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Year 2020, Volume: 6 Issue: 1, 1 - 12, 31.03.2020

Vebil Yıldırım

https://doi.org/10.19072/ijet.689703

Abstract

References

  • U. Güven, and O. Altay, “Elastic–plastic solid disk with nonuniform heat source subjected to external pressure”, International Journal of Mechanical Sciences, vol. 42(5), pp. 831-842, 2000.
  • H. Jahed, and R. Shirazi, “Loading and unloading behaviour of a thermoplastic disc”, International Journal of Pressure Vessels and Piping, vol. 78, pp. 637–645, 2001.
  • V.S. Gogulwar, and K.C. Deshmukh, “An inverse quasi-static thermal stresses in an annular disc”, Proceeding of ICADS, Narosa Publishing House, New Delhi, 2002.
  • V.S. Kulkarni, and K.C. Deshmukh, “Thermal stresses in a thick annular disc, Journal of Thermal Stresses, vol. 31(4), pp. 331-342, 2008.
  • M.S. Genç, G. Özşik, and H. Yapıcı, “A numerical study of the thermally induced stress distribution in a rotating hollow disc heated by a moving heat source acting on one of the side surfaces”, Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, vol. 223(8), pp. 1877-1887, 2009.
  • M.Z. Nejad, and A. Afshin, “Transient thermoelastic analysis of pressurized rotating disks subjected to arbitrary boundary and initial conditions”, Chinese Journal of Engineering, Article ID 894902, 13 pages, 2014. http://dx.doi.org/10.1155/2014/894902
  • M. Rattan, A. Kaushik, and N. Chamoli, “Steady state creep behavior of thermally graded isotropic rotating disc of composite taking into account the thermal residual stress”, European Journal of Mechanics A/Solids, vol. 60, pp. 315-326, 2016.
  • J. Kaur, P. Thakur, and S.B. Singh, “Steady thermal stresses in a thin rotating disc of finitesimal deformation with mechanical load”, Journal of Solid Mechanics, vol. 8(1), pp. 204-211, 2016.
  • P. Nayak, K. Saha, “Elastic limit angular speed of solid and annular disks under thermomechanical loading”, International Journal of Engineering, Science and Technology, vol. 8(2), pp. 30-45, 2016.
  • V. Yıldırım, “Heat-induced, pressure-induced and centrifugal-force-induced exact axisymmetric thermo-mechanical analyses in a thick-walled spherical vessel, an infinite cylindrical vessel, and a uniform disc made of an isotropic and homogeneous material”, International Journal of Engineering & Applied Sciences (IJEAS), vol. 9 (2), pp. 66-87, 2017.
  • F. Vivio, and V. Vullo, “Elastic stress analysis of rotating converging conical disks subjected to thermal load and having variable density along the radius”, International Journal of Solids and Structures, vol. 44, pp. 7767–7784, 2007.
  • V. Vullo, and F. Vivio, “Elastic stress analysis of non-linear variable thickness rotating disks subjected to thermal load and having variable density along the radius”, International Journal of Solids and Structures, vol. 45, pp. 5337–5355, 2008.
  • G.J. Nie, and R.C. Batra, “Stress analysis and material tailoring in isotropic linear thermoelastic incompressible functionally graded rotating disks of variable thickness”, Compos. Struct., vol. 92, pp. 720–729, 2010.
  • M. Garg, B.S. Salaria, and V.K. Gupta, “Effect of thermal gradient on steady state creep in a rotating disc of variable thickness”, Procedia Eng., vol. 55, 542e547. 2013.
  • E. Çetin, A. Kurşun, Ş. Aksoy, and M.T. Çetin, “Elastic stress analysis of annular bi-material discs with variable thickness under mechanical and thermomechanical loads”, World Academy of Science, Engineering and Technology, International Journal of Mechanical, Aerospace, Industrial, Mechatronic and Manufacturing Engineering, vol. 8(2), pp. 288-292, 2014.
