48
Views
0
CrossRef citations to date
0
Altmetric
Original Article

Multi-objective metaheuristic approach for analyzing static and dynamic behaviors of functionally graded Timoshenko beams

&
Received 12 Jul 2023, Accepted 18 Nov 2023, Published online: 28 Nov 2023

References

  • B. Saleh, J. Jiang, R. Fathi, T. Al-hababi, Q. Xu, L. Wang, D. Song, and A. Ma, 30 Years of functionally graded materials: an overview of manufacturing methods, applications and future challenges, Compos. B Eng., vol. 201, pp. 108376, 2020. DOI: 10.1016/j.compositesb.2020.108376.
  • S. Nikbakt, S. Kamarian, and M. Shakeri, A review on optimization of composite structures Part I: laminated composites, Compos. Struct., vol. 195, pp. 158–185, 2018. DOI: 10.1016/j.compstruct.2018.03.063.
  • S. Nikbakht, S. Kamarian, and M. Shakeri, A review on optimization of composite structures Part II: functionally graded materials, Compos. Struct., vol. 214, pp. 83–102, 2019. DOI: 10.1016/j.compstruct.2019.01.105.
  • A.S. Sayyad, and Y.M. Ghugal, Modeling and analysis of functionally graded sandwich beams: a review, Mech. Adv. Mater. Struct., vol. 26, no. 21, pp. 1776–1795, 2019. DOI: 10.1080/15376494.2018.1447178.
  • P.S. Ghatage, V.R. Kar, and P.E. Sudhagar, On the numerical modelling and analysis of multi-directional functionally graded composite structures: a review, Compos. Struct., vol. 236, pp. 111837, 2020. DOI: 10.1016/j.compstruct.2019.111837.
  • P. Zahedinejad, C. Zhang, H. Zhang, and S. Ju, A comprehensive review on vibration analysis of functionally graded beams, Int. J. Str. Stab. Dyn., vol. 20, no. 04, pp. 2030002, 2020. DOI: 10.1142/S0219455420300025.
  • X.-F. Li, A unified approach for analyzing static and dynamic behaviors of functionally graded Timoshenko and Euler–Bernoulli beams, J. Sound Vib., vol. 318, no. 4–5, pp. 1210–1229, 2008. DOI: 10.1016/j.jsv.2008.04.056.
  • S.-L. Sun, X.-Y. Zhang, and X.-F. Li, A consistent shear beam theory for free vibration of functionally graded beams based on physical neutral plane, Mech. Adv. Mater. Struct., vol. 0, pp. 1–11, 2023. DOI: 10.1080/15376494.2023.2185709.
  • S. Kamarian, M. Shakeri, M. Yas, M. Bodaghi, and A. Pourasghar, Free vibration analysis of functionally graded nanocomposite sandwich beams resting on Pasternak foundation by considering the agglomeration effect of CNTs, J. Sandw. Struct. Mater., vol. 17, no. 6, pp. 632–665, 2015. DOI: 10.1177/1099636215590280.
  • M.H. Yas, S. Kamarian, and A. Pourasghar, Free vibration analysis of functionally graded beams resting on variable elastic foundations using a generalized power-law distribution and GDQ method, Ann. Solid Struct. Mech., vol. 9, no. 1–2, pp. 1–11, 2017. DOI: 10.1007/s12356-017-0046-9.
  • S. Rajasekaran, and H. Bakhshi Khaniki, Finite element static and dynamic analysis of axially functionally graded nonuniform small-scale beams based on nonlocal strain gradient theory, Mech. Adv. Mater. Struct., vol. 26, no. 14, pp. 1245–1259, 2019. DOI: 10.1080/15376494.2018.1432797.
  • Z. Zhang, Y. Li, H. Wu, H. Zhang, H. Wu, S. Jiang, and G. Chai, Mechanical analysis of functionally graded graphene oxide-reinforced composite beams based on the first-order shear deformation theory, Mech. Adv. Mater. Struct., vol. 27, no. 1, pp. 3–11, 2020. DOI: 10.1080/15376494.2018.1444216.
