A static analysis of nonuniform column by stochastic finite element method using weighted integration approach
Email:
tdhien@utc.edu.vn
Từ khóa:
Nonuniform column, weighed integration method, SFEM, random field
Tóm tắt
In general, the fluctuation of the elastic modulus of materials is crucial in structural analysis. This paper develops a stochastic finite element method (SFEM) for analyzing a nonuniform column considering the random process in elastic modulus. This random process of elastic modulus is assumed as a one-dimensional Gaussian random field. The weighted integration method is used to discretize the random field and establish the stochastic finite element formulation to compute the first and second moments of displacement fields. The results of the proposed approach are validated with those of the previous study. The response variability of displacement of column and effect of the parameter of the random field is investigated in detail.Tài liệu tham khảo
Communications Science Journal, 70(2019) 95-103. https://doi.org/10.25073/tcsj.70.2.2
[2]. P. M. Phuc, Analysis free vibration of the functionally grade material cracked plates with varying thickness using the phase-field theory, Transport and Communications Science Journal, 70 (2019) 122-31. https://doi.org/10.25073/tcsj.70.2.5
[3]. G Stefanou, The stochastic finite element method: Past, present and future, Computer Methods in Applied Mechanics and Engineering, 198(2009) 1031-51. http://dx.doi.org/10.1016/j.cma.2008.11.007
[4]. W. K. Liu, T. Belytschko, A.Mani, Random field finite elements, International Journal for Numerical Methods in Engineering, 23(1986) 1831-45. http://dx.doi.org/10.1002/nme.1620231004
[5]. M. Kleiber, T. D. Hien, The stochastic finite element method : basic perturbation technique and computer implementation: Wiley, 1992. https://onlinelibrary.wiley.com/doi/abs/10.1002/asm.3150100412
[6]. M. Kaminski, The Stochastic Perturbation Method for Computational Mechanics: WIKEY, 2013. https://www.wiley.com/en-us/The+Stochastic+Perturbation+Method+for+Computational+Mechanics-p-9780470770825
[7]. R. G. Ghanem, P.D.Spanos, Spectral stochastic finite-element formulation for reliability-analysis, Journal of Engineering Mechanics-Asce, 117 (1991) 2351-72. https://doi.org/10.1061/(ASCE)0733-9399(1991)117:10(2351)
[8]. H. G. Matthies, C. E. Brenner, C. G. Bucher, Guedes Soares C. Uncertainties in probabilistic numerical analysis of structures and solids-Stochastic finite elements, Structural Safety, 19 (1997) 283-336. http://dx.doi.org/10.1016/S0167-4730(97)00013-1
[9]. A. D. Kiureghian, P. L. Liu, Structural Reliability under Incomplete Probability Information, Journal of Engineering Mechanics, 112 (1986) 85-104. https://doi.org/10.1061/(ASCE)0733-9399(1986)112:1(85)
[10]. E. Vanmarcke, M. Grigoriu, Stochastic Finite Element Analysis of Simple Beams, Journal of Engineering Mechanics, 109 (1983) 1203-14. https://doi.org/10.1061/(ASCE)0733-9399(1983)109:5(1203)
[11]. H-C.Noh, T. Park, Response variability of laminate composite plates due to spatially random material parameter, Computer Methods in Applied Mechanics and Engineering, 200 (2011) 2397-406. http://dx.doi.org/10.1016/j.cma.2011.03.020
[12]. H-C Noh, Stochastic finite element analysis of composite plates considering spatial randomness of material properties and their correlations, Steel and Composite Structures, 11 (2011) 115-30. https://doi.org/10.12989/scs.2011.11.2.115
[13]. H.C. Noh, Effect of multiple uncertain material properties on the response variability of in-plane and plate structures, Computer Methods in Applied Mechanics and Engineering, 195 (2006) 2697-718. https://doi.org/10.1016/j.cma.2005.06.026
[14]. T. D. Hien, N. D. Hung, N. T. Kien, H. C. Noh, The variability of dynamic responses of beams resting on elastic foundation subjected to vehicle with random system parameters, Applied Mathematical Modelling, 67 (2019) 676-87. https://doi.org/10.1016/j.apm.2018.11.018
[15]. S. Kitipornchai, J. Yang, K. M. Liew, Random vibration of the functionally graded laminates in thermal environments, Computer Methods in Applied Mechanics and Engineering, 195 (2006) 1075-95. http://dx.doi.org/10.1016/j.cma.2005.01.016
[16]. S. Rahman, B. N. Rao, A perturbation method for stochastic meshless analysis in elastostatics, International Journal for Numerical Methods in Engineering, 50(2001) 1969-1991. https://doi.org/10.1002/nme.106
[17]. H. X. Nguyen, T. Duy Hien, J. Lee, H. Nguyen-Xuan, Stochastic buckling behaviour of laminated composite structures with uncertain material properties, Aerospace Science and Technology, 66 (2017) 274-83. https://doi.org/10.1016/j.ast.2017.01.028
[18]. T. D. Hien, B. T. Thanh, N.T. Quynh Giang, Uncertainty qualification for the free vibration of a functionally graded material plate with uncertain mass density, IOP Conference Series: Earth and Environmental Science, 143(2018) 012021. http://dx.doi.org/10.1088/1755-1315/143/1/012021
[19]. C. Ding, X. Hu, X.Cui, G. Li, Y. Cai, K.K.Tamma, Isogeometric generalized n th order perturbation-based stochastic method for exact geometric modeling of (composite) structures: Static and dynamic analysis with random material parameters, Computer Methods in Applied Mechanics and Engineering, 346(2019) 1002-1024. https://doi.org/10.1016/j.cma.2018.09.032
