Advances in nano research

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On application of machine learning techniques for predicting the bending and buckling behavior of FGM nanobeams

  • Aman Garg (State Key Laboratory of Intelligent Manufacturing Equipment and Technology, School of Mechanical Science and Engineering, Huazhong University of Science and Technology) ;
  • Mohamed-Ouejdi Belarbi (Laboratoire de Recherche en Genie Civil, LRGC, Universite de Biskra) ;
  • Li Li (State Key Laboratory of Intelligent Manufacturing Equipment and Technology, School of Mechanical Science and Engineering, Huazhong University of Science and Technology) ;
  • Abdelouahed Tounsi (Department of Civil and Environmental Engineering, King Fahd University of Petroleum &Minerals)
  • Received : 2022.03.14
  • Accepted : 2024.10.15
  • Published : 2024.11.25
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Abstract

The present article aims to carry out a comparative study between various machine learning based algorithms, which can predict the bending and buckling behavior of functionally graded (FG) nanobeams accurately. The algorithm has been developed in the framework of two regression machine learning models namely, Gaussian Process Regression (GPR), and Random Forest (RF). Geometric and material properties are taken as the variables including length-to-thickness ratio, power-law index, and nonlocal parameter. For having random non-biased input dataset, the Sobol sequence has been used. Using these values, maximum deflections and critical buckling loads are obtained. These values along with the corresponding input variables, surrogate models were formulated. It has been observed that the GPR model is able to predict the behavior of FG nanobeams more accurately as compared to the behavior predicted by RF surrogate model even for an unseen dataset.

Keywords

Acknowledgement

This work is partially supported by the Innovation-Driven Development Special Fund Project of Guangxi (Grant No. Guike AA23062040), the Key Research and Development Program of Guangxi (Grant No. Guike AB23026106), the National Natural Science Foundation of China (Grant No. 52175095), the Science and Technology Planning Project of Liuzhou (Grant Nos. 2022AAA0102, and 2022AAA0104), and the Young Top-notch Talent Cultivation Program of Hubei Province of China.

References

  1. Amine, Z., Houari, M.S.A., Bousahla, A.A. and Tounsi, A. (2015), "A mechanical response of functionally graded nanoscale beam: an assessment of a refined nonlocal shear deformation theory beam theory", Struct. Eng. Mech., 54(4), 693-710. https://doi.org/10.12989/sem.2015.54.4.693.
  2. Ates, B., Koytepe, S., Ulu, A., Gurses, C. and Thakur, V.K. (2020), "Chemistry, structures, and advanced applications of nanocomposites from biorenewable resources", Chem. Rev., 120(17), 9304-9362. https://doi.org/10.1021/acs.chemrev.9b00553.
  3. Azandariani, M.G., Gholami, M. and Nikzad, A. (2022), "Eringen's nonlocal theory for non-linear bending analysis of BGF Timoshenko nanobeams", Adv. Nano Res., 12(1), 37-47. https://doi.org/10.12989/anr.2022.12.1.037.
  4. Banh, T.T., Luu, N.G., Lieu, Q.X., Lee, J., Kang, J. and Lee, D. (2021), "Multiple bi-directional FGMs topology optimization approach with a preconditioned conjugate gradient multigrid", Steel Compos. Struct., 41(3), 382-402. https://doi.org/10.12989/scs.2021.41.3.385.
  5. Barretta, R., Fabbrocino, F., Luciano, R., and deSciarra F.M. (2018), "Closed-form solutions in stress-driven two-phase integral elasticity for bending of functionally graded nanobeams", Physica E, 97, 13-30. https://doi.org/10.1016/j.physe.2017.09.026.
  6. Belarbi, M.O., Houari, M.S.A., Daikh, A.A., Garg, A., Merzouki T., Chalak, H.D. and Hirane, H. (2021), "Nonlocal finite element model for the bending and buckling analysis of functionally graded nanobeams using a novel shear deformation theory", Compos. Struct., 264, 113712. https://doi.org/10.1016/j.compstruct.2021.113712.
  7. Belarbi, M.O., Li, L., Houari, M.S.A., Garg, A., Chalak, H.D., Dimitri, R. and Tornabene, F. (2022), "Nonlocal vibration of functionally graded nanoplates using a layerwise theory", Math. Mech. Solids, 27(12), 2634-2661. https://doi.org/10.1177/10812865221078571.
  8. Belarbi, M.-O., Khechai, A., Houari, M.S.A., Bessaim, A., Hirane, H. and Garg, A. (2024), "Free vibration behavior of sandwich FGM beams: Parametric and uncertainty analysis", J. Vib. Eng. Technol., 1-23. https://doi.org/10.1007/s42417-024-01452-7.
