Estimation of Thermoelastic State of a Thermally Sensitive Functionally Graded Thick Hollow Cylinder: A Mathematical Model
الموضوعات :V. K Manthena 1 , N.K Lamba 2 , G.D Kedar 3
1 - Department of Mathematics, Priyadarshini J.L. College of Engineering, Nagpur , India
2 - Department of Mathematics, Shri Lemdeo Patil Mahavidyalaya, Nagpur, India
3 - Department of Mathematics, RTM Nagpur University, Nagpur, India
الکلمات المفتاحية: Temperature distribution, Thermal stresses, Functionally graded hollow cylinder, Thermo-sensitivity,
ملخص المقالة :
The object of the present paper is to study temperature distribution and thermal stresses of a functionally graded thick hollow cylinder with temperature dependent material properties. All the material properties except Poisson’s ratio are assumed to be dependent on temperature. The nonlinear heat conduction with temperature dependent thermal conductivity and specific heat capacity is reduced to linear form by applying Kirchhoff’s variable transformation. Solution for the two dimensional heat conduction equation with internal heat source is obtained in the transient state. The influence of thermo-sensitivity on the thermal and mechanical behavior is examined. For theoretical treatment all physical and mechanical quantities are taken as dimensional, whereas for numerical computations we have considered non-dimensional parameters. A mathematical model is constructed for both homogeneous and nonhomogeneous case. Numerical computations are carried out for ceramic-metal-based functionally graded material (FGM), in which alumina is selected as ceramic and nickel as metal. The results are illustrated graphically.
[1] Al-Hajri M., Kalla S. L., 2004, On an integral transform involving Bessel functions, Proceedings of the International Conference on Mathematics and its Applications, Kuwait.
[2] Awaji H., Takenaka H., Honda S., Nishikawa T., 2001, Temperature/Stress distributions in a stress-relief-type plate of functionally graded materials under thermal shock, JSME International Journal Series A Solid Mechanics and Material Engineering 44: 1059-1065.
[3] Ching H. K., Chen J. K., 2007, Thermal stress analysis of functionally graded composites with temperature-dependent material properties, Journal of Mechanics of Materials and Structures 2: 633-653.
[4] Farid M., Zahedinejad P., Malekzadeh P., 2010, Three-dimensional temperature dependent free vibration analysis of functionally graded material curved panels resting on two-parameter elastic foundation using a hybrid semi-analytic differential quadrature method, Materials & Design 31: 2-13.
[5] Hata T., 1982, Thermal stresses in a non-homogeneous thick plate under steady distribution of temperature, Journal of Thermal Stresses 5: 1-11.
[6] Hosseini S. M., Akhlaghi M., 2009, Analytical solution in transient thermo-elasticity of functionally graded thick hollow cylinders, Mathematical Methods in the Applied Sciences 32: 2019-2034.
[7] Kassir K., 1972, Boussinesq problems for non-homogeneous solid, Proceedings of the American Society of Civil Engineers Definition, Journal of the Engineering Mechanics Division 98: 457-470.
[8] Kumar R., Devi Sh., Sharma V., 2017, Axisymmetric problem of thick circular plate with heat sources in modified couple stress theory, Journal of Solid Mechanics 9: 157-171.
[9] Kumar R., Manthena V.R., Lamba N.K., Kedar G.D., 2017, Generalized thermoelastic axi-symmetric deformation problem in a thick circular plate with dual phase lags and two temperatures, Material Physics and Mechanics 32: 123-132.
[10] Kushnir R. M., Protsyuk Yu., 2008, Thermal stressed state of layered thermally sensitive cylinders and spheres under the conditions of convective-radiation heat transfer, Mathematical Modeling Inform Technology 40: 103-112.
[11] Kushnir R. M., Popovych V.S., 2011, Heat Conduction Problems of Thermo-Sensitive Solids under Complex Heat Exchange, Intech.
[12] Lamba N.K., Walde R.T., Manthena V.R., Khobragade N.W., 2012, Stress functions in a hollow cylinder under heating and cooling Process, Journal of Statistics and Mathematics 3: 118-124.
[13] Liew K. M., Kitipornchai S., Zhang X. Z., Lim C. W., 2003, Analysis of the thermal stress behaviour of functionally graded hollow circular cylinders, The International Journal of Solids and Structures 40: 2355-2380.
