Stochastic Buckling Analysis of Non-Uniform Columns Using Stochastic Finite Elements with Discretization Random Field by the Point Method
Received: 9 February 2022 | Revised: 9 March 2022 | Accepted: 10 March 2022 | Online: 25 March 2022
Corresponding author: X. T. Nguyen
Abstract
This study examined the discretization random field of the elastic modulus by a point method to develop a stochastic finite element method for the stochastic buckling of a non-uniform column. The formulation of stochastic analysis of a non-uniform column was constructed using the perturbation method in conjunction with the finite element method. The spectral representation was used to generate a random field to employ the Monte Carlo simulation for validation with a stochastic finite element approach. The results of the stochastic buckling problem of non-uniform columns with the random field of elastic modulus by comparing the first-order perturbation technique were in good agreement with those obtained from the Monte Carlo simulation. The numerical results showed that the response of the coefficient of variation of critical loads increased when the ratio of the correlation distance of the random field increased.
Keywords:
non-uniform column, buckling, stochastic FEM, spectral representation, random fieldDownloads
References
P. V. Phe and N. X. Huy, "A numerical study on the effect of adhesives on the behavior of gfrp-flexural strengthened wide flange steel beams," Transport and Communications Science Journal, vol. 71, no. 5, pp. 541–552, 2020.
Y. Almoosi, J. McConnell, and N. Oukaili, "Evaluation of the Variation in Dynamic Load Factor Throughout a Highly Skewed Steel I-Girder Bridge," Engineering, Technology & Applied Science Research, vol. 11, no. 3, pp. 7079–7087, Jun. 2021. DOI: https://doi.org/10.48084/etasr.4106
Y. Almoosi and N. Oukaili, "The Response of a Highly Skewed Steel I-Girder Bridge with Different Cross-Frame Connections," Engineering, Technology & Applied Science Research, vol. 11, no. 4, pp. 7349–7357, Aug. 2021. DOI: https://doi.org/10.48084/etasr.4137
P. C. Nguyen, "Nonlinear Inelastic Earthquake Analysis of 2D Steel Frames," Engineering, Technology & Applied Science Research, vol. 10, no. 6, pp. 6393–6398, Dec. 2020. DOI: https://doi.org/10.48084/etasr.3855
P. C. Nguyen, B. Le-Van, and S. D. T. V. Thanh, "Nonlinear Inelastic Analysis of 2D Steel Frames : An Improvement of the Plastic Hinge Method," Engineering, Technology & Applied Science Research, vol. 10, no. 4, pp. 5974–5978, Aug. 2020. DOI: https://doi.org/10.48084/etasr.3600
P. C. Nguyen, T. T. Tran, and T. Nghia Nguyen, "Nonlinear time-history earthquake analysis for steel frames," Heliyon, vol. 7, no. 8, Aug. 2021, Art. no. e06832. DOI: https://doi.org/10.1016/j.heliyon.2021.e06832
P. H. V. Nguyen and P. C. Nguyen, "Effects of Shaft Grouting on the Bearing Behavior of Barrette Piles: A Case Study in Ho Chi Minh City," Engineering, Technology & Applied Science Research, vol. 11, no. 5, pp. 7653–7657, Oct. 2021. DOI: https://doi.org/10.48084/etasr.4389
V. T. A. Ninh, "Fundamental frequencies of bidirectional functionally graded sandwich beams partially supported by foundation using different beam theories," Transport and Communications Science Journal, vol. 72, no. 4, pp. 452–467, 2021. DOI: https://doi.org/10.47869/tcsj.72.4.5
S. Timoshenko and J. M. Gere, Theory of elastic stability, 2nd ed. New York, NY, USA: McGraw-Hill, 1961.
Z. P. Bazant and L. Cedolin, Stability of Structures: Elastic, Inelastic, Fracture and Damage Theories. Singapore: World Scientific, 2010. DOI: https://doi.org/10.1142/7828
C. M. Wang and C. Y. Wang, Exact Solutions for Buckling of Structural Members. Boca Raton, FL, USA: CRC Press, 2004. DOI: https://doi.org/10.1201/9780203483534
L. T. Trinh and T. Binh, Stability of Structures. Hanoi, Vietnam: Science and Technics Publishing House, 2006.
M. Eisenberger, "Buckling loads for variable cross-section members with variable axial forces," International Journal of Solids and Structures, vol. 27, no. 2, pp. 135–143, Jan. 1991. DOI: https://doi.org/10.1016/0020-7683(91)90224-4
L. Marques, L. S. da Silva, and C. Rebelo, "Rayleigh-Ritz procedure for determination of the critical load of tapered columns," Steel and Composite Structures, vol. 16, no. 1, pp. 047–060, Jan. 2014. DOI: https://doi.org/10.12989/scs.2014.16.1.045
S. Y. Lee and Y. H. Kuo, "Elastic stability of non-uniform columns," Journal of Sound and Vibration, vol. 148, no. 1, pp. 11–24, Jul. 1991. DOI: https://doi.org/10.1016/0022-460X(91)90818-5
Q. S. Li, "Stability of non-uniform columns under the combined action of concentrated follower forces and variably distributed loads," Journal of Constructional Steel Research, vol. 64, no. 3, pp. 367–376, Mar. 2008. DOI: https://doi.org/10.1016/j.jcsr.2007.07.006
G. V. Sankaran and G. V. Rao, "Stability of tapered cantilever columns subjected to follower forces," Computers & Structures, vol. 6, no. 3, pp. 217–220, Jun. 1976. DOI: https://doi.org/10.1016/0045-7949(76)90033-X
S. K. Bifathima, "Bucking Analysis of a Cracked Stepped Column by using Finite Element Method," International Journal of Advance Research in Science and Engineering, vol. 4, no. 9, pp. 12–21, Sep. 2015.