  9. Benahmed, A., Fahsi, B., Zidour, M., Bourada, F. and Tounsi, A. (2019), "Critical buckling of functionally graded nanoscale beam with porosities using nonlocal higher-order shear deformation", Struct. Eng. Mech., 69(4), 457-466. https://doi.org/10.12989/SEM.2019.69.4.457.
  10. Bouhadra, A., Menasira, A. and Rachedi, M.A. (2021), "Boundary conditions effect for buckling analysis of porous functionally graded nanobeam", Adv. Nano Res., 10(4), 2021, 313-325. https://doi.org/10.12989/anr.2021.10.4.313.
  11. Chaht, F.L., Kaci, A., Houari, M.S.A., Tounsi, A. and Beg, O.A. (2015), "Bending and buckling analyses of functionally graded material (FGM) size-dependent nanoscale beams including the thickness stretching effect", Steel Compos. Struct., 18(2), 425-442. https://doi.org/10.12989/scs.2015.18.2.425.
  12. Ebrahimi, F. and Barati, M.R. (2016a), "An exact solution for buckling analysis of embedded piezo- electro- magnetically actuated nanoscale beams", Adv. Nano Res., 4(2), 65-84. https://doi.org/10.12989/anr.2016.4.2.065.
  13. Ebrahimi, F. and Barati, M.R. (2016b), "Thermal buckling analysis of size-dependent FG nanobeams based on the third-order shear deformation beam theory", Acta Mech. Solida Sin., 29, 547-554. https://doi.org/10.1016/S0894-9166(16)30272-5.
  14. Ebrahimi, F. and Barati, M.R. (2017), "A nonlocal strain gradient refined beam model for buckling analysis of size-dependent shear-deformable curved FG nanobeams", Compos. Struct., 159, 174-182. https://doi.org/10.1016/j.compstruct.2016.09.058.
  15. Ebrahimi, F., Ali, J. and Rajendran, S. (2020), "Thermal buckling analysis of magneto-electro-elastic porous FG beam in thermal environment", Adv. Nano Res., 8(1), 83-94. https://doi.org/10.12989/ANR.2020.8.1.083.
  16. Ebrahimi, T., Nejad, M.Z., Jahankohan, H. and Hadi, A. (2021), "Thermoelastoplastic response of FGM linearly hardening rotating thick cylindrical pressure vessels", Steel Compos. Struct., 38(2), 189-211. https://doi.org/10.12989/scs.2021.38.2.189.
  17. Eltaher, M.A., Khater, M.E. and Emam, S.A. (2016), "A review on nonlocal elastic models for bending, buckling, vibrations, and wave propagation of nanoscale beams", Appl. Math. Model. 40, 4109-4128. https://doi.org/10.1016/j.apm.2015.11.026.
  18. Ehyaei, J., Ebrahimi, F. and Salari, E. (2016), "Nonlocal vibration analysis of FG nano beams with different boundary conditions", Adv. Nano Res., 4(2), 85-111. https://doi.org/10.12989/anr.2016.4.2.085.
  19. El-sherbiny, Sh.G., Wageh, S., Elhalafawy, S.M. and Sharshar, A.A. (2013), "Carbon nanotube antennas analysis and applications: review", Adv. Nano Res., 1(1), 13-27. https://doi.org/10.12989/anr.2013.1.1.013.
  20. Eringen, A.C. (1983), "On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves", J. Appl. Phys., 54(9), 4703-4710. https://doi.org/10.1063/1.332803.
  21. Garg, A. and Chalak, H.D. (2019), "A review on analysis of laminated composite and sandwich structures under hygrothermal conditions", Thin-Walled Struct., 142, 205-226. https://doi.org/10.1016/j.tws.2019.05.005.
  22. Garg, A., Belarbi, M.O., Chalak, H.D. and Chakrabarti A. (2021a), "A review of the analysis of sandwich FGM structures", Compos. Struct., 258, 113427. https://doi.org/10.1016/j.compstruct.2020.113427.
  23. Garg, A., Chalak, H.D., Zenkour, A.M., Belarbi, M.O. and Houari M.S.A. (2021b), "A review of available theories and methodologies for the analysis of nano isotropic, nano functionally graded, and CNT reinforced nanocomposite structures", Arch. Comput. Methods Eng., 1-34. https://doi.org/10.1007/s11831-021-09652-0.
