Abstract
Predicting the critical buckling loads of functionally graded material (FGM) plates using an analytical method requires solving complex equations with various modes of deformation to determine the minimum loads. The approach is too complex for application in engineering practice. In this paper, a data-driven model using the artificial neural network (ANN) is proposed for the critical buckling load of FGM plates, as an alternative tool for practicing engineers. A database is first developed for randomly selected inputs using an analytical solution based on first-order shear deformation theory for simply supported FGM plates. The database is then divided into a training dataset with 80% of the data and a testing dataset with 20% of the data for developing and validating, respectively, the ANN model. The ANN model developed using six hidden layers with 32 nodes in each layer is found to match the data with a coefficient of determination of 99.95%. Using the ANN model, the stochastic characteristic of the critical buckling load is examined with respect to randomness of the input parameters. The study reveals that along with the dimensional parameters, the critical buckling load is significantly affected by the randomness of the volume fraction ratio and ratio of the modulus of elasticity of the ceramic and the metal.
Similar content being viewed by others
Data availability
The data required to reproduce these findings will be made available on request.
References
Zhao X, Lee Y, Liew KM (2009) Mechanical and thermal buckling analysis of functionally graded plates. Compos Struct 90(2):161–171
Bodaghi M, Saidi A (2010) Levy-type solution for buckling analysis of thick functionally graded rectangular plates based on the higher-order shear deformation plate theory. Appl Math Model 34(11):3659–3673
Shariat BS, Eslami M (2007) Buckling of thick functionally graded plates under mechanical and thermal loads. Compos Struct 78(3):433–439
Thai H-T, Choi D-H (2012) An efficient and simple refined theory for buckling analysis of functionally graded plates. Appl Math Model 36(3):1008–1022
Thai H-T, Kim S-E (2013) Closed-form solution for buckling analysis of thick functionally graded plates on elastic foundation. Int J Mech Sci 75:34–44
Thai H-T, Choi D-H (2013) Analytical solutions of refined plate theory for bending, buckling and vibration analyses of thick plates. Appl Math Model 37(18–19):8310–8323
Thai H-T, Vo TP (2013) A new sinusoidal shear deformation theory for bending, buckling, and vibration of functionally graded plates. Appl Math Model 37(5):3269–3281
Nguyen T-K, Vo TP, Thai H-T (2014) Vibration and buckling analysis of functionally graded sandwich plates with improved transverse shear stiffness based on the first-order shear deformation theory. Proc Inst Mech Eng C J Mech Eng Sci 228(12):2110–2131
Van Tung H, Duc ND (2010) Nonlinear analysis of stability for functionally graded plates under mechanical and thermal loads. Compos Struct 92(5):1184–1191
Huan DT, Tu TM, Quoc TH (2017) Analytical solutions for bending, buckling and vibration analysis of functionally graded cylindrical panel. Vietnam J Sci Technol 55(5):587
Tran M-T et al (2020) Free vibration of stiffened functionally graded circular cylindrical shell resting on Winkler–Pasternak foundation with different boundary conditions under thermal environment. Acta Mech 231(6):2545–2564
Thinh TI et al (2016) Vibration and buckling analysis of functionally graded plates using new eight-unknown higher order shear deformation theory. Lat. Am. J. solids struct. 13(3):456–477
Tu TM et al (2017) Bending analysis of functionally graded plates using new eight-unknown higher order shear deformation theory 62(3):311–324
Van Long N, Quoc TH, Tu TMJ (2016) Bending and free vibration analysis of functionally graded plates using new eight-unknown shear deformation theory by finite-element method. Int J Adv Struct Eng. 8(4):391–399
Belabed Z et al (2014) An efficient and simple higher order shear and normal deformation theory for functionally graded material (FGM) plates. Compos B Eng 60:274–283
Yang J, Liew K, Kitipornchai S (2005) Second-order statistics of the elastic buckling of functionally graded rectangular plates. Compos Sci Technol 65(7–8):1165–1175
McCulloch WS, Pitts W (1943) A logical calculus of the ideas immanent in nervous activity. Bull Math Biophys 5(4):115–133
LeCun Y, Bengio Y (1995) Convolutional networks for images, speech, and time series. The handbook of brain theory and neural networks 3361(10):1995
Carreira-Perpinan MA, Hinton GE (2005) On contrastive divergence learning. in Aistats. Citeseer.