  • X.-T. He, W.-M. Li, J.-Y. Sun, and Z.-X. Wang, An elasticity solution of functionally graded beams with different moduli in tension and compression, Mech. Adv. Mater. Struct., vol. 25, no. 2, pp. 143–154, 2018. DOI: 10.1080/15376494.2016.1255808.
  • A. Pourasghar, and Z. Chen, Nonlinear vibration and modal analysis of FG nanocomposite sandwich beams reinforced by aggregated CNTs, Polym. Eng. Sci., vol. 59, no. 7, pp. 1362–1370, 2019. DOI: 10.1002/pen.25119.
  • C.H. Thai, A.J.M. Ferreira, H. Nguyen-Xuan, and P. Phung-Van, A size dependent meshfree model for functionally graded plates based on the nonlocal strain gradient theory, Compos. Struct., vol. 272, pp. 114169, 2021. DOI: 10.1016/j.compstruct.2021.114169.
  • C.H. Thai, P.T. Hung, H. Nguyen-Xuan, and P. Phung-Van, A size-dependent meshfree approach for magneto-electro-elastic functionally graded nanoplates based on nonlocal strain gradient theory, Eng. Struct., vol. 292, pp. 116521, 2023. DOI: 10.1016/j.engstruct.2023.116521.
  • P.T. Hung, C.H. Thai, and P. Phung-Van, A C0-HSDT free vibration of magneto-electro-elastic functionally graded porous plates using a moving Kriging meshfree method, Aerosp. Sci. Technol., vol. 137, pp. 108266, 2023. DOI: 10.1016/j.ast.2023.108266.
  • A. Karamanli, Free vibration analysis of two directional functionally graded beams using a third order shear deformation theory, Compos. Struct., vol. 189, pp. 127–136, 2018. DOI: 10.1016/j.compstruct.2018.01.060.
  • F. Bourada, A.A. Bousahla, M. Bourada, A. Azzaz, A. Zinata, and A. Tounsi, Dynamic investigation of porous functionally graded beam using a sinusoidal shear deformation theory, Wind Struct., vol. 28, no. 1, pp. 019–030, 2019.
  • X.Y. Li, X.H. Wang, Y.Y. Chen, Y. Tan, and H.J. Cao, Bending, buckling and free vibration of an axially loaded timoshenko beam with transition parameter: direction of axial force, Int. J. Mech. Sci., vol. 176, pp. 105545, 2020. DOI: 10.1016/j.ijmecsci.2020.105545.
  • K. Magnucki, D. Witkowski, and J. Lewiński, Bending and free vibrations of beams with symmetrically varying mechanical properties—Shear effect, Mech. Adv. Mater. Struct., vol. 27, no. 4, pp. 325–332, 2020. DOI: 10.1080/15376494.2018.1472350.
  • P. Sharma, and R. Singh, A numerical study on free vibration analysis of axial FGM beam, Mater. Today Proc., vol. 44, pp. 1664–1668, 2021. DOI: 10.1016/j.matpr.2020.11.827.
  • I. Ahmadi, J. Sladek, and V. Sladek, Size dependent free vibration analysis of 2D-functionally graded curved nanobeam by meshless method, Mech. Adv. Mater. Struct., pp. 1–22, 2023. DOI: 10.1080/15376494.2023.2195400.
  • F. Rahmani, R. Kamgar, and R. Rahgozar, Analysis of metallic and functionally graded beams using isogeometric approach and Carrera Unified Formulation, Mech. Adv. Mater. Struct., vol. 30, no. 4, pp. 894–911, 2023. DOI: 10.1080/15376494.2022.2028042.
  • P. Phung-Van, and C.H. Thai, A novel size-dependent nonlocal strain gradient isogeometric model for functionally graded carbon nanotube-reinforced composite nanoplates, Eng. Comput., vol. 38, no. S3, pp. 2027–2040, 2022. DOI: 10.1007/s00366-021-01353-3.
  • P. Phung-Van, Q.X. Lieu, A.J.M. Ferreira, and C.H. Thai, A refined nonlocal isogeometric model for multilayer functionally graded graphene platelet-reinforced composite nanoplates, Thin-Walled Struct., vol. 164, pp. 107862, 2021. DOI: 10.1016/j.tws.2021.107862.
