Thermo-Mechanical Stress Analysis of a Linearly Functionally Graded Rotating Disk with Uniform and Tapered Cross Sections
Main Article Content
Abstract
Functional gradation of materials in a component, whether metal-metal, metal-ceramic, or ceramic-ceramic, offers benefits such as high toughness and strength at elevated temperatures, which are desirable traits in rotating disks. With the advent of FGMs, isotropic material components began to be replaced. In the present study, Thermo-mechanical stress analysis on rotating disks was performed for isotropic materials (both metal and ceramic), and their results were compared with those of a linearly varying functionally graded (FG) disk. The approach utilized is the Variational principle, deriving the solution through Galerkin's error minimization method. Comparison plots of displacement, radial and tangential strains, as well as radial, tangential, and von Mises stresses, were presented to illustrate the advantages of advanced materials such as FGMs (functionally graded materials) over isotropic materials. The study reveals the benefits of functional grading of disks over those made of isotropic materials. Moreover, the analysis was performed for uniform as well as tapered disk profiles.
Article Details

This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
References
Miyamoto Y, Kaysser WA, Rabin BH, Kawasaki A, Ford RG. Functionally Graded Materials. Materials Technology Series. Boston: Springer US; 1999;5
Madan R, Bhowmick S. A review on application of FGM fabricated using solid-state processes. Advances in Materials and Processing Technologies. 2020:1–12.
Al-Sanabani FA, Madfa AA, Al-Qudaimi NH. Alumina ceramic for dental applications: A review article.
Almasi D, Sadeghi M, Lau WJ, Roozbahani F, Iqbal N. Functionally graded polymeric materials: A brief review of current fabrication methods and introduction of a novel fabrication method. Materials Science and Engineering C. 2016;64:102–107.
Durodola JF, Attia O. Deformation and stresses in functionally graded rotating disks. Composites Science and Technology. 2000;60(7):987–995.
Bayat M, Saleem M, Sahari BB, Hamouda AMS, Mahdi E. Analysis of functionally graded rotating disks with variable thickness. Mechanics Research Communications. 2008;35(5):283–309.
Peng XL, Li XF. Thermal stress in rotating functionally graded hollow circular disks. Composite Structures. 2010;92(8):1896–1904.
Allam MNM, Tantawy R, Zenkour AM. Thermoelastic stresses in functionally graded rotating annular disks with variable thickness. Journal of Theoretical and Applied Mechanics. 2018:1029.
Tutuncu N, Temel B. An efficient unified method for thermoelastic analysis of functionally graded rotating disks of variable thickness. Mechanics of Advanced Materials and Structures. 2013;20(1):38–46.
Shahriari B, Safari M. Stress analysis of FGM rotating disk subjected to mechanical and thermal loads in aircraft gas turbine engine. Mechanics of Advanced Composite Structures. 2019.
Nie GJ, Batra RC. Stress analysis and material tailoring in isotropic linear thermoelastic incompressible functionally graded rotating disks of variable thickness. Composite Structures. 2010;92(3):720–729.
Abdalla HMA, Casagrande D, Moro L. Thermo-mechanical analysis and optimization of functionally graded rotating disks. The Journal of Strain Analysis for Engineering Design. 2020;55(5–6):159–171.
Madan R, Saha K, Bhowmick S. Limit speeds and stresses in power law functionally graded rotating disks. Advances in Materials Research. 2020;9(2):115–131.
Rabia B, Tahar HD, Abderezak R. Interfacial stresses in porous PFGM-RC hybrid beam. Advances in Materials Research. 2024;13(1):37–53.
Madan R, Bhowmick S. Material modelling and limit angular speed analysis of porous trigonometric functionally graded rotating disk. Advances in Materials and Processing Technologies. 2022:1–13.
Garg A, Belarbi MO, Li L, Chalak HD, Tounsi A, Zenkour AM. Comparative study on the buckling analysis of exponential, power and sigmoidal sandwich FGM plates under hygro-thermal conditions. Advances in Materials Research. 2024;13(6):431–462.
Suresh S, Mortensen A. Functionally graded metals and metal-ceramic composites: Part 2 Thermomechanical behaviour. International Materials Reviews. 1997;42(3):85–116.
Bruck HA, Rabin BH. Evaluation of rule-of-mixtures predictions of thermal expansion in powder-processed Ni-Al2O3 composites. Journal of the American Ceramic Society. 2004;82(10):2927–2930.
Mori T, Tanaka K. Average stress in matrix and average elastic energy of materials with misfitting inclusions. Acta Metallurgica. 1973;21(5):571–574.
Nakamura T, Wang T, Sampath S. Determination of properties of graded materials by inverse analysis and instrumented indentation. Acta Materialia. 2000;48(17):4293–4306.
Bhattacharyya M, Kapuria S, Kumar AN. On the stress to strain transfer ratio and elastic deflection behavior for Al/SiC functionally graded material. Mechanics of Advanced Materials and Structures. 2007;14(4):295–302.
