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, Finite difference method, Thermal stress analysis, Artificial neural network, Training algorithms
References
- [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] 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] 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] 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] 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] 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] 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] 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] 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] 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.