[20]. T. De Larrard, J. B. Colliat, F. Benboudjema, J. M. Torrenti, G. Nahas, Effect of the Young modulus variability on the mechanical behaviour of a nuclear containment vessel, N
[2]. P. M. Phuc, Analysis free vibration of the functionally grade material cracked plates with varying thickness using the phase-field theory, Transport and Communications Science Journal, 70 (2019) 122-31. https://doi.org/10.25073/tcsj.70.2.5
[3]. G Stefanou, The stochastic finite element method: Past, present and future, Computer Methods in Applied Mechanics and Engineering, 198(2009) 1031-51. http://dx.doi.org/10.1016/j.cma.2008.11.007
[4]. W. K. Liu, T. Belytschko, A.Mani, Random field finite elements, International Journal for Numerical Methods in Engineering, 23(1986) 1831-45. http://dx.doi.org/10.1002/nme.1620231004
[5]. M. Kleiber, T. D. Hien, The stochastic finite element method : basic perturbation technique and computer implementation: Wiley, 1992. https://onlinelibrary.wiley.com/doi/abs/10.1002/asm.3150100412
[6]. M. Kaminski, The Stochastic Perturbation Method for Computational Mechanics: WIKEY, 2013. https://www.wiley.com/en-us/The+Stochastic+Perturbation+Method+for+Computational+Mechanics-p-9780470770825
[7]. R. G. Ghanem, P.D.Spanos, Spectral stochastic finite-element formulation for reliability-analysis, Journal of Engineering Mechanics-Asce, 117 (1991) 2351-72. https://doi.org/10.1061/(ASCE)0733-9399(1991)117:10(2351)
[8]. H. G. Matthies, C. E. Brenner, C. G. Bucher, Guedes Soares C. Uncertainties in probabilistic numerical analysis of structures and solids-Stochastic finite elements, Structural Safety, 19 (1997) 283-336. http://dx.doi.org/10.1016/S0167-4730(97)00013-1
[9]. A. D. Kiureghian, P. L. Liu, Structural Reliability under Incomplete Probability Information, Journal of Engineering Mechanics, 112 (1986) 85-104. https://doi.org/10.1061/(ASCE)0733-9399(1986)112:1(85)
[10]. E. Vanmarcke, M. Grigoriu, Stochastic Finite Element Analysis of Simple Beams, Journal of Engineering Mechanics, 109 (1983) 1203-14. https://doi.org/10.1061/(ASCE)0733-9399(1983)109:5(1203)
[11]. H-C.Noh, T. Park, Response variability of laminate composite plates due to spatially random material parameter, Computer Methods in Applied Mechanics and Engineering, 200 (2011) 2397-406. http://dx.doi.org/10.1016/j.cma.2011.03.020
[12]. H-C Noh, Stochastic finite element analysis of composite plates considering spatial randomness of material properties and their correlations, Steel and Composite Structures, 11 (2011) 115-30. https://doi.org/10.12989/scs.2011.11.2.115
[13]. H.C. Noh, Effect of multiple uncertain material properties on the response variability of in-plane and plate structures, Computer Methods in Applied Mechanics and Engineering, 195 (2006) 2697-718. https://doi.org/10.1016/j.cma.2005.06.026
[14]. T. D. Hien, N. D. Hung, N. T. Kien, H. C. Noh, The variability of dynamic responses of beams resting on elastic foundation subjected to vehicle with random system parameters, Applied Mathematical Modelling, 67 (2019) 676-87. https://doi.org/10.1016/j.apm.2018.11.018
[15]. S. Kitipornchai, J. Yang, K. M. Liew, Random vibration of the functionally graded laminates in thermal environments, Computer Methods in Applied Mechanics and Engineering, 195 (2006) 1075-95. http://dx.doi.org/10.1016/j.cma.2005.01.016
[16]. S. Rahman, B. N. Rao, A perturbation method for stochastic meshless analysis in elastostatics, International Journal for Numerical Methods in Engineering, 50(2001) 1969-1991. https://doi.org/10.1002/nme.106
[17]. H. X. Nguyen, T. Duy Hien, J. Lee, H. Nguyen-Xuan, Stochastic buckling behaviour of laminated composite structures with uncertain material properties, Aerospace Science and Technology, 66 (2017) 274-83. https://doi.org/10.1016/j.ast.2017.01.028
[18]. T. D. Hien, B. T. Thanh, N.T. Quynh Giang, Uncertainty qualification for the free vibration of a functionally graded material plate with uncertain mass density, IOP Conference Series: Earth and Environmental Science, 143(2018) 012021. http://dx.doi.org/10.1088/1755-1315/143/1/012021
[19]. C. Ding, X. Hu, X.Cui, G. Li, Y. Cai, K.K.Tamma, Isogeometric generalized n th order perturbation-based stochastic method for exact geometric modeling of (composite) structures: Static and dynamic analysis with random material parameters, Computer Methods in Applied Mechanics and Engineering, 346(2019) 1002-1024. https://doi.org/10.1016/j.cma.2018.09.032
[20]. T. De Larrard, J. B. Colliat, F. Benboudjema, J. M. Torrenti, G. Nahas, Effect of the Young modulus variability on the mechanical behaviour of a nuclear containment vessel, N
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19/02/2020
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29/03/2020
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10/04/2020
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28/05/2020
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Kiểu trích dẫn
Ta Duy, H. (1590598800). A static analysis of nonuniform column by stochastic finite element method using weighted integration approach . Tạp Chí Khoa Học Giao Thông Vận Tải, 71(4), 359-367. https://doi.org/10.25073/tcsj.71.4.5
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