335)
  23. Zhang, J. and Ellingwood, B. (1996), "SFEM for reliability of structures with material nonlinearities", J Struct Eng-ASCE, 122, 701-704. https://doi.org/10.1061/(ASCE)0733-9445(1996)122:6(701)

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