An Analytical Solution for Temperature Distribution and Thermal Strain of FGM Cylinders with Varying Thickness and Temperature-Dependent Properties Using Perturbation Technique
Document Type : Research Paper
Authors
1 Faculty of Mechanical And Mechatronics Engineering, Shahrood University of Technology, Semnan,Iran
2 Department of Mechanical Engineering, Shahrood University of Technology, Shahrood, Iran,
Abstract
This research presents temperature distribution and thermal strain of functionally graded material cylinders with varying thickness and temperature-dependency properties that are subjected to heat fluxes in their inner and outer layers. The heterogeneous distribution of properties is modeled as a power function. Using first-order temperature theory and the energy method, governing equations are extracted. The system of governing differential equations is a system of nonlinear differential equations with variable coefficients, which are solved by using the analytical method of the matched asymptotic expansion of the perturbations technique. Results obtained from temperature distribution, heat flux, and thermal strain for different heterogeneous constants and temperature-dependency properties are discussed. They show that heterogeneity has a significant impact on the temperature field and thermal strain inside functionally graded cylinders. Moreover, it is observed that heterogeneity has no impact on the direction of heat flux vector inside the body; however, any changes in heterogeneity would change the magnitude of heat flux. The results obtained from the analytical method were compared with those of previous studies and FEM, which showed good agreement.
Keywords
[1] Zhao X., Zhang Z.M., Zhang B.H., 2014, Research on rolling–extrusion forming of variable wall thickness cylinder parts, Materials Research Innovations 18(2): S2-940-S2-945.
[2] Grigorenko A.Y., Müller W.H., Grigorenko Y.M., Vlaikov G.G., 2016, Recent Developments in Anisotropic Heterogeneous Shell Theory: Applications of Refined and Three-dimensional Theory—Volume IIB, Springer.
[3] Kasaeian A., Vatan S.N., Daneshmand S., 2011, FGM materials and finding an appropriate model for the thermal conductivity, Procedia engineering (14): 3199-3204.
[4] Li W., Han B., Research and Application of Functionally Gradient Materials, in: IOP Conference Series: Materials Science and Engineering, IOP Publishing, 022065.
[5] Dai H-L., Rao Y-N., Dai T., 2016, A review of recent researches on FGM cylindrical structures under coupled physical interactions, 2000–2015, Composite Structures 152: 199-225.
[6] Zimmerman R.W., Lutz M.P., 1999, Thermal stresses and thermal expansion in a uniformly heated functionally graded cylinder, Journal of Thermal Stresses 22(2): 177-188.
[7] Awaji H., Sivakumar R., 2001, Temperature and Stress Distributions in a Hollow Cylinder of Functionally Graded Material: The Case of Temperature‐Independent Material Properties, Journal of the American Ceramic Society 84(5): 1059-1065.
[8] El-Naggar A., Abd-Alla A., Fahmy M., Ahmed S., 2002, Thermal stresses in a rotating non-homogeneous orthotropic hollow cylinder, Heat and Mass Transfer 39(1): 41-46.
[9] Shao Z., 2005, Mechanical and thermal stresses of a functionally graded circular hollow cylinder with finite length, International Journal of Pressure Vessels and Piping 82(3): 155-163.
[10] Ruhi M., Angoshtari A., Naghdabadi R., 2005, Thermoelastic analysis of thick-walled finite-length cylinders of functionally graded materials, Journal of Thermal Stresses 28(4): 391-408.
[11] Ootao Y., Tanigawa Y., 2006, Transient thermoelastic analysis for a functionally graded hollow cylinder, Journal of Thermal Stresses 29(11): 1031-1046.
[12] Shao Z., Ma G., 2008, Thermo-mechanical stresses in functionally graded circular hollow cylinder with linearly increasing boundary temperature, Composite Structures 83(3): 259-265.
[13] Bahtui A., Eslami M., 2007, Coupled thermoelasticity of functionally graded cylindrical shells, Mechanics research communications 34(1): 1-18.
[14] Akbari Alashti R., Khorsand M., Tarahhomi M., 2012, Asymmetric thermo-elastic analysis of long cylindrical shells of functionally graded materials by differential quadrature method, Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 226(5): 1133-1147.
[15] Tokovyy Y.V., Ma C.-C., 2008, Analysis of 2D non-axisymmetric elasticity and thermoelasticity problems for radially inhomogeneous hollow cylinders, Journal of Engineering Mathematics 61(2-4): 171-184.
[16] Peng X., Li X., 2010, Thermoelastic analysis of a cylindrical vessel of functionally graded materials, International journal of pressure vessels and piping 87(5): 203-210.
