Modelling of One-directional Functionally Graded Circular Plates with Artificial Neural Network

Öz

In functionally graded materials (FGMs), a combination is provided based on a volume ratio to prevent cracks in the interfaces of different materials and to prevent irregularities in the material transition region. The volumetric distribution between the components determines the mechanical performance of the FGMs.  In this study, the thermo-mechanical behavior of the functionally graded circular plate (FGCPs) was investigated. The thermo-mechanical behavior depends on the equivalent stress values, and the equivalent stress values depend on the volumetric distribution of the components of the material, ie the compositional gradient upper values. Numerical analysis was performed for 60 different compositional gradient peaks in the range [0.01-5], models based on volumetric distribution were established and equivalent stress values were calculated. In the artificial neural network (ANN), three different training algorithms, Levenberg-Marquardt, Gradient Descent With Momentum Backpropagation and Gradient Descent With Adaptive Learning Rate Backpropagation, were created and compared. According to the results of the analysis, Levenberg-Marquart algorithm showed an average success rate of over 90%. It is thought that the models installed in ANN will provide insight in determining the thermo-mechanical behavior of FGCPs and will save work-timei.

Anahtar Kelimeler

• One-Directional Functionally Graded Circular Plates,Artificial Neural Network

Modelling of One-directional Functionally Graded Circular Plates with Artificial Neural Network

Öz

In functionally graded materials (FGMs), a combination is provided based on a volume ratio to prevent cracks in the interfaces of different materials and to prevent irregularities in the material transition region. The volumetric distribution between the components determines the mechanical performance of the FGMs.  In this study, the thermo-mechanical behavior of the functionally graded circular plate (FGCPs) was investigated. The thermo-mechanical behavior depends on the equivalent stress values, and the equivalent stress values depend on the volumetric distribution of the components of the material, ie the compositional gradient upper values. Numerical analysis was performed for 60 different compositional gradient peaks in the range [0.01-5], models based on volumetric distribution were established and equivalent stress values were calculated. In the artificial neural network (ANN), three different training algorithms, Levenberg-Marquardt, Gradient Descent With Momentum Backpropagation and Gradient Descent With Adaptive Learning Rate Backpropagation, were created and compared. According to the results of the analysis, Levenberg-Marquart algorithm showed an average success rate of over 90%. It is thought that the models installed in ANN will provide insight in determining the thermo-mechanical behavior of FGCPs and will save work-timei.

Anahtar Kelimeler

• One-Directional Functionally Graded Circular Plates,Artificial Neural Network,Training Algorithms,Finite Difference Method

Kaynakça

1. Referanslar[1] Ruys A., Popov E., Sun D., Russell J., Murray C., ‘‘Functionally graded electrical/thermal ceramic systems’’, Journal of the European Ceramic Society, vol. 21, no.10-11, pp.2025-2029, December 2001. Doi: DOI: 10.1016/S0955-2219(01)00165-0
2. [2] Kakac S., Pramuanjaroenkij A., Zhou X.Y., ‘‘A review of numerical modeling of solid oxide fuel cells’’, International Journal of Hydrogen Energy, vol.32, no.7, pp.761-786, May, 2007. Doi: 10.1016/j.ijhydene.2006.11.028
3. [3] Koizumi M., Niino M., ‘‘Overview of FGM research in Japan’’, MRS Bulletin, vol.20, no.1,pp.19-21, January, 1995. Available: https://doi.org/10.1557/S0883769400048867 [5] Shabana Y.M., 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/S0020-7683(97)00253-9
4. [6] Praveen G.N., Reddy J.N., ‘‘Nonlinear transient thermoelastic analysis of functionally graded ceramic-metal plates. International Journal of Solids and Structures’’, vol.35, no.33, pp.4457-4476, November 1998. Doi: 10.1016/S0020-7683(97)00253-9
5. [7] Xiang Y., Zhou Y., ‘‘A dynamic multi-colony artificial bee colony algorithm for multi-objective optimization’’, Applied Soft Computing, vol.35, pp.766-785, October 2015.doi: 10.1016/j.asoc.2015.06.033
6. [8] Nemat-Alla M., ‘‘Reduction of thermal stresses by developing two-dimensional functionally graded materials’’, International Journal of Solids and Structures, vol.40, no.26, pp.7339-7356, December 2003. Doi: 10.1016/j.ijsolstr.2003.08.017
7. [9] Ghannadpour S.A.M., Ovesy H.R., Nassirnia M., ‘‘Buckling analysis of functionally graded plates under thermal loadings using the finite strip method’’, Computers & Structures, vol.108-109, pp.93-99, October 2012. Doi: 10.1016/j.compstruc.2012.02.011
8. [10] Ootao Y., Kawamura R., Tanigawa Y., Nakamura T., ‘‘Neural network optimization of material composition of a functionally graded material plate at arbitrary temperature range and temperature rise’’, Archive of Applied Mechanics, vol.68, no.10, pp. 662-676, 1998. Doi :10.1016/j.compstruc.2012.02.011

