NURBS-based Isogeometric Analysis and Refined Plate Theory Application on a Functionally Graded Plate Subjected to Random Loads

Authors

  • Nguyen Trong Hiep University of Transport and Communications, Vietnam
  • Dao Sy Dan University of Transport and Communications, Vietnam
  • Nguyen Dang Diem University of Transport and Communications, Vietnam
  • Dao Ngoc Tien Hanoi Architectural University, Vietnam
Volume: 13 | Issue: 2 | Pages: 10243-10248 | April 2023 | https://doi.org/10.48084/etasr.5478

Abstract

In structural design standards, loads are often assumed to be random quantities to give load factors. This study deals with the Stochastic Isogeometric Analysis (SIGA) for a Functionally Graded Plate (FGP) subjected to random distribution loads. The spatial random variation of distribution loads is modeled as a homogeneous Gaussian random field in the plane of the functionally graded plate. The governing equation of the functional grade plate is derived using the NURBS-based isogeometric analysis and the refined plate theory. SIGA is developed based on standard NURBS-based isogeometric analysis in conjunction with the first-order perturbation expansions of random loads. This approach was verified with Monte Carlo simulation, and the numerical results showed the effect of random loads on the variation of displacements and stresses of the functionally graded plate.

Keywords:

SIGA, random loads, functionally graded plate, random field

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References

I. Shiota and Y. Miyamoto, Eds., Functionally Graded Materials 1996, 1st ed. Amsterdam, Netherlands: Elsevier Science, 1997.

M. Koizumi, "FGM activities in Japan," Composites Part B: Engineering, vol. 28, no. 1, pp. 1–4, Jan. 1997. DOI: https://doi.org/10.1016/S1359-8368(96)00016-9

Y. Miyamoto, W. A. Kaysser, B. H. Rabin, A. Kawasaki, and R. G. Ford, Eds., Functionally Graded Materials: Design, Processing and Applications, Boston, MA, USA: Springer, 1999. DOI: https://doi.org/10.1007/978-1-4615-5301-4

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

L. T. Ha and N. T. K. Khue, "Free Vibration of Functionally Graded Porous Nano Beams," Transport and Communications Science Journa, vol. 70, no. 2, pp. 95–103, Aug. 2019.

V. T. A. Ninh, "Fundamental Frequencies of Bidirectional Functionally Graded Sandwich Beams Partially Sorted by Foundation Using Different Beam Theories," Transport and Communications Science Journal, vol. 72, no. 4, pp. 452–467, May 2011. DOI: https://doi.org/10.47869/tcsj.72.4.5

K. Soncco, K. N. Betancourt, R. Arciniega, and J. N. Reddy, "Postbuckling analysis of nonlocal functionally graded beams," Latin American Journal of Solids and Structures, vol. 18, Oct. 2021. DOI: https://doi.org/10.1590/1679-78256699

J. K. Lee and B. K. Lee, "Coupled Flexural-Torsional Free Vibration of an Axially Functionally Graded Circular Curved Beam," Mechanics of Composite Materials, vol. 57, no. 6, pp. 833–846, Jan. 2022. DOI: https://doi.org/10.1007/s11029-022-10003-8

T. D. Hien and N. N. Lam, "Vibration of functionally graded plate resting on viscoelastic elastic foundation subjected to moving loads," IOP Conference Series: Earth and Environmental Science, vol. 143, no. 1, Dec. 2018, Art. no. 012024. DOI: https://doi.org/10.1088/1755-1315/143/1/012024

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. vol. 70, no. 2, pp. 122-31, 2019

Q.-H. Pham, P.-C. Nguyen, V. K. Tran, Q. X. Lieu, and T. T. Tran, "Modified nonlocal couple stress isogeometric approach for bending and free vibration analysis of functionally graded nanoplates," Engineering with Computers, Sep. 2022. DOI: https://doi.org/10.1007/s00366-022-01726-2

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

Y. Karmi, Y. Khadri, S. Tekili, A. Daouadji, and E. M. Daya, "Dynamic Analysis of Composite Sandwich Beams with a Frequency-Dependent Viscoelastic Core under the Action of a Moving Load," Mechanics of Composite Materials, vol. 56, no. 6, pp. 755–768, Jan. 2021. DOI: https://doi.org/10.1007/s11029-021-09921-w