  24. Garg, A., Chalak, H.D., Belarbi M.O., Chakrabarti, A. and Houari, M.S.A. (2021c), "Finite element-based free vibration analysis of power-law, exponential and sigmoidal functionally graded sandwich beams", J. Inst. Eng. C, 102, 1167-1201. https://doi.org/10.1007/s40032-021-00740-5.
  25. Garg, A., Belarbi, M.O., Tounsi, A., Li, L., Singh, A. and Mukhopadhyay, T. (2022), "Predicting elemental stiffness matrix of FG nanoplates using Gaussian Process Regression based surrogate model in framework of layerwise model", Eng. Anal. Bound. Elem., 143, 779-795. https://doi.org/10.1016/j.enganabound.2022.08.001.
  26. Garg, A., Shukla, N.K., Raja, M.R., Chalak, H.D., Belarbi, M.O., Tounsi, A., Li, L. and Zenkour, A.M. (2023a), "Finite element based free vibration analysis of sandwich FGM plates under hygro-thermal conditions using zigzag theory", Steel Compos. Struct., 49(5), 547-570. https://doi.org/10.12989/scs.2023.49.5.547.
  27. Garg, A., Mukhopadhyay, T, Belarbi, M.O. and Li, L. (2023b), "Random forest-based surrogates for transforming the behavioral predictions of laminated composite plates and shells from FSDT to Elasticity solutions", Compos. Struct., 309, 116756. https://doi.org/10.1016/j.compstruct.2023.116756.
  28. Garg, A., Mukhopadhyay, T, Belarbi, M.-O., Chalak, H.D., Singh, A. and Zenkour, A.M. (2023c), "On accurately capturing the through-thickness variation of transverse shear and normal stresses for composite beams using FSDT coupled with GPR", Compos. Struct., 305, 116551. https://doi.org/10.1016/j.compstruct.2022.116551.
  29. Garg, A., Shukla, N.K., Belarbi, M.-O., Barnawi, A.B., Raman, R., Sharma, A. and Li, L. (2024a), "Free vibration analysis of bio-inspired helicoidal laminated composite square and annular plates having circular openings using isogeometric analysis", Structure, 69, 107429. https://doi.org/10.1016/j.istruc.2024.107429.
  30. Garg, A., Sabherwal, P., Shukla, N.K., Li, L., Raja, M.R., Sharma, A., Raman, R. and Chalak, H.D. (2024b), "Free vibration analysis of laminated composite and sandwich shells using wavelet finite element method", Mech. Adv. Mater. Struct., 1-9. https://doi.org/10.1080/15376494.2024.2380090.
  31. Garg, A., Li, L. and Sharma, A. (2024c), "Free vibration analysis of bio-inspired double- and cross-helicoidal laminated composite plates", Mech. Based Des. Struct., 1-17. https://doi.org/10.1080/15397734.2024.2357755.
  32. Garg, A., Sharma, A., Zheng, W. and Li, L. (2024d), "Dactyl club and nacre-inspired impact resistant behavior of layered structures: A review of present trends and prospects", Mater. Today Commun., 41, 110553. https://doi.org/10.1016/j.mtcomm.2024.110553.
  33. Garg, A. and Li, L. (2024), "Data-driven uncertainty quantification and sensitivity studies in free vibration behavior of bio-inspired helicoidal laminated composite cylindrical shells", Mech. Adv. Mater. Struct., 1-16. https://doi.org/10.1080/15376494.2024.2355369.
  34. Ghayesh, M.H. and Farajpour, A. (2019), "A review on the mechanics of functionally graded nanoscale and microscale structures", Int. J. Eng. Sci. 137, 8-36. https://doi.org/10.1016/j.ijengsci.2018.12.001.
  35. Hadi, A., Nejad, M.Z., Rastgoo, A. and Hosseini, M. (2018), "Buckling analysis of FGM Euler-Bernoulli nano-beams with 3D-varying properties based on consistent couple-stress theory", Steel Compos. Struct., 26(6), 663-672. https://doi.org/10.12989/scs.2018.26.6.663.
  36. Hakima, M., Bousahla, A.A., Heireche, H., Bourada, F., Bedia, E.A.A, Tounsi, A., Mahmoud, S.R., Tounsi, A. and Benrahou, K.H. (2020), "Investigation on hygro-thermal vibration of P-FG and symmetric S-FG nanobeam using integral Timoshenko beam theory", Adv. Nano Res., 8(4), 293-305. https://doi.org/10.12989/anr.2020.8.4.293.
  37. Houari, M.S.A., Bessaim, A., Bernard, F., Tounsi, A. and Mahmoud, S.R. (2018), "Buckling analysis of new quasi-3D FG nanobeams based on nonlocal strain gradient elasticity theory and variable length scale parameter", Steel Compos. Struct., 28(1), 13-24. https://doi.org/10.12989/SCS.2018.28.1.013.
