Modeling of 2D Functionally Graded Circular Plates with Artificial Neural Network

Abstract

The thermo-mechanical properties of the functionally graded material (FGM) depend on the volumetric distribution that determines the material character, which is very important in order to overcome different operating conditions and stress levels. Three different training algorithms are used in an Artificial Neural Network (ANN) to determine the equivalent stress levels of a hollow disc that is functionally graded in two directions. The data set was created by choosing the most important four different equivalent stress values (σ_(eqv max max) ,σ_(eqv max min) ,σ_(eqv min max) ,σ_(eqv min min)) that determine the material structure in thermo-mechanical analysis. Performance estimation was performed in three different training algorithms (Gradient Descent Backpropagation, Gradient Descent with Momentum Backpropagation, BFGS Quasi-Newton Backpropagation Algorithm). In this study, termomechanical behaviour was numerically determined by using finite difference method at different compositional gradient upper values to train ANN.

Keywords

• Two-Directional Functionally Graded Circular Plates
• Artificial Neural Network
• Training Algorithms
• Finite difference method
• thermal stress analysis

References

1. [1] Koizumi M. and Niino M., ‘‘Overview of FGM research in Japan’’, MRS Bulletin, vol.20, no.1,pp.19-21, 1995. DOI: https://doi.org/10.1557/S0883769400048867
2. [2] Ruys A., Popov E., Sun D., Russell J., and Murray C., “Functionally graded electrical/thermal ceramic systems.’’. Journal of the European Ceramic Society, vol.21,no.10- 11,pp.2025 – 2029 , 2001.
3. [3] Shabana Y.M. and Noda N., ‘‘Thermo-elastic-plastic stresses in functionally graded materials subjected to thermal loading taking residual stresses of the fabrication process into consideration’’, Composites Part B: Engineering, vol.32, no.2, pp.111-121, 2001. DOI: 10.1016/S1359-8368(00)00049-4
4. [4] Boğa C., ‘‘Elastic Analysis of an Hollow Cylinder Made from Functionally Graded Material Exposed to Internal Pressure’’International Scientific and Vocational Studies Journal, vol.2 ,no.1, pp.56 – 66 , 2018.
5. [5] Wang Q. ,Li Q, Wu D,Yu Y,Tin-Loi F , Ma J ,Gao W, ‘‘ Machine learning aided static structural reliability analysis for functionally graded frame structures’’, Applied Mathematical Modelling , vol.78 ,pp.792–815, 2020. https://doi.org/10.1016/j.apm.2019.10.007
6. [6] Do D.T.T. ,Nguyen-Xuan H. ,Lee J., ‘‘ Material optimization of tri-directional functionally graded plates by using deep neural network and isogeometric multimesh design approach’’, Applied Mathematical Modelling,vol. 87 ,pp.501–533,2020.
7. [7] Ghatage P.S.,Kar V.R., P., Sudhagara E., ‘‘On the numerical modelling and analysis of multi-directional functionally graded composite structures: A review’’,Composite Structures , vol.236 ,pp.111837, 2020.
8. [8] Karsh P.K,Mukhopadhyay T., Dey S., ‘‘Stochastic dynamic analysis of twisted functionally graded plates’’, Composites Part B,vol. 147 ,pp.259–278, 2018.