  • O. Sayman, “Thermal stress analysis in an aluminum metal-matrix orthotropic disc”, Journal of Reinforced Plastics and Composites, vol. 23, pp. 1473-1479, 2004.
  • H. Çallıoğlu, M. Topçu, and G. Altan, “Stress analysis of curvilinearly orthotropic rotating discs under mechanical and thermal loading”, Journal of Reinforced Plastics and Composites, vol. 24(8), pp. 831-838, 2005.
  • H. Çallıoğlu, “Thermal stress analysis of curvilinear orthotropic rotating disks”, Journal of Thermoplastic Composite Materials, vol. 20, pp. 357-369, 2007.
  • F. Sen, and M. Sayer, “Elasto-plastic thermal stress analysis in a thermoplastic composite disc under uniform temperature using FEM”, Mathematical and Computational Applications, vol. 11(1), pp. 31-39, 2006.
  • G. Altan, M. Topçu, N.B. Bektaş, and B.D. Altan, “Elastic-plastic thermal stress analysis of an aluminum composite disc under parabolic thermal load distribution”, J. Mech. Sci. Technol., 22(12), pp. 2318–2327, 2008.
  • F. Mohammadi, A. Hadadian, and G.J. Singh, “Analytical solution of pressurized rotating composite disk under thermal loading”, Proceedings of the World Congress on Engineering II: WCE 2010, London, U.K. (4 pages) 2010.
  • M.T. Mustafa, S.M. Zubair, and A.F.M. Arif, “Thermal analysis of orthotropic annular fins with contact resistance: A closed-form analytical solution”, Appl. Therm. Eng., vol. 31, pp. 937–945, 2011.
  • G. Kansal, and M. Parvez, “Thermal stress analysis of orthotropic graded rotating discs”, International Journal of Modern Engineering Research (IJMER), vol. 2(5), pp. 3381-3885, 2012.
  • I.H. Stampouloglou, and E.E. Theotokoglou, “The radially nonhomogeneous thermoelastic axisymmetric problem”, International Journal of Mechanical Sciences, vol. 120, pp. 311–321, 2017.
  • W. Shang-Sheng, “Analysis on transient thermal stresses in an annular fin”, Journal of Thermal Stresses, vol. 20, pp. 591–615, 1997.
  • C.H. Chiu, and O.K.C. Chen, “Thermal stresses in annular fins with temperature dependent conductivity under periodic boundary condition”, Journal of Thermal Stresses, vol. 25(5), pp. 475–492, 2002.
  • M. Bayat, M. Saleem, B.B. Sahari, A.M.S. Hamouda, and E. Mahdi, “Thermo elastic analysis of a functionally graded rotating disk with small and large deflections”, Thin-Wall Struct, vol. 45, pp. 677–691, 2007.
  • S.A.H. Kordkheili, and R. Naghdabadi, “Thermoelastic analysis of a functionally graded rotating disk”, Composite Structures, vol. 79, pp. 508–516, 2007.
  • A.G. Arani, M.R. Mozdianfard, Z.K. Maraghi, and A.R. Shajari, “Thermo-piezo-magneto-mechanical stresses analysis of FGPM hollow rotating thin disk”, Int. J. Mech. Mater. Des., vol. 6, pp. 341–349, 2010.
  • A.M. Afsar, J. Go, “Finite element analysis of thermoelastic feld in a rotating FGM circular disk”, Appl. Math. Model, vol. 34, pp. 3309–3320, 2010.
  • X.L. Peng, and X.F. Li, “Thermal stress in rotating functionally graded hollow circular discs”, Composite Structures, vol. 92 (8), pp. 1896–1904, 2010.
  • A. Kursun, M. Topçu, and T. Tetik, “Stress analysis of functionally graded disc under thermal and mechanical loads”, ICM11, Engineering Procedia, vol. 10, pp. 2949–2954, 2011.