Madan R, Bhowmick S. Modeling of functionally graded materials to estimate effective thermo-mechanical properties. World Journal of Engineering. 2021.
Das P, Benslimane A, Islam MA, Mondal D, Nazim MS. A thermo-mechanically loaded rotating FGM cylindrical pressure vessels under parabolic changing properties: An analytical and numerical analysis. Heliyon. 2024.
Kadum Njim E, et al. Numerical and analytical investigation of free vibration behavior of porous functionally graded sandwich plates. Mechanics of Advanced Composite Structures. 2024.
Alhous ZFA, Jweeg MJ, Njim EK, Mouthanna A, Flayyih MA, Madan R, Khobragade P, Rai PK. Nonlinear frequency and dynamic response of PLA polymeric imperfect FG sandwich plates under hygrothermal conditions. Coupled Systems Mechanics. 2025;14(1):1–19.
Abbas EN, Abud Ali ZAA, Njim EK, Flayyih MA, Madan R. Analytical and numerical investigation of free vibration of nanoparticle-reinforced composite cylindrical shells. Diagnostyka. 2025:1–12.
Njim EK, Hasan HR, Jweeg MJ, Al-Waily M, Hameed AA, Youssef AM, Elsayed FM. Experimental and numerical analysis of uni-axial buckling of single-phase functionally graded porous polymeric sandwich plates. BIO Web of Conferences. 2024;97:00002.
Njim EK, Bakhy SH, Al-Waily M. Analytical and numerical investigation of free vibration behavior for sandwich plate with functionally graded porous metal core. Journal of Science and Technology. 2021;29(3).
Njim EK, et al. Mechanical properties of sandwiched construction with composite and hybrid core structure. Advances in Polymer Technology. 2024:3803199.
Hadji L, Avcar M, Civalek Ö. An analytical solution for the free vibration of FG nanoplates. Journal of the Brazilian Society of Mechanical Sciences and Engineering. 2021;43(9):418.
Viet NV, Zaki W, Wang Q. Free vibration characteristics of sectioned unidirectional/bidirectional functionally graded material cantilever beams based on finite element analysis. Applied Mathematics and Mechanics (English Edition). 2020;41(12):1787–1804.
Lu Y, Chen X. Nonlinear parametric dynamics of bidirectional functionally graded beams. Shock and Vibration. 2020;2020:1–13.
Hadji L, Madan R, Bernard F. Thermal buckling in multi-directional porous plates: The effects of material grading and aspect ratio. Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering. 2024;238(4):412–426.
Hadji L, Plevris V, Madan R, Ait Atmane H. Multi-directional functionally graded sandwich plates: Buckling and free vibration analysis with refined plate models under various boundary conditions. Computation. 2024;12(4):65.
Hadji L, Plevris V, Madan R. A static and free vibration analysis of porous functionally graded beams. The 2nd International Conference on Civil Infrastructure and Construction. 2023:433–441.
Madan R, Bhowmick S, Hadji L, Alnujaie A. Limit angular speed analysis of porous functionally graded rotating disk under thermo-mechanical loading. Materials and Manufacturing Processes. 2023.
Raad H, Najim E, Jweeg M, AlWaily M, Hadji L, Madan R. Vibration analysis of sandwich plates with hybrid composite cores combining porous polymer and foam structures. Journal of Computational Applied Mechanics. 2024;55(3).
Hangai Y, Ishihara A, Utsunomiya T, Kuwazuru O, Yoshikawa N. Fabrication of two layers porous aluminum varying porosity by friction powder sintering process and its compression properties. Journal of the Japan Institute of Metals. 2016;80(6):390–393.
Madan R, Bhowmick S. Fabrication, microstructural characterization and finite element analysis of functionally graded Al-Al2O3 disk using powder metallurgy technique. Materials Today Communications. 2022;32:103878.
Hadji L, Bernard F, Safa A, Tounsi A. Bending and free vibration analysis for FGM plates containing various distribution shape of porosity. Advances in Materials Research. 2021;10(2):115–135.
Njim EK, Al-Maamori MH, Madan R, Bakhy SH, Al-Waily M, Khobragade P, Hadji L. Numerical and analytical investigation of free vibration behavior of porous functionally graded sandwich plates. Mechanics of Advanced Composite Structures. 2025;12(3):555–568.
Sondhi L, Sahu RK, Kumar R, Yadav S, Bhowmick S, Madan R. Functionally graded polar orthotropic rotating disks: investigating thermo-elastic behavior under different boundary conditions. International Journal on Interactive Design and Manufacturing. 2023.
Parihar RS, Setti SG, Sahu RK. Recent advances in the manufacturing processes of functionally graded materials: a review. Science and Engineering of Composite Materials. 2018;25(2):309–336.