  38. Huang, X., Chang, L., Zhao, H. and Cai, Z. (2022), "Study on craniocerebral dynamics response and helmet protective performance under the blast waves", Mater. Des., 224, 111408. https://doi.org/10.1016/j.matdes.2022.111408.
  39. Li, J., Wang, Z., Zhang, S., Lin, Y., Wang, L., Sun, C. and Tan, J. (2023), "A novelty mandrel supported thin-wall tube bending cross-section quality analysis: a diameter-adjustable multi-point contact mandrel", Int. J. Adv. Manuf. Technol., 124, 4615-4637. https://doi.org/10.1007/s00170-023-10838-y.
  40. Li, L. and Hu, Y. (2016), "Nonlinear bending and free vibration analyses of nonlocal strain gradient beams made of functionally graded material", Int. J. Eng. Sci., 107, 77-97. https://doi.org/10.1016/j.ijengsci.2016.07.011.
  41. Li, F., Chen, J., Zhou, L. and Kujala, P. (2024), "Investigation of ice wedge bearing capacity based on an anisotropic beam analogy", Ocean Eng., 302, 117611. https://doi.org/10.1016/j.oceaneng.2024.117611
  42. Madenci, E. and Ozkili, Y.O. (2021), "Free vibration analysis of open-cell FG porous beams: analytical, numerical and ANN approaches", Steel Compos. Struct., 40(2), 157-173. https://doi.org/10.12989/scs.2021.40.2.157.
  43. McFarland, A.W. and Colton, J.S. (2005) "Role of material microstructure in plate stiffness with relevance to micro-cantilever sensors", J. Micromech. Microeng., 15, 1060-1067. https://doi.org/10.1088/0960-1317/15/5/024.
  44. Ming, Y., Gholizadeh, M., Khadimallah, M.A. and Issakhov, A. (2021), "Computer simulation for stability performance of sandwich annular system via adaptive tuned deep learning neural network optimization", Adv. Nano Res., 11(1), 83-99. https://doi.org/10.12989/anr.2021.11.1.083.
  45. Nejad, M.Z., Hadi, A., Omidvari, A. and Rastgoo, A. (2018), "Bending analysis of bi-directional functionally graded Euler-Bernoulli nano-beams using integral form of Eringen's nonlocal elasticity theory", Struct. Eng. Mech., 67(4), 417-425. https://doi.org/10.12989/sem.2018.67.4.417.
  46. Rahmani, O. and Jandaghian, A.A. (2015), "Buckling analysis of functionally graded nanobeams based on a nonlocal third-order shear deformation theory", Appl. Phys. A, 119, 1019-1032. https://doi.org/10.1007/s00339-015-9061-z.
  47. Sabherwal, P., Belarbi, M.O., Raman, R., Garg, A., Li, L., Chalak, H.D., Houari, M.S.A. and Avcar, M. (2024), "Free vibration analysis of laminated sandwich plates using wavelet finite element method", AIAA J, 62(2), 824-832. https://doi.org/10.2514/1.J063364.
  48. Sayyad, A.S. and Ghugal, Y.M. (2020), "Bending, buckling and free vibration analysis of size-dependent nanoscale FG beams using refined models and Eringen's nonlocal theory", Int. J. Appl. Mech., 12(1), 2050007. https://doi.org/10.1142/S1758825120500076.
  49. Sharma, A., Tonk, A., Garg, A., Li, L. and Chalak, H.D. (2023a), "First-ply failure analysis of bioinspired double and cross-helicoidal laminated sandwich plates", AIAA J., 61(11), 5087-5095. https://doi.org/10.2514/1.J063176.
  50. Shen, H.S. and Xiang, Y. (2021), "Assessment of negative poisson's ratio effect on thermal post-buckling of FG-GRMMC laminated cylindrical panels", Adv. Nano. Res., 10(5), 423-435. https://doi.org/10.12989/anr.2021.10.5.423.
  51. Singh, P.S. and Azam, M.S. (2021), "Size dependent vibration of embedded functionally graded nanoplate in hygrothermal environment by Rayleigh-Ritz method", Adv. Nano Res., 10(1), 25-42. https://doi.org/10.12989/anr.2021.10.1.025.
  52. Thai, H.T. and Vo, T.P. (2012), "A nonlocal sinusoidal shear deformation beam theory with application to bending, buckling, and vibration of nanobeams", Int. J. Eng. Sci., 54, 58-66. https://doi.org/10.1016/j.ijengsci.2012.01.009.
