Structural Engineering and Mechanics

  • 제86권3호
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  • Pages.349-359
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  • 2023
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  • 1225-4568(pISSN)
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  • 1598-6217(eISSN)
테크노프레스 (Techno-Press)
권호 표지
DOI QR코드

DOI QR Code

Reliability-based stochastic finite element using the explicit probability density function

  • 투고 : 2022.05.28
  • 심사 : 2023.03.27
  • 발행 : 2023.05.10
⟨ 이전 논문 다음 논문 ⟩

초록

This paper presents a technique for determining the optimal number of elements in stochastic finite element analysis based on reliability analysis. Using the change-of-variable perturbation stochastic finite element approach, the probability density function of the dynamic responses of stochastic structures is explicitly determined. This method combines the perturbation stochastic finite element method with the change-of-variable technique into a united model. To further examine the relationships between the random fields, discretization of the random field parameters, such as the variance function and the scale of fluctuation, is also performed. Accordingly, the reliability index is calculated based on the explicit probability density function of responses with Gaussian or non-Gaussian random fields in any number of elements corresponding to the random field discretization. The numerical examples illustrate the effectiveness of the proposed method for a one-dimensional cantilever reinforced concrete column and a two-dimensional steel plate shear wall. The benefit of this method is that the probability density function of responses can be obtained explicitly without the use simulation techniques. Any type of random variable with any statistical distribution can be incorporated into the calculations, regardless of the restrictions imposed by the type of statistical distribution of random variables. Consequently, this method can be utilized as a suitable guideline for the efficient implementation of stochastic finite element analysis of structures, regardless of the statistical distribution of random variables.

키워드

과제정보

The authors would like to thank the anonymous reviewers for their contributions to the manuscript's improvement.