Hinton GE, Osindero S, Teh Y-W (2006) A fast learning algorithm for deep belief nets. Neural Comput 18(7):1527–1554
Ranzato MA et al (2007) Unsupervised learning of invariant feature hierarchies with applications to object recognition. In: 2007 IEEE conference on computer vision and pattern recognition. IEEE
Duong HT et al (2020) Optimization design of rectangular concrete-filled steel tube short columns with balancing composite motion optimization and data-driven model. In: Structures. Elsevier
Le T-T (2021) Prediction of tensile strength of polymer carbon nanotube composites using practical machine learning method. J Compos Mater 55(6):787–811
Le T-T, Phan HC (2020) Prediction of ultimate load of rectangular CFST columns using interpretable machine learning method. Adv Civ Eng 2020:8855069
Oh D et al (2020) Burst pressure prediction of API 5L X-grade dented pipelines using deep neural network. J Mar Sci Eng 8(10):766
Phan HC, Duong HT (2021) Predicting burst pressure of defected pipeline with principal component analysis and adaptive neuro fuzzy inference system. Int J Pressure Vessels Piping 189:104274
Ootao Y, Tanigawa Y, Nakamura T (1999) Optimization of material composition of FGM hollow circular cylinder under thermal loading: a neural network approach. Compos B Eng 30(4):415–422
Liu G et al (2001) Material characterization of functionally graded material by means of elastic waves and a progressive-learning neural network. Compos Sci Technol 61(10):1401–1411
Jodaei A, Jalal M, Yas M (2012) Free vibration analysis of functionally graded annular plates by state-space based differential quadrature method and comparative modeling by ANN. Compos B Eng 43(2):340–353
Han X, Xu D, Liu G-R (2003) A computational inverse technique for material characterization of a functionally graded cylinder using a progressive neural network. Neurocomputing 51:341–360
Nazari A, Milani AA, Zakeri M (2011) Modeling ductile to brittle transition temperature of functionally graded steels by artificial neural networks. Comput Mater Sci 50(7):2028–2037
Reddy J (2000) Analysis of functionally graded plates. Int J Numer Meth Eng 47(1–3):663–684
Yin S et al (2014) Isogeometric locking-free plate element: a simple first order shear deformation theory for functionally graded plates. Compos Struct 118:121–138
Hosseini-Hashemi S et al (2010) Free vibration of functionally graded rectangular plates using first-order shear deformation plate theory. Appl Math Model 34(5):1276–1291
Thai H-T, Choi D-H (2013) Size-dependent functionally graded Kirchhoff and Mindlin plate models based on a modified couple stress theory. Compos Struct 95:142–153
Reddy JN (2006) Theory and analysis of elastic plates and shells. CRC Press, Boca Raton
Rumelhart DE, Hinton GE, Williams RJ, Learning internal representations by error propagation. 1985, California Univ San Diego La Jolla Inst for Cognitive Science
Phan HC, Dhar AS (2021) Predicting pipeline burst pressures with machine learning models. Int J Pressure Vessels Piping, 2021
Ho TK (1995) Random decision forests. In: Proceedings of 3rd international conference on document analysis and recognition. IEEE
Ho TK (1998) The random subspace method for constructing decision forests. IEEE Trans Pattern Anal Mach Intell 20(8):832–844
Friedman JH (2001) Greedy function approximation: a gradient boosting machine. Ann Stat 29:1189–1232
Boser BE, Guyon IM, Vapnik VN (1992) A training algorithm for optimal margin classifiers. In: Proceedings of the fifth annual workshop on computational learning theory
Cortes C, Vapnik V (1995) Support-vector networks. Mach Learn 20(3):273–297
Vapnik V (1998) Statistical learning theory. Wiley, New York
Funding
This research was funded by ARES-CCD (Académie de Recherche et d’Enseignement supérieur - Commission de la Coopération au Développement) in the framework of the Institutional Support to Vietnam National University of Agriculture (VNUA).
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflicts of interest
The authors declare no conflict of interest.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Duong, H.T., Phan, H.C., Tran, T.M. et al. Assessment of critical buckling load of functionally graded plates using artificial neural network modeling. Neural Comput & Applic 33, 16425–16437 (2021). https://doi.org/10.1007/s00521-021-06238-6
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00521-021-06238-6