  53. Tounsi, A., Benguediab, S., Houari, M.S.A. and Semmah, A. (2013), "A new nonlocal beam theory with thickness stretching effect for nanobeams", Int. J. Nanosci., 12(4), 1350025. https://doi.org/10.1142/S0219581X13500257.
  54. Trinh, M.C. and Jun, H. (2021), "Stochastic vibration analysis of functionally graded beams using artificial neural networks", Struct. Eng. Mech., 78(5), 529-543. https://doi.org/10.12989/sem.2021.78.5.529.
  55. Vaishali, Mukhopadhyay, T., Karsh, P.K., Basu, B. and Dey, S. (2020), "Machine learning based stochastic dynamic analysis of functionally graded shells", Compos. Struct., 237, 111870. https://doi.org/10.1016/j.compstruct.2020.111870.
  56. Wang, Q., Li, Q., Wu, D., Yu, Y., Tin-Loi, F., Ma, J. and Gao, W. (2020), "Machine learning aided static structural reliability analysis for functionally graded frame structures", Appl. Math. Model., 78, 792-815. https://doi.org/10.1016/j.apm.2019.10.007.
  57. Wang, Q., Wu, D., Tin-Loi, F. and Gao, W. (2019), "Machine learning aided stochastic structural free vibration analysis for functionally graded bar-type structures", Thin-Walled Struct., 144, 106315. https://doi.org/10.1016/j.tws.2019.106315.
  58. Wang, Z., Zhou, T., Zhang, S., Sun, C., Li, J. and Tan, J. (2023), "Bo-LSTM based cross-sectional profile sequence progressive prediction method for metal tube rotate draw bending", Adv. Eng. Inform., 58, 102152. https://doi.org/10.1016/j.aei.2023.102152.
  59. Wang, Z., Yuan, Y., Zhang, S., Lin, Y. and Tan, J. (2024), "A multi-state fusion informer integrating transfer learning for metal tube bending early wrinkling prediction", Appl. Soft Comput. 151, 110991. https://doi.org/10.1016/j.asoc.2023.110991.
  60. Wang, Y. and Sigmund, O. (2023), "Multi-material topology optimization for maximizing structural stability under thermo-mechanical loading" Comput. Methods Appl. Mech. Eng., 407, 115938. https://doi.org/10.1016/j.cma.2023.115938.
  61. Wang, Y. and Sigmund, O. (2024), "Topology optimization of multi-material active structures to reduce energy consumption and carbon footprint", Struct. Multidiscip. Optim., 67(1), 5. https://doi.org/10.1007/s00158-023-03698-3.
  62. Xu, J., Chang, L., Chen, T., Ren, T., Zhang, Y. and Cai, Z. (2023), "Study of the bending properties of variable stiffness chain mail fabrics", Compos. Struct., 322, 117369. https://doi.org/10.1016/j.compstruct.2023.117369.
  63. Xu, J., Zhang, Y., Huang, Y., Chang, L., Chen, T., Ren, T. and Cai, Z. (2024), "Dynamic response of chain mail fabrics with variable stiffness", Int. J. Mech. Sci., 264, 108840. https://doi.org/10.1016/j.ijmecsci.2023.108840.
  64. Zerrouki, A.K.R., Zidour, M., Bousahla, A.A., Tounsi, A., Bourada, F., Tounsi, A., Benrahou, K.H. and Mahmoud S.R. (2021), "Effect of nonlinear FG-CNT distribution on mechanical properties of functionally graded nano-composite beam", Struct. Eng. Mech., 78(2), 117-124. https://doi.org/10.12989/sem.2021.78.2.117.
  65. Zhang, C., Khorshidi, H., Najafi, E. and Ghasemi, M. (2023), "Fresh, mechanical and microstructural properties of alkali-activated composites incorporating nanomaterials: A comprehensive review", J. Clean. Prod., 384, 135390. https://doi.org/10.1016/j.jclepro.2022.135390.
  66. Zhang, W., Zheng, D., Huang, Y. and Kang, S. (2024), "Experimental and simulative analysis of flexural performance in UHPC-RC hybrid beams", Constr. Build. Mater., 436, 136889. https://doi.org/10.1016/j.conbuildmat.2024.136889.
  67. Zhou, X., Wang, P., Al-Dhaifallah, M., Rawa, M. and Khadimallah, M.A. (2022), "A machine learning-based model for the estimation of the critical thermo-electrical responses of the sandwich structure with magneto- electro-elastic face sheet", Adv. Nano Res., 12(1), 81-99. https://doi.org/10.12989/anr.2022.12.1.081.