참고문헌

  1. Aldosary, M., Wang, J. and Li, C. (2018), "Structural reliability and stochastic finite element methods: State-of-the-art review and evidence-based comparison", Eng. Comput., 35(6), 2165-2214. https://doi.org/10.1108/EC-04-2018-0157.
  2. Aslett, L.J., Nagapetyan, T. and Vollmer, S.J. (2017), "Multilevel Monte Carlo for reliability theory", Reliab. Eng. Syst. Saf., 165, 188-196. https://doi.org/10.1016/j.ress.2017.03.003.
  3. Borri, A. and Speranzini, E. (1997), "Structural reliability analysis using a standard deterministic finite element code", Struct. Saf., 19(4), 361-382. https://doi.org/10.1016/S0167-4730(97)00017-9.
  4. Cao, R., Sun, Z., Wang, J. and Guo, F. (2021), "An efficient reliability analysis strategy for low failure probability problems", Struct. Eng. Mech., 78(2), 209-218. https://doi.org/10.12989/sem.2021.78.2.209.
  5. Chakraborty, S. and Dey, S.S. (2000), "Stochastic finite element simulation of uncertain structures subjected to earthquake", Shock Vib., 7(5), 309-320. https://doi.org/10.1155/2000/730364
  6. Council, B.S.S. (2000), Prestandard and Commentary for the Seismic Rehabilitation of Buildings, Report FEMA-356, Washington, DC.
  7. da S Jr, C.A. and Beck, A.T. (2015), "New method for efficient Monte Carlo-Neumann solution of linear stochastic systems", Probab. Eng. Mech., 40, 90-96. https://doi.org/10.1016/j.probengmech.2015.02.006.
  8. Der Kiureghian, A. and Ke, J.B. (1988), "The stochastic finite element method in structural reliability", Probab. Eng. Mech., 3(2), 83-91. https://doi.org/10.1016/0266-8920(88)90019-7.
  9. Ditlevsen, O. and Madsen, H.O. (1996), Structural Reliability Methods, Vol. 178, Wiley, New York.
  10. Elishakoff, I. and Liping, Z. (1993), "Random vibration of structures by the finite element method", Comput. Meth. Appl. Mech. Eng., 105(3), 359-373. https://doi.org/10.1016/0045-7825(93)90063-4.
  11. Garakaninezhad, A. and Bastami, M. (2019), "An evolutionary approach for structural reliability", Struct. Eng. Mech., 71(4), 329-339. https://doi.org/10.12989/sem.2019.71.4.329.
  12. Gasser, M. and Schueller, G.I. (1997), "Reliability-based optimization of structural systems", Math. Meth. Oper. Res., 46(3), 287-307. https://doi.org/10.1007/BF01194858.
  13. Hachem, M.M., Moehle, J.P. and Mahin, S.A. (2003), "Performance of circular reinforced concrete bridge columns under bidirectional earthquake loading", Pacific Earthquake Engineering Research Center, Berkeley, CA.
  14. Igusa, T. and Der Kiureghian, A. (1988), "Response of uncertain systems to stochastic excitation", J. Eng. Mech., 114(5), 812-832. https://doi.org/10.1061/(ASCE)0733-9399(1988)114:5(812).
  15. Kaminski, M. (2009), "Perturbation-based stochastic finite element method using polynomial response function for the elastic beams", Mech. Res. Commun., 36(3), 381-390. https://doi.org/10.1016/j.mechrescom.2008.11.001.
  16. Keshtegar, B. and Meng, Z. (2017), "A hybrid relaxed first-order reliability method for efficient structural reliability analysis", Struct. Saf., 66, 84-93. https://doi.org/10.1016/j.strusafe.2017.02.005.
  17. Lee, G.Y. (2020), "A natural frequency sensitivity based stabilization in spectral stochastic finite element method for frequency response analysis", Struct. Eng. Mech., 75(3), 311-325. https://doi.org/10.12989/sem.2020.75.3.311.
  18. Li, C.C. and Der Kiureghian, A. (1993), "Optimal discretization of random fields", J. Eng. Mech., 119(6), 1136-1154. https://doi.org/10.1061/(ASCE)0733-9399(1993)119:6(1136).
  19. Li, D., Zheng, Z.L., Yang, R. and Zhang, P. (2018), "Analytical solutions for stochastic vibration of orthotropic membrane under random impact load", Mater., 11(7), 1231. https://doi.org/10.3390/ma11071231.
  20. Liu, P.L. and Liu, K.G. (1993), "Selection of random field mesh in finite element reliability analysis", J. Eng. Mech., 119(4), 667-680. https://doi.org/10.1061/(ASCE)0733-9399(1993)119:4(667).
  21. Liu, Z., Ruan, X., Liu, Z. and Lu, H. (2019), "Probability density evolution analysis of stochastic nonlinear structure under nonstationary ground motions", Struct. Infrastr. Eng., 15(8), 1049-1059. https://doi.org/10.1080/15732479.2019.1599963.
  22. Lubell, A.S., Prion, H.G., Ventura, C.E. and Rezai, M. (2000), "Unstiffened steel plate shear wall performance under cyclic loading", J. Struct. Eng., 126(4), 453-460. https://doi.org/10.1061/(ASCE)0733-9445(2000)126:4(453).
  23. Mahadevan, S. and Haldar, A. (1991), "Practical random field discretization in stochastic finite element analysis", Struct. Saf., 9(4), 283-304. https://doi.org/10.1016/0167-4730(91)90050-J.
  24. Manjuprasad, M. and Manohar, C.S. (2007), "Adaptive random field mesh refinements in stochastic finite element reliability analysis of structures", Comput. Model. Eng. Sci., 19(1), 23.
  25. Mustafa, A. and Takewaki, I. (2010), "Deterministic and probabilistic representation of near-field pulse-like ground motion", Soil Dyn. Earthq. Eng., 30(5), 412-422. https://doi.org/10.1016/j.soildyn.2009.12.013.