[17] Chang W.-J., Lee H.-L., Yang Y.-C., 2011, Estimation of heat flux and thermal stresses in functionally graded hollow circular cylinders, Journal of Thermal Stresses 34(7): 740-755.
[18] Aziz A., Torabi M., 2013, Thermal stresses in a hollow cylinder with convective boundary conditions on the inside and outside surfaces, Journal of Thermal Stresses 36(10): 1096-1111.
[19] Xin L., Dui G., Yang S., Zhou D., 2015, Solutions for behavior of a functionally graded thick-walled tube subjected to mechanical and thermal loads, International Journal of Mechanical Sciences 98: 70-79.
[20] M. Ghannad, M. Parhizkar Yaghoobi, 2015, A thermoelasticity solution for thick cylinders subjected to thermo-mechanical loads under various boundary conditions, International Journal of Advanced Design and Manufacturing Technology 8(4): 1-12.
[21] M. Ghannad, M. Parhizkar Yaghoobi, 2017, 2D thermo elastic behavior of a FG cylinder under thermomechanical loads using a first order temperature theory, International Journal of Pressure Vessels and Piping 149: 75-92.
[22] Daneshmehr A., Rajabpoor A., Hadi A., 2015, Size dependent free vibration analysis of nanoplates made of functionally graded materials based on nonlocal elasticity theory with high order theories, International Journal of Engineering Science 95: 23-35.
[23] Zamani Nejad M., Hadi A., 2016, Non-local analysis of free vibration of bi-directional functionally graded Euler–Bernoulli nano-beams, International Journal of Engineering Science 105: 1-11.
[24] Zamani Nejad M., Hadi A., 2016, Eringen’s non-local elasticity theory for bending analysis of bi-directional functionally graded Euler–Bernoulli nano-beams, International Journal of Engineering Science 106: 1-9.
[25] Zamani Nejad M., Hadi A., Rastgoo A., 2016, Buckling analysis of arbitrary two-directional functionally graded Euler–Bernoulli nano-beams based on nonlocal elasticity theory, International Journal of Engineering Science 103: 1-10.
[26] Zamani Nejad M., Jabbari M., Hadi A., 2017, A review of functionally graded thick cylindrical and conical shells, Journal of Computational Applied Mechanics 48(2): 357-370.
[27] Khoshgoftar M., Ghorbanpour Arani A., Arefi M., 2009, Thermoelastic analysis of a thick walled cylinder made of functionally graded piezoelectric material, Smart Materials and Structures 18(11): 115007.
[28] Ghorbanpour A., Loghman A., Abdollahitaheri A., Atabakhshian V., 2011, Electrothermomechanical behavior of a radially polarized rotating functionally graded piezoelectric cylinder, Journal of Mechanics of Materials and Structures 6(6): 869-882.
[29] Parhizkar Yaghoobi M., Ghaffari I., Ghannad M., 2018, Stress and active control analysis of functionally graded piezoelectric material cylinder and disk under electro-thermo-mechanical loading, Journal of Intelligent Material Systems and Structures 29(5) 924-937.
[30] Atrian A., Fesharaki J.J., Nourbakhsh S., 2015, Thermo-electromechanical behavior of functionally graded piezoelectric hollow cylinder under non-axisymmetric loads, Applied Mathematics and Mechanics 36(7): 939-954.
[31] Loghman A., Nasr M., Arefi M., 2017, Nonsymmetric thermomechanical analysis of a functionally graded cylinder subjected to mechanical, thermal, and magnetic loads, Journal of Thermal Stresses 40(6): 765-782.
[32] Meshkini M., Firoozbakhsh K., Jabbari M., SelkGhafari A., 2017, Asymmetric mechanical and thermal stresses in 2D-FGPPMs hollow cylinder, Journal of Thermal Stresses, 40(4): 448-469.
[33] Zamani Nejad M., Hadi A., Farajpour A., 2017, Consistent couple-stress theory for free vibration analysis of Euler-Bernoulli nano-beams made of arbitrary bi-directional functionally graded materials, Structural Engineering and Mechanics 63(2): 161-169.
[34] Hadi A., Zamani Nejad M., Hosseini M., 2018, Vibrations of three-dimensionally graded nanobeams, International Journal of Engineering Science 128: 12-23.
[35] Hadi A., Zamani Nejad M., Rastgoo A., Hosseini M., 2018, Buckling analysis of FGM Euler-Bernoulli nano-beams with 3D-varying properties based on consistent couple-stress theory, Steel and Composite Structures 26(6): 663-672.