  • J.F. Gong, P.J. Ming, L.K. Xuan, and W.P. Zhang, “Thermoelastic analysis of three-dimensional functionally graded rotating disks based on finite volume method”, Proceedings of the Institution of Mechanical Engineers Part C., Journal of Mechanical Engineering Science, vol. 228(4), pp. 583–598, 2014.
  • D. Gonczi, and I. Ecsedi, “Thermoelasic analysis of functionally graded hollow circular disk”, Arch Mech Eng, vol. LXII, pp. 5–18, 2015.
  • V. Yıldırım, “Thermomechanical characteristics of a functionally graded mounted uniform disc with/without rigid casing”, The Journal of Aerospace Technology and Management (JATM), vol. 11: e2919 (25 pages), 2019.
  • R. Chiba, “Stochastic thermal stresses in an FGM annular disc of variable thickness with spatially random heat transfer coefficients”, Meccanica, vol. 44, pp. 159–176, 2009.
  • M. Bayat, M. Saleem, B.B. Sahari, A.M.S Hamouda, and E. Mahdi, “Mechanical and thermal stresses in a functionally graded rotating disk with variable thickness due to radially symmetry loads”, Int. Journal of Pressure Vessels and Piping, vol. 86, pp. 357–372, 2009.
  • M. Bayat, B.B. Sahari, M. Saleem, A. Ali, and S.V. Wong, “Thermoelastic solution of a functionally graded variable thickness rotating disk with bending based on the first-order shear deformation theory”, Thin-Wall Struct., vol. 47, pp. 568–582, 2009.
  • M. Bayat, B.B. Sahari, M. Saleem, A.M.S. Hamouda, and J.N. Reddy, “Thermo elastic analysis of functionally graded rotating disks with temperature-dependent material properties: uniform and variable thickness”, Journal of Mechanics and Materials in Design, vol. 5(3), pp. 263–279, 2009.
  • M. Bayat, A.H. Mohazzab, B.B. Sahari, and M. Saleem, “Exact solution for functionally graded variable-thickness rotating disc with heat source, Proceedings of the Institution of Mechanical Engineers-Part C., Journal of Mechanical Engineering Science, vol. 224(11), pp. 2316–2331, 2010.
  • G. Arani, A. Loghman, A. Shajari, and S.A.R. Amir, “Semi-analytical solution of magneto-thermo-elastic stresses for functionally graded variable thickness rotating disks”, J. Mech. Sci. Technol., vol. 24(10), pp. 2107–2117, 2010.
  • M. Damircheli, and M. Azadi, “Temperature and thickness effects on thermal and mechanical stresses of rotating FG-disks”, Journal of Mechanical Science and Technology, vol. 25(3), pp. 827-836, 2011.
  • A. Hassani, M.H. Hojjati, G. Farrahi, and R.A. Alashti, “Semi-exact elastic solutions for thermo-mechanical analysis of functionally graded rotating disks”, Composite Structures, vol. 93(12), pp. 3239–3251, 2011.
  • N. Tutuncu, and B. Temel, “An efficient unified method for thermoelastic analysis of functionally graded rotating disks of variable thickness”, Mechanics of Advanced Materials and Structures, vol. 20(1), pp. 38-46, 2013.
  • M.E. Golmakani, “Large deflection thermoelastic analysis of shear deformable functionally graded variable thickness rotating disk”, Composites: Part B, vol. 45, pp. 1143-1155, 2013.
  • A. Kurşun, and M. Topçu, “Thermal stress analysis of functionally graded disc with variable thickness due to linearly increasing temperature load”, Arab J Sci Eng, vol. 38, pp. 3531–3549, 2013.
  • E. Mahdavi, R. AkbariAlashti, A.C. Darabi, and M. Alizadeh, “Linear thermoplastic analysis of FGM rotating discs with variable thickness”, Iranian Journal Of Mechanical Engineering, vol. 14(2), pp. 73-87, 2013.
  • M. Jabbari, M. Ghannad, and M.Z. Nejad, “Effect of thickness profile and FG function on rotating disks under thermal and mechanical loading”, Journal of