  26. Ni, P., Li, J., Hao, H., Yan, W., Du, X. and Zhou, H. (2020), "Reliability analysis and design optimization of nonlinear structures", Reliab. Eng. Syst. Saf., 198, 106860. https://doi.org/10.1016/j.ress.2020.106860.
  27. Rezaeian, S. (2010), "Stochastic modeling and simulation of ground motions for performance-based earthquake engineering", University of California, Berkeley.
  28. Rong, B., Rui, X. and Tao, L. (2012), "Perturbation finite element transfer matrix method for random eigenvalue problems of uncertain structures", J. Appl. Mech., 79(2), 1. https://doi.org/10.1115/1.4005574.
  29. Salimi, M.R. and Yazdani, A. (2018), "Reliability-based fragility analysis of nonlinear structures under the actions of random earthquake loads", Struct. Eng. Mech., 66(1), 75-84. https://doi.org/10.12989/sem.2018.66.1.075.
  30. Sudret, B. and Der Kiureghian, A. (2000), "Stochastic finite element methods and reliability: A state-of-the-art report", Department of Civil and Environmental Engineering, University of California, Berkeley, CA.
  31. Sudret, B. and Der Kiureghian, A. (2002), "Comparison of finite element reliability methods", Probab. Eng. Mech., 17(4), 337-348. https://doi.org/10.1016/S0266-8920(02)00031-0.
  32. Takewaki, I. and Ben-Haim, Y. (2005), "Info-gap robust design with load and model uncertainties", J. Sound Vib., 288(3), 551-570. https://doi.org/10.1016/j.jsv.2005.07.005.
  33. Udoeyo, F.F. and Ugbem, P.I. (1995), "Dimensional variations in reinforced-concrete members", J. Struct. Eng., 121(12), 1865-1867. https://doi.org/10.1061/(ASCE)0733-9445(1995)121:12(1865).
  34. Vanmarcke, E. (2010), Random Fields: Analysis and Synthesis, World Scientific.
  35. Vanmarcke, E. and Grigoriu, M. (1983), "Stochastic finite element analysis of simple beams", J. Eng. Mech., 109(5), 1203-1214. https://doi.org/10.1061/(ASCE)0733-9399(1983)109:5(1203).
  36. Vlachos, C. (2016), "Stochastic characterization and simulation of ground motions based on earthquake scenarios", Columbia University.
  37. Warburton, G.B. (1995), Dynamics of Structures, McGraw-Hill, New York.
  38. Wu, F., Yao, L.Y., Hu, M. and He, Z.C. (2017), "A stochastic perturbation edge-based smoothed finite element method for the analysis of uncertain structural-acoustics problems with random variables", Eng. Anal. Bound. Elem., 80, 116-126. https://doi.org/10.1016/j.enganabound.2017.03.008.
  39. Xia, B. and Yu, D. (2013), "Response probability analysis of random acoustic field based on perturbation stochastic method and change-of-variable technique", J. Vib. Acoust, 135(5), 1. https://doi.org/10.1115/1.4024853.
  40. Xia, B., Yu, D. and Liu, J. (2014), "Transformed perturbation stochastic finite element method for static response analysis of stochastic structures", Finite Elem. Anal. Des., 79, 9-21. https://doi.org/10.1016/j.finel.2013.10.003.
  41. Xue, Q., Wu, C.W., Chen, C.C. and Chen, K.C. (2008), "The draft code for performance-based seismic design of buildings in Taiwan", Eng. Struct., 30(6), 1535-1547. https://doi.org/10.1016/j.engstruct.2007.10.002.
  42. Yan, S. and Guo, L. (2015), "Calculation of scale of fluctuation and variance reduction function", Trans. Tianjin Univ., 21(1), 41-49. https://doi.org/10.1007/s12209-015-2298-y.
  43. Yang, M., Zhang, D. and Han, X. (2020), "New efficient and robust method for structural reliability analysis and its application in reliability-based design optimization", Comput. Meth. Appl. Mech. Eng., 366, 113018. https://doi.org/10.1016/j.cma.2020.113018.
  44. Yang, Y., Peng, J., Zhang, J. and Cai, C.S. (2018), "A new method for estimating the scale of fluctuation in reliability assessment of reinforced concrete structures considering spatial variability", Adv. Struct. Eng., 21(13), 1951-1962. https://doi.org/10.1177/1369433218760891.
  45. Yazdani, A. and Eftekhari, S.N. (2015), "The effect of structural properties and ground motion variables on the global response of structural systems", Civil Eng. Environ. Syst., 32(3), 216-229. https://doi.org/10.1080/10286608.2015.1046032.
  46. Yazdani, A. and Takada, T. (2011), "Probabilistic study of the influence of ground motion variables on response spectra", Struct. Eng. Mech., 39(6), 877-893. https://doi.org/10.12989/sem.2011.39.6.877.
  47. Zhang, D., Zhang, J., Yang, M., Wang, R. and Wu, Z. (2022), "An enhanced finite step length method for structural reliability analysis and reliability-based design optimization", Struct. Multidisc. Optim., 65(8), 231. https://doi.org/10.1007/s00158-022-03294-x.
  48. Zhang, Y., Sun, Z., Yan, Y., Yu, Z. and Wang, J. (2020), "A novel reliability analysis method based on Gaussian process classification for structures with discontinuous response", Struct. Eng. Mech., 75(6), 771-784. https://doi.org/10.12989/sem.2020.75.6.771.
  49. Zhao, Y., Deng, Z. and Han, Y. (2020), "Dynamic response analysis of structure with hybrid random and interval uncertainties", Chaos Solit. Fract., 131, 109495. https://doi.org/10.1016/j.chaos.2019.109495.