[36] Zamani Nejad M., Hadi A., Omidvari A., Rastgoo A., 2018, Bending analysis of bi-directional functionally graded Euler-Bernoulli nano-beams using integral form of Eringen's non-local elasticity theory, Structural Engineering and Mechanics 67(4): 417-425.
[37] Ghaffari I., Parhizkar Yaghoobi M., Ghannad M., 2018, Complete mechanical behavior analysis of FG Nano Beam under non-uniform loading using non-local theory, Materials Research Express 5(1): 015016.
[38] Zarezadeh E., Hosseini V., Hadi A., 2019, Torsional vibration of functionally graded nano-rod under magnetic field supported by a generalized torsional foundation based on nonlocal elasticity theory, Mechanics Based Design of Structures and Machines: 1-16.
[39] Barati A., Adeli M.M., Hadi A., 2020, Static torsion of bi-directional functionally graded microtube based on the couple stress theory under magnetic field, International Journal of Applied Mechanics 12(02): 2050021.
[40] Dehshahri K., Zamani Nejad M., Ziaee S., Niknejad A., Hadi A., 2020, Free vibrations analysis of arbitrary three-dimensionally FGM nanoplates, Advances in nano research 8(2): 115-134.
[41] Barati A., Hadi A., Zamani Nejad M., Noroozi R., 2020, On vibration of bi-directional functionally graded nanobeams under magnetic field, Mechanics Based Design of Structures and Machines: 1-18.
[42] Noroozi R., Barati A., Kazemi A., Norouzi S., Hadi A., 2020, Torsional vibration analysis of bi-directional FG nano-cone with arbitrary cross-section based on nonlocal strain gradient elasticity, Advances in nano research 8(1): 13-24.
[43] Ghannad M., Rahimi G.H., Zamani Nejad M., 2013, Elastic analysis of pressurized thick cylindrical shells with variable thickness made of functionally graded materials, Composites Part B: Engineering 45(1): 388-396.
[44] Jabbari M., Zamani Nejad M., 2018, Mechanical and thermal stresses in radially functionally graded hollow cylinders with variable thickness due to symmetric loads, Australian Journal of Mechanical Engineering: 1-14.
[45] Zamani Nejad M., Jabbari M., Ghannad M., 2017, A general disk form formulation for thermo-elastic analysis of functionally graded thick shells of revolution with arbitrary curvature and variable thickness, Acta Mechanica 228(1): 215-231.
[46] Mehditabar A., Rahimi G.H., Fard K.M., 2018, Thermoelastic Analysis of Rotating Functionally Graded Truncated Conical Shell by the Methods of Polynomial Based Differential Quadrature and Fourier Expansion-Based Differential Quadrature, Mathematical Problems in Engineering 2018.
[47] Wang Y., Liu D., Wang Q., Zhou J., 2018, Thermoelastic interaction in functionally graded thick hollow cylinder with temperature-dependent properties, Journal of Thermal Stresses 41(4): 399-417.
[48] Benjeddou A., Andrianarison O., 2005, A thermopiezoelectric mixed variational theorem for smart multilayered composites, Computers & Structures 83(15-16): 1266-1276.
[49] Mahboubi Nasrekani F., Eipakchi H., 2015, Nonlinear Analysis of Cylindrical Shells with Varying Thickness and Moderately Large Deformation under Nonuniform Compressive Pressure Using the First-Order Shear Deformation Theory, Journal of Engineering Mechanics 141(5): 04014153.
[50] Nayfeh A.H., 2011, Introduction to perturbation techniques, John Wiley & Sons.
[51] Omidi Bidgoli M., Arefi M., Loghman A., 2018, Thermoelastic behaviour of FGM rotating cylinder resting on friction bed subjected to a thermal gradient and an external torque, Australian Journal of Mechanical Engineering: 1-9.
[52] Omidi Bidgoli M., Loghman A., Arefi M., 2019, The Effect of Grading Index on Two-dimensional Stress and Strain Distribution of FG Rotating Cylinder Resting on a Friction Bed Under Thermomechanical Loading, Journal of Stress Analysis 3(2): 75-82.
[53] Omidi Bidgoli M., Loghman A., Arefi M., 2019, Three-Dimensional Thermo-Elastic Analysis of a Rotating Cylindrical Functionally Graded Shell Subjected to Mechanical and Thermal Loads Based on the FSDT Formulation, Journal of Applied Mechanics and Technical Physics 60(5) 899-907.
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Volume 51, Issue 1
June 2020Pages 144-156
- Receive Date: 28 December 2019
- Revise Date: 07 May 2020
- Accept Date: 20 May 2020