M. Shitikova and A. Krusser, "Force Driven Vibrations of Nonlinear Plates on a Viscoelastic Winkler Foundation Under the Harmonic Moving Load," International Journal for Computational Civil and Structural Engineering, vol. 17, no. 4, pp. 161–180, Dec. 2021. DOI: https://doi.org/10.22337/2587-9618-2021-17-4-161-180

M. Rezaiee-Pajand, A. R. Masoodi, and A. Alepaighambar, "Lateral-Torsional Buckling of a Bidirectional Exponentially Graded Thin-Walled C-Shaped Beam," Mechanics of Composite Materials, vol. 58, no. 1, pp. 53–68, Mar. 2022. DOI: https://doi.org/10.1007/s11029-022-10011-8

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

J. D. S. Becho, M. Greco, and D. N. Maciel, "Shear contribution on viscoelastic behavior of beams modeled using plane frame elements with Reissner kinematics," Latin American Journal of Solids and Structures, vol. 19, Jan. 2022. DOI: https://doi.org/10.1590/1679-78256709

B. Mohammadzadeh, Y. J. Kang, S. Kim, M. M. Cabral-Pinto, and Z. D. Nejad, "Nonlinear dynamic investigation of plates: Considering seismic loads, strain rate, material, and geometrical nonlinearities," Structures, vol. 33, pp. 1967–1986, Oct. 2021. DOI: https://doi.org/10.1016/j.istruc.2021.04.069

A. W. de Q. R. Reis, R. B. Burgos, and M. F. F. de Oliveira, "Nonlinear Dynamic Analysis of Plates Subjected to Explosive Loads," Latin American Journal of Solids and Structures, vol. 19, Jan. 2022. DOI: https://doi.org/10.1590/1679-78256706

L. Zhang et al., "High-hardness polyurea coated steel plates subjected to combined loadings of shock wave and fragments," Latin American Journal of Solids and Structures, vol. 19, Mar. 2022. DOI: https://doi.org/10.1590/1679-78256882

A. Daşdemir, "A Modal Analysis of Forced Vibration of a Piezoelectric Plate with Initial Stress by the Finite-Element Simulation," Mechanics of Composite Materials, vol. 58, no. 1, pp. 69–80, Mar. 2022. DOI: https://doi.org/10.1007/s11029-022-10012-7

N. V. Thuan and T. D. Hien, "Variablility in Frequencies of Vehicle Vibration Anlysis with Muiltiple Randrom Variables," Transport and Communications Science Journal, vol. 72, no. 2, pp. 215–226, Feb. 2021. DOI: https://doi.org/10.47869/tcsj.72.2.7

A. Khvostov, S. Zhukov, S. Tropkin, and A. Chauskin, "Evaluation of the Reliability of Building Structures in Simulia Abaqus: Modeling of Stochastic Material Properties," International Journal for Computational Civil and Structural Engineering, vol. 17, no. 3, pp. 182–189, Sep. 2021. DOI: https://doi.org/10.22337/2587-9618-2021-17-3-182-189

K. Ribeiro, D. D. Loriggio, and M. de V. Real, "Reliability analysis of very slender columns subjected to creep," Latin American Journal of Solids and Structures, vol. 18, Oct. 2021. DOI: https://doi.org/10.1590/1679-78256569

D. T. Hang, X. T. Nguyen, and D. N. Tien, "Stochastic Buckling Analysis of Non-Uniform Columns Using Stochastic Finite Elements with Discretization Random Field by the Point Method," Engineering, Technology & Applied Science Research, vol. 12, no. 2, pp. 8458–8462, Apr. 2022. DOI: https://doi.org/10.48084/etasr.4819

N. T. Nguyen, H. D. Ta, T. N. Van, and T. N. Dao, "Stochastic finite element analysis of the free vibration of non-uniform beams with uncertain material," Journal of Materials and Engineering Structures «JMES», vol. 9, no. 1, pp. 29–37, Apr. 2022.