Verma RK, Parganiha D, Chopkar M. A review on fabrication and characteristics of functionally graded aluminum matrix composites fabricated by centrifugal casting method. SN Applied Sciences. 2021;3(2):227.
Madan R, Bhowmick S. A review on application of FGM fabricated using solid-state processes. Advances in Materials and Processing Technologies. 2020;6(3):608–619.
Fujii T, Murakami R, Kobayashi N, Tohgo K, Shimamura Y. Uniform porous and functionally graded porous titanium fabricated via space holder technique with spark plasma sintering for biomedical applications. Advanced Powder Technology. 2022;33(6).
Li Y, Feng Z, Hao L, Huang L, Xin C, Wang Y, Bilotti E, Essa K, Zhang H, Li Z, Yan F, Peijs T. A review on functionally graded materials and structures via additive manufacturing: From multi-scale design to versatile functional properties. Advanced Materials Technologies. 2020;5(6):1900981.
Bobbio LD, Bocklund B, Simsek E, Ott RT, Kramer MJ, Liu ZK, Beese AM. Design of an additively manufactured functionally graded material of 316 stainless steel and Ti-6Al-4V with Ni-20Cr, Cr, and V intermediate compositions. Additive Manufacturing. 2022;51.
Deshmukh PS, Sathiaraj D. A review on twin wire arc additive manufacturing of metals and alloys: Microstructure and mechanical properties. Lecture Notes in Mechanical Engineering. 2022:67.
Dielemans G, Briels D, Jaugstetter F, Henke K, Dörfler K. Additive manufacturing of thermally enhanced lightweight concrete wall elements with closed cellular structures. Journal of Facade Design and Engineering. 2021;9(1):59–72.
Dong G, Tang Y, Li D, Zhao YF. Design and optimization of solid lattice hybrid structures fabricated by additive manufacturing. Additive Manufacturing. 2020;33.
Mallick A, Gangi Setti S, Sahu RK. Centrifugally cast functionally graded materials: Fabrication and challenges for probable automotive cylinder liner application. Ceramics International. 2023;49(6):8649–8682.
Madan R, Bhowmick S. Fabrication, microstructural characterization and finite element analysis of functionally graded Al-Al2O3 disk using powder metallurgy technique. Materials Today Communications. 2022;32.
Madan R, Bhowmick S. Fabrication and microstructural characterization of Al-SiC based functionally graded disk. Aircraft Engineering and Aerospace Technology. 2022.
Ansari M, Jabari E, Toyserkani E. Opportunities and challenges in additive manufacturing of functionally graded metallic materials via powder-fed laser directed energy deposition: A review. Journal of Materials Processing Technology. 2021;294:117117.
Ayan Y, Kahraman N. Fabrication and characterization of functionally graded material structure containing two dissimilar steels (ER70S-6 and 308LSi) by wire arc additive manufacturing. Materials Today Communications. 2022;33:104457.
Singh RK, Singh RC. Evaluation of the mechanical and microstructural properties of an Al7075/B4C/Gr FGM plate fabricated using a stir casting process. Journal of Mechanical Science and Technology. 2024;38(10):5389–5398.
Kumar V, Kumari P. Fabrication and characterization of Cu/SiC-based axially functionally graded beam. Advanced Engineering Materials. 2022;24(5).
Wei C, Cheng J, Zhang M, Zhou R, Wei B, Yu X, Luo L, Chen P. Fabrication of diamond/W–Cu functionally graded material by microwave sintering. Nuclear Engineering and Technology. 2022;54(3):975–983.
Cho JR, Ha DY. Volume fraction optimization for minimizing thermal stress in Ni–Al2O3 functionally graded materials. Materials Science and Engineering A. 2002;334(1–2):147–155.
Maleki Jebeli S, Shariat Panahi M. An evolutionary approach for simultaneous optimization of material property distribution and topology of FG structures. Engineering Computations. 2015;32(2):234–257.
Jiang F, Zhao W, Chen L, Zheng C, Chen H. Combined shape and topology optimization for sound barrier by using the isogeometric boundary element method. Engineering Analysis with Boundary Elements. 2021;124:124–136.
Mostafa Shaaban A, Anitescu C, Atroshchenko E, Rabczuk T. Shape optimization by conventional and extended isogeometric boundary element method with PSO for two-dimensional Helmholtz acoustic problems. Engineering Analysis with Boundary Elements. 2020;113:156–169.
Madan R, Saha K, Bhowmick S. Limit elastic analysis of rotating annular disks having sigmoid-FGM composition based on MROM. World Journal of Engineering. 2019;16(6):806–813.
Nejad MZ, Rastgoo A, Hadi A. Exact elasto-plastic analysis of rotating disks made of functionally graded materials. International Journal of Engineering Science. 2014;85:47–57.
Lakshman S, Subhashis S, Kashinath S, Shubhankar B. Limit elastic speeds of functionally graded annular disks. FME Transactions. 2018;46(4):603–611.