  • F.W. Glover, and G.A. Kochenberger, Handbook of Metaheuristics, Vol. 57, Springer Science & Business Media, Berlin, Germany, 2006.
  • I.H. Osman, and G. Laporte, Metaheuristics: a bibliography, Ann Oper Res., vol. 63, no. 5, pp. 511–623, 1996. DOI: 10.1007/BF02125421.
  • X.-S. Yang, Engineering Optimization: An Introduction with Metaheuristic Applications, John Wiley, Hoboken, NJ, 2010.
  • X.-S. Yang, Nature-Inspired Metaheuristic Algorithms, 2nd ed., Luniver Press, Rome, 2010.
  • S. Kamarian, M.H. Yas, A. Pourasghar, and M. Daghagh, Application of firefly algorithm and ANFIS for optimisation of functionally graded beams, J. Exp. Theor. Artif. Intell., vol. 26, no. 2, pp. 197–209, 2014. DOI: 10.1080/0952813X.2013.813978.
  • M.H. Yas, S. Kamarian, and A. Pourasghar, Application of imperialist competitive algorithm and neural networks to optimise the volume fraction of three-parameter functionally graded beams, J. Exp. Theor. Artif. Intell., vol. 26, no. 1, pp. 1–12, 2014. DOI: 10.1080/0952813X.2013.782346.
  • C.M.C. Roque, and P.A.L.S. Martins, Differential evolution for optimization of functionally graded beams, Compos. Struct., vol. 133, pp. 1191–1197, 2015. DOI: 10.1016/j.compstruct.2015.08.041.
  • C.M.C. Roque, P.A.L.S. Martins, A.J.M. Ferreira, and R.M.N. Jorge, Differential evolution for free vibration optimization of functionally graded nano beams, Compos. Struct., vol. 156, pp. 29–34, 2016. DOI: 10.1016/j.compstruct.2016.03.052.
  • P.H. Anh, and T.T. Duong, Weight optimisation of functionally graded beams using modified differential evolution, STCE, vol. 13, no. 2, pp. 48–63, 2019. DOI: 10.31814/stce.nuce201905.
  • M.-X. He, and J.-Q. Sun, Multi-objective structural-acoustic optimization of beams made of functionally graded materials, Compos. Struct., vol. 185, pp. 221–228, 2018. DOI: 10.1016/j.compstruct.2017.11.004.
  • P. Phung-Van, A.J.M. Ferreira, and C.H. Thai, Computational optimization for porosity-dependent isogeometric analysis of functionally graded sandwich nanoplates, Compos. Struct., vol. 239, pp. 112029, 2020. DOI: 10.1016/j.compstruct.2020.112029.
  • P. Phung-Van, C.H. Thai, M. Abdel-Wahab, and H. Nguyen-Xuan, Optimal design of FG sandwich nanoplates using size-dependent isogeometric analysis, Mech. Mater., vol. 142, pp. 103277, 2020. DOI: 10.1016/j.mechmat.2019.103277.
  • H.M. Abo-Bakr, R.M. Abo-Bakr, S.A. Mohamed, and M.A. Eltaher, Multi-objective shape optimization for axially functionally graded microbeams, Compos. Struct., vol. 258, pp. 113370, 2021. DOI: 10.1016/j.compstruct.2020.113370.
  • C.-P. Wu, and K.-W. Li, Multi-objective optimization of functionally graded beams using a genetic algorithm with non-dominated sorting, J. Compos. Sci., vol. 5, no. 4, pp. 92, 2021. DOI: 10.3390/jcs5040092.
  • F. Rahmani, R. Kamgar, and R. Rahgozar, Optimum material distribution of porous functionally graded plates using Carrera unified formulation based on isogeometric analysis, Mech. Adv. Mater. Struct., vol. 29, no. 20, pp. 2927–2941, 2022. DOI: 10.1080/15376494.2021.1881845.
  • E. Viola, and F. Tornabene, Free vibrations of three parameter functionally graded parabolic panels of revolution, Mech. Res. Commun., vol. 36, no. 5, pp. 587–594, 2009. DOI: 10.1016/j.mechrescom.2009.02.001.