[14] Manthena V.R., Lamba N.K., Kedar G.D., 2016, Spring backward phenomenon of a transversely isotropic functionally graded composite cylindrical shell, Journal of Applied and Computational Mechanics 2: 134-143.
[15] Manthena V.R., Lamba N.K., Kedar G.D., 2017, Thermal stress analysis in a functionally graded hollow elliptic-cylinder subjected to uniform temperature distribution, Applications and Applied Mathematics 12: 613-632.
[16] Manthena V.R., Kedar G.D., 2017, Transient thermal stress analysis of a functionally graded thick hollow cylinder with temperature dependent material properties, Journal of Thermal Stresses 41: 568-582.
[17] Manthena V.R., Lamba N.K., Kedar G.D., 2018, Mathematical modeling of thermoelastic state of a thick hollow cylinder with nonhomogeneous material properties, Journal of Solid Mechanics 10: 142-156.
[18] Manthena V.R., Lamba N.K., Kedar G.D., 2018, Thermoelastic analysis of a rectangular plate with nonhomogeneous material properties and internal heat source, Journal of Solid Mechanics 10: 200-215.
[19] Moosaie A., 2012, Steady symmetrical temperature field in a hollow spherical particle with temperature-dependent thermal conductivity, Archives of Mechanics 64: 405-422.
[20] Moosaie A., 2015, Axisymmetric steady temperature field in FGM cylindrical shells with temperature-dependent heat conductivity and arbitrary linear boundary conditions, Archives of Mechanics 67: 233-251.
[21] Noda N., 1991, Thermal stresses in materials with temperature dependent properties, Applied Mechanics Reviews 44: 383-397.
[22] Peng X. L., Li X. F., 2010, Thermo-elastic analysis of a cylindrical vessel of functionally graded materials, International Journal of Pressure Vessels Piping 87: 203-210.
[23] Popovych V. S., 1990, Modeling of heat fields in thin thermo-sensitive plates, Modeling and Optimization of Complex Mechanical Systems 1990: 70-75.
[24] Popovych V. S., Garmatii G. Yu., 1993, Analytic-numerical methods of constructing solutions of heat-conduction problems for thermo-sensitive bodies with convective heat transfer, Pidstrigach Institute for Applied Problems of Mechanics and Mathematics 1993: 13-93.
[25] Popovych V. S., Fedai B. N., 1997, The axi-symmetric problem of thermo-elasticity of a multilayer thermo-sensitive tube, Journal of Mathematical Sciences 86: 2605-2610.
[26] Popovych V. S., Makhorkin I. M., 1998, On the solution of heat-conduction problems for thermo-sensitive bodies, Journal of Mathematical Sciences 88: 352-359.
[27] Popovych V. S., Kalynyak B. M., 2005, Thermal stressed state of a thermally sensitive cylinder in the process of convective heating, Mathematics Metody Fiz Mekh Polya 48: 126-136.
[28] Popovych V. S., Harmatii H. Yu., Vovk O. M., 2006, Thermoelastic state of a thermo-sensitive space with a spherical cavity under convective-radiant heat exchange, Mathematics Metody Fiz Mekh Polya 49: 168-176.
[29] Popovych V. S., 2014, Methods for determination of the thermo-stressed state of thermally sensitive solids under complex heat exchange conditions, Encyclopedia of Thermal Stresses 6: 2997-3008.
[30] Popovych V. S., Kalynyak B. M., 2016, Mathematical modeling and methods for the determination of the static thermoelastic state of multilayer thermally sensitive cylinders, Journal of Mathematical Sciences 215: 218-242.
[31] Rakocha I., Popovych V. S., 2016, The mathematical modeling and investigation of the stress-strain state of the three-layer thermosensitive hollow cylinder, Acta Mechanica et Automatica 10: 181-188.
[32] Tang S., 1968, Thermal stresses in temperature dependent isotropic plates, Journal of Spacecrafts and Rockets 5: 987-990.
[33] Thawait A.K., Sondhi L., Sanyal Sh., Bhowmick Sh., 2017, Elastic analysis of functionally graded variable thickness rotating disk by element based material grading, Journal of Solid Mechanics 9: 650-662.
[34] Tripathi J. J., Kedar G. D., Deshmukh K. C., 2017, Generalized thermoelastic problem of a thick circular plate with axisymmetric heat supply due to internal heat generation, Journal of Solid Mechanics 9: 115-125.