9. [9] Dikici B and Tuntas R., ‘‘An artificial neural network (ANN) solution to the prediction of age-hardening and corrosion behavior of an Al/TiC functional gradient material (FGM), Journal of Composite Materials, 0(0) 1–15,2020.
10. [10] Mantari J.L. and Monge J.C., “Buckling. free vibration and bending analysis of functionally graded sandwich plates based on an optimized hyperbolic unified formulation’’, International Journal of Mechanical Sciences,vol.119, pp.170–186 , 2016.
11. [11] Nazari F., Abolbashari M.H., Hosseini S.M., “ Three Dimensional Natural Frequency Analysis of Sandwich Plates with Functionally Graded Core Using Hybrid Meshless Local Petrov-Galerkin Method and Artificial Neural Network’’. CMES, vol.105 no.4,pp.271-299, 2015.
12. [12] Jodaei A., Jalal M.,Yas M.H., “Free vibration analysis of functionally graded annular plates by state-space based differential quadrature method and comparative modeling by ANN’’, Composites: Part B , vol.43,pp. 340–353, 2012.
13. [13] Cho J.R., Ha D.Y., ‘‘Optimal tailoring of 2D volume-fraction distributions for heat-resisting functionally graded materials using FDM’’, Computer Methods in Applied Mechanics and Engineering, vol.191, no:29-30, pp.3195-3211, 2002.
14. [14] Na K.S., Kim J.H., ‘‘Volume fraction optimization for step-formed functionally graded plates considering stress and critical temperature’’, Composite Structures, vol.92, no.6, pp.1283-129092:1283-1290, 2010.
15. [15] Cho J.R. and Shin S.W., ‘‘Material composition optimization for heat-resisting FGMs by artificial neural network’’, Composites Part A: Applied Science and Manufacturing, vol.35, no:5, pp.585-594, 2004.
16. [16] Demirbaş M. D., Çakır D. ‘‘Thermal Stress Analysis in Two-Directional Functionally Graded Plates with Artificial Neural Network Training Algorithms’’, International Journal of Engineering Research and Development vol.11, no.2, pp.442-450, 2019.
17. [17] Demirbaş M. D., Çakır D., Arslan S., Öztürk C ‘‘.Equivalent stress analysis of functionally graded rectangular plates by genetic programming International Scientific and Vocational Studies Journal, vol.2, pp.67-80, 2018.
18. [18] Çakır D.,Demirbaş M. D., ‘‘Modelling of One-directional Functionally Graded Circular Plates with Artificial Neural Network’’, International Scientific and Vocational Studies Journal, vol.3,no.1,pp.42-50, 2019.
19. [19] Apalak M.K., Demirbaş M.D., ‘‘Improved Mathematical Models of Thermal Residual Stresses in Functionally Graded Adhesively Bonded Joints: A Critical Review’’ ,Reviews of Adhesion and Adhesives, vol. 7,no.4,pp.367-416, 2019.
20. [20] Demirbaş M.D. , SOFUOĞLU D. ‘‘Thermal Stress Control in Functionally Graded Plates with Artificial Neural Network, International Scientific and Vocational Studies Journal,vol.2, no.1, pp.39-55, 2018.
21. [21] Demirbaş M. D.,‘‘Düzlem İçi Isıl Yüke Maruz Tek Yönlü İşlevsel Kademelendirilmiş Plaka ve Disk Bağlantılarının Isıl Gerilme Analizi’’, Erciyes Üniversitesi, Fen Bilimleri Enstitüsü, Makine Mühendisliği, Yüksek Lisans, 2009.
22. [22] MATLAB. Mathematical software, version 2009a, TheMathWorks.Available: http://www.mathworks.com.7
23. [23] Apalak M. K. , Demirbaş M. D. ‘‘Thermal Residual Stresses İn İn-Plane Functionally Graded Clamped Hollow Circular Plates’’, Subjected To An Edge Heat Flux Proceedıngs Of The Instıtutıon Of Mechanıcal Engıneers Part L-Journal Of Materıals-Desıgn And Applıcatıons, Cilt:229, s236-260, 2015.
24. [24] Apalak M. K. , Demirbaş M. D. ‘‘ Thermal residual stresses in adhesively bonded in-plane functionally graded clamped circular hollow Plates’’, Journal Of Adhesıon Scıence And Technology, vol.27, pp.1590-1623, 2013.
25. [25] Demirbaş M.D., “Düzlem İçi Isıl Yüke Maruz İki Yönlü Kademelendirilmiş Dikdörtgen ve Dairesel Plakaların Isıl Gerilme Analizi’’,Erciyes Üniversitesi,Fen Bilimleri Enstitüsü. Doktora Tezi, Kayseri, 207s, 2012.
26. [26] Mori, T., Tanaka, K., ‘‘ Average stress in matrix and average elastic energy of materials with misfittings inclusions.’’ Acta Metallurgica, 21(5): 517-574, 1973.
27. [27] Nemat-Alla, M., Ahmed, K.I.E., Hassab-Allah, I., ‘‘Elastic-plastic analysis of two-dimensional functionally graded materials under thermal loading’’, International Journal of Solids and Structures, vol.46, no.14-15,pp.2774-2786, 2009.
28. [28] M. Luy, U. Saray, “Wind speed estimation for missing wind data with three different backpropagation algorithms,” Energy Education Science and Technology Part A: Energy Science and Research, vol. 30, no. 1, pp. 45–54, 2012.
29. [29] Metrotra K., Mohan C.K., Ranka S., ‘‘ Elements of artificial neural networks, 1997.
30. [30] Güler H., ‘‘Çinko-Alüminyum Alaşımlarının Korozyon Davranışına Alaşım Elementlerinin Etkisinin Yapay Sinir Ağıyla Tahmini’’.Sakarya Üniversitesi Fen Bilimleri Enstitüsü,Yüksek Lisans,Sakarya, 2007.
31. [31] Rumelhart, D.E., Hinton, G.E., Williams, R.J., ‘‘Learning representations by backpropagation errors’’, Nature, vol.323, pp.533-536, 1986.
32. [32] G.W. NG , ‘‘Application of Neural Networks to Adaptive Control of Nonlinear Systems’’, 1997.