9. [11] Ootao Y., Kawamura R., Tanigawa Y., Imamura R., ‘‘Optimization of material composition of nonhomogeneous hollow sphere for thermal stress relaxation making use of neural network’’, Computer Methods in Applied Mechanics and Engineering, no.18, no. 1-2, pp. 185-201, November 1999. Doi : 10.1016/S0045-7825(99)00055-9
10. [12] Ali M.M., Khompatraporn C., Zabinsky Z.B., ‘‘A Numerical Evaluation of Several Stochastic Algorithms on Selected Continuous Global Optimization Test Problems’’, Journal of Global Optimization, vol.31, no.4, pp.635-672, 2005. Available: https://link.springer.com/article/10.1007/s10898-004-9972-2
11. [13] Turteltaub S., ‘‘Optimal control and optimization of functionally graded materials for thermomechanical processes’’, International Journal of Solids and Structures, vol.39, no.12, pp.3175-3197, June 2002. Doi : 10.1016/S0020-7683(02)00243-3
12. [14] Bouchafa A., Benzair A., Tounsi A., Draiche K., Mechab İ., Adda Bedia E.A., ‘‘Analytical modelling of thermal residual stresses in exponential functionally graded material system’’,Materials & Design, vol.31, no.1, pp.560-563, January 2010. Doi : 10.1016/j.matdes.2009.07.010
13. [15] 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. Doi : 10.1016/S0045-7825(02)00256-6
14. [16] 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, May 2010. Doi : 10.1016/S0045-7825(02)00256-6
15. [17] Cho J.R., 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, May 2004. Doi : 10.1016/j.compositesa.2003.12.003
16. [18] Demirbaş M. D., Çakır D. ‘‘Thermal Stress Control in Functionally Graded Plates with Artificial Neural Network’’, Internatıonal Scıentıfıc And Vocatıonal Journal, Vol:2, no:1, pp:39-55, 2018, doi: 10.29137/umagd.485604
17. [19] 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 cilt.11, no.2, ss 442-450, June 2019. Doi : 10.29137/umagd.485604
18. [20] 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, cilt.2, ss.67-80, 2018. Available: https://dergipark.org.tr/download/article-file/515242
19. [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] Öztürk C., ‘‘Yapay Sinir Ağlarının Yapay Arı Kolonisi Algoritması İle eğitilmesi’’, Erciyes Üniversitesi Fen Bilimleri Enstitüsü, Bilgisayar Mühendisliği, Ocak, 2011.
20. [23] Manngard M., Kronqvist J., Böling J.M., ‘‘Structural learning in artificial neural networks using sparse optimization’’, Neurocomputing, vol.272, no.10, pp.660-667, 2018.
21. [24] Ham F.M., Kostanic I., ‘‘Principles of Neurocomputing for Science and Engineering, 2001
22. [25] Hagan M.T., Menhaj M., ‘‘Training feed-forward networks with the Marquardt algorithm’’, IEEE Transactions on Neural Networks, vol.5, no.6, pp.989-993, 1994.
23. [26] Rumelhart D.E., Hinton G.E., Williams R.J., ‘‘Learning representations by backpropagation errors’’, Nature, vol.323, pp.533-536, 1986.
24. [27] Metrotra K., Mohan C.K., Ranka S., ‘‘ Elements of artificial neural networks, 1997.
25. [28] Oğuz M., ‘‘Yalıtkan malzemelerde elektiriksel dayanımın yapay sinir ağları ile belirlenmesi, İstanbul Teknik Üniversitesi Fen Bilimleri Enstitüsü, Elektrik Mühendisliği Haziran, 2001.
26. [29] Parlos A.G., Muthusami J., Atiya A.F, ‘‘Incipient fault detection and identification in progress systems using accelerated neural network learning’’, Nuclear Technology, vol.105, pp.145, 1994.
27. [30] MATLAB. Mathematical software, version 2009a, TheMathWorks.Available: http://www.mathworks.com.7
28. [31] 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, Ss.236-260, 2015.doi: 10.1177/1464420713509699
29. [32] 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, Cilt.27, ss.1590-1623, 2013.doi: 10.1080/01694243.2012.747732
30. [33] Çakır D ,‘‘ Fonksiyonel Kademelendirilmiş Plakalarda Malzeme Kompozisyonunun Yapay Sinir Ağı ve Genetik Programlama İle Belirlenmesi’’, Erciyes Üniversitesi Fen Bilimleri Enstitüsü, Makine Mühendisliği, Yüksel Lisans, 2018[34]Mori, T., Tanaka, K., 1973. ‘‘ Average stress in matrix and average elastic energy of materials with misfittings inclusions.’’ Acta Metallurgica, 21(5): 517-574.doi: 10.1016/0001-6160(73)90064-3