  • H. Eskandar, A. Sadollah, A. Bahreininejad, and M. Hamdi, Water cycle algorithm – A novel metaheuristic optimization method for solving constrained engineering optimization problems, Comput. Struct., vol. 110–111, pp. 151–166, 2012. DOI: 10.1016/j.compstruc.2012.07.010.
  • A. Sadollah, H. Eskandar, and J.H. Kim, Water cycle algorithm for solving constrained multi-objective optimization problems, Appl. Soft Comput., vol. 27, pp. 279–298, 2015. DOI: 10.1016/j.asoc.2014.10.042.
  • A. Sadollah, H. Eskandar, A. Bahreininejad, and J.H. Kim, Water cycle algorithm with evaporation rate for solving constrained and unconstrained optimization problems, Appl. Soft Comput., vol. 30, pp. 58–71, 2015. DOI: 10.1016/j.asoc.2015.01.050.
  • S.S. Haroon, and T.N. Malik, Evaporation rate-based water cycle algorithm for short-term hydrothermal scheduling, Arab. J. Sci. Eng., vol. 42, no. 7, pp. 2615–2630, 2017. DOI: 10.1007/s13369-016-2262-8.
  • N. Ghaffarzadeh, Water cycle algorithm based power system stabilizer robust design for power systems, J. Electr. Eng., vol. 66, no. 2, pp. 91–96, 2015. DOI: 10.1515/jee-2015-0014.
  • J. Bahl, and B. Muralidharan, Optimization of a hybrid phase-change memory cell using the water cycle algorithm, J. Comput. Electron., vol. 18, no. 4, pp. 1192–1200, 2019. DOI: 10.1007/s10825-019-01384-6.
  • H.M. Hasanien, Transient stability augmentation of a wave energy conversion system using a water cycle algorithm-based multiobjective optimal control strategy, IEEE Trans. Ind. Inf., vol. 15, no. 6, pp. 3411–3419, 2019. DOI: 10.1109/TII.2018.2871098.
  • A. Sadollah, H. Sayyaadi, and A. Yadav, A dynamic metaheuristic optimization model inspired by biological nervous systems: neural network algorithm, Appl. Soft Comput., vol. 71, pp. 747–782, 2018. DOI: 10.1016/j.asoc.2018.07.039.
  • J.S. Chohan, N. Mittal, R. Kumar, S. Singh, S. Sharma, J. Singh, K.V. Rao, M. Mia, D.Y. Pimenov, and S.P. Dwivedi, Mechanical strength enhancement of 3D printed acrylonitrile butadiene styrene polymer components using neural network optimization algorithm, Polymers, vol. 12, no. 10, pp. 2250, 2020. DOI: 10.3390/polym12102250.
  • M.S. AbouOmar, H.-J. Zhang, and Y.-X. Su, Fractional order fuzzy PID control of automotive PEM fuel cell air feed system using neural network optimization algorithm, Energies, vol. 12, no. 8, pp. 1435, 2019. DOI: 10.3390/en12081435.
  • M. Fawzi, A.A. El-Fergany, and H.M. Hasanien, Effective methodology based on neural network optimizer for extracting model parameters of PEM fuel cells, Int. J. Energy Res., vol. 43, no. 14, pp. 8136–8147, 2019. DOI: 10.1002/er.4809.
  • Y. Zhang, Z. Jin, and Y. Chen, Hybrid teaching–learning-based optimization and neural network algorithm for engineering design optimization problems, Knowl. Based Syst., vol. 187, pp. 104836, 2020. DOI: 10.1016/j.knosys.2019.07.007.
  • Y. Zhang, Z. Jin, and Y. Chen, Hybridizing grey wolf optimization with neural network algorithm for global numerical optimization problems, Neural Comput. Appl., vol. 32, no. 14, pp. 10451–10470, 2020. DOI: 10.1007/s00521-019-04580-4.
  • K. Deb, A. Pratap, S. Agarwal, and T. Meyarivan, A fast and elitist multiobjective genetic algorithm: NSGA-II, IEEE Trans. Evol. Computat., vol. 6, no. 2, pp. 182–197, 2002. DOI: 10.1109/4235.996017.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.