P. C. Nguyen, D. D. Pham, T. T. Tran, and T. Nghia-Nguyen, "Modified Numerical Modeling of Axially Loaded Concrete-Filled Steel Circular-Tube Columns," Engineering, Technology & Applied Science Research, vol. 11, no. 3, pp. 7094–7099, Jun. 2021. DOI: https://doi.org/10.48084/etasr.4157
C. E. Brenner and C. Bucher, "A contribution to the SFE-based reliability assessment of nonlinear structures under dynamic loading," Probabilistic Engineering Mechanics, vol. 10, no. 4, pp. 265–273, Jan. 1995. DOI: https://doi.org/10.1016/0266-8920(95)00021-6
H. G. Matthies, C. E. Brenner, C. G. Bucher, and C. Guedes Soares, "Uncertainties in probabilistic numerical analysis of structures and solids-Stochastic finite elements," Structural Safety, vol. 19, no. 3, pp. 283–336, Jan. 1997. DOI: https://doi.org/10.1016/S0167-4730(97)00013-1
M. Kleiber and T. D. Hien, The Stochastic Finite Element Method: Basic Perturbation Technique and Computer Implementation, 1st edition. Chichester, UK: Wiley, 1993.
W. K. Liu, T. Belytschko, and A. Mani, "Random field finite elements," International Journal for Numerical Methods in Engineering, vol. 23, no. 10, pp. 1831–1845, 1986. DOI: https://doi.org/10.1002/nme.1620231004
E. Vanmarcke and M. Grigoriu, "Stochastic Finite Element Analysis of Simple Beams," Journal of Engineering Mechanics, vol. 109, no. 5, pp. 1203–1214, Oct. 1983. DOI: https://doi.org/10.1061/(ASCE)0733-9399(1983)109:5(1203)
T. D. Hien, "A Static Analysis of Nonuniform Column By Stochastic Finite Element Method Using Weighted Integration Approach," Transport and Communications Science Journal, vol. 71, no. 4, pp. 359–367, May 2020. DOI: https://doi.org/10.25073/tcsj.71.4.5
R. Ganesan and V. K. Kowda, "Buckling of Composite Beam-columns with Stochastic Properties," Journal of Reinforced Plastics and Composites, vol. 24, no. 5, pp. 513–543, Mar. 2005. DOI: https://doi.org/10.1177/0731684405045017
N. V. Thuan and T. D. Hien, "Stochastic Perturbation-Based Finite Element for Free Vibration of Functionally Graded Beams with an Uncertain Elastic Modulus," Mechanics of Composite Materials, vol. 56, no. 4, pp. 485–496, Sep. 2020. DOI: https://doi.org/10.1007/s11029-020-09897-z
M. A. Hariri-Ardebili, S. M. Seyed-Kolbadi, V. E. Saouma, J. Salamon, and B. Rajagopalan, "Random finite element method for the seismic analysis of gravity dams," Engineering Structures, vol. 171, pp. 405–420, Sep. 2018. DOI: https://doi.org/10.1016/j.engstruct.2018.05.096
T.-T. Tran and D. Kim, "Uncertainty quantification for nonlinear seismic analysis of cabinet facility in nuclear power plants," Nuclear Engineering and Design, vol. 355, Dec. 2019, Art. no. 110309. DOI: https://doi.org/10.1016/j.nucengdes.2019.110309
T.-T. Tran, K. Salman, S.-R. Han, and D. Kim, "Probabilistic Models for Uncertainty Quantification of Soil Properties on Site Response Analysis," ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems, Part A: Civil Engineering, vol. 6, no. 3, Sep. 2020, Art. no. 04020030. DOI: https://doi.org/10.1061/AJRUA6.0001079
S. S. Rao, The finite element method in engineering, 4th ed. Amsterdam, Netherlands: Elsevier/Butterworth Heinemann, 2005. DOI: https://doi.org/10.1016/B978-075067828-5/50002-0
T. J. R. Hughes, The Finite Element Method: Linear Static and Dynamic Finite Element Analysis. New York, NY, USA: Dover Publications, 2012.
M. Shinozuka and G. Deodatis, "Simulation of Stochastic Processes by Spectral Representation," Applied Mechanics Reviews, vol. 44, no. 4, pp. 191–204, Apr. 1991. DOI: https://doi.org/10.1115/1.3119501
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