M. Talha and B. N. Singh, "Stochastic perturbation-based finite element for buckling statistics of FGM plates with uncertain material properties in thermal environments," Composite Structures, vol. 108, pp. 823–833, Feb. 2014. DOI: https://doi.org/10.1016/j.compstruct.2013.10.013

T. D. Hien, B. T. Thanh, N. N. Long, N. Van Thuan, and D. T. Hang, "Investigation Into The Response Variability of A Higher-Order Beam Resting on A Foundation Using A Stochastic Finite Element Method," in CIGOS 2019, Innovation for Sustainable Infrastructure, Singapore, 2020, pp. 117–122. DOI: https://doi.org/10.1007/978-981-15-0802-8_15

T. D. Hien, N. D. Hung, N. T. Kien, and H. C. Noh, "The variability of dynamic responses of beams resting on elastic foundation subjected to vehicle with random system parameters," Applied Mathematical Modelling, vol. 67, pp. 676–687, Mar. 2019. DOI: https://doi.org/10.1016/j.apm.2018.11.018

T. D. Hien, N. D. Diem, G. V. Tan, V. V. Hiep, N. V. Thuan, "Stochastic Higher-order Finite Element Model for the Free Vibration of a Continuous Beam resting on Elastic Support with Uncertain Elastic Modulus", Engineering, Technology & Applied Science Research, vol. 13, no. 1, pp. 985-9990, 2023. DOI: https://doi.org/10.48084/etasr.5456

H. C. Noh, "A formulation for stochastic finite element analysis of plate structures with uncertain Poisson’s ratio," Computer Methods in Applied Mechanics and Engineering, vol. 193, no. 45, pp. 4857–4873, Nov. 2004. DOI: https://doi.org/10.1016/j.cma.2004.05.007

K. Li, W. Gao, D. Wu, C. Song, and T. Chen, "Spectral stochastic isogeometric analysis of linear elasticity," Computer Methods in Applied Mechanics and Engineering, vol. 332, pp. 157–190, Apr. 2018. DOI: https://doi.org/10.1016/j.cma.2017.12.012

S. Rahman, "A Galerkin isogeometric method for Karhunen–Loève approximation of random fields," Computer Methods in Applied Mechanics and Engineering, vol. 338, pp. 533–561, Aug. 2018. DOI: https://doi.org/10.1016/j.cma.2018.04.026

T. D. Hien and H. C. Noh, "Stochastic isogeometric analysis of free vibration of functionally graded plates considering material randomness," Computer Methods in Applied Mechanics and Engineering, vol. 318, pp. 845–863, May 2017. DOI: https://doi.org/10.1016/j.cma.2017.02.007

H. D. Ta and P.-C. Nguyen, "Perturbation based stochastic isogeometric analysis for bending of functionally graded plates with the randomness of elastic modulus," Latin American Journal of Solids and Structures, vol. 17, Sep. 2020. DOI: https://doi.org/10.1590/1679-78256066

L. Piegl and W. Tiller, The NURBS Book. Springer, 1996. DOI: https://doi.org/10.1007/978-3-642-97385-7

J. A. Cottrell, T. J. R. Hughes, and Y. Bazilevs, Isogeometric Analysis: Toward Integration of CAD and FEA. Chichester, UK: John Wiley & Sons, 2009. DOI: https://doi.org/10.1002/9780470749081

R. P. Shimpi and H. G. Patel, "A two variable refined plate theory for orthotropic plate analysis," International Journal of Solids and Structures, vol. 43, no. 22, pp. 6783–6799, Nov. 2006. DOI: https://doi.org/10.1016/j.ijsolstr.2006.02.007

T. D. Hien and N. N. Lam, "Investigation into the Effect Of Random Load on the Variability of Response of Plate by Using a Monte Carlo Simulation," International Journal of Civil Engineering and Technology, vol. 7, no. 5, pp. 169–176, Sep. 2016.

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

S. Benyoucef, I. Mechab, A. Tounsi, A. Fekrar, H. Ait Atmane, and E. A. Adda Bedia, "Bending of thick functionally graded plates resting on Winkler–Pasternak elastic foundations," Mechanics of Composite Materials, vol. 46, no. 4, pp. 425–434, Nov. 2010. DOI: https://doi.org/10.1007/s11029-010-9159-5

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[1]
Hiep, N.T., Dan, D.S., Diem, N.D. and Tien, D.N. 2023. NURBS-based Isogeometric Analysis and Refined Plate Theory Application on a Functionally Graded Plate Subjected to Random Loads. Engineering, Technology & Applied Science Research. 13, 2 (Apr. 2023), 10243–10248. DOI:https://doi.org/10.48084/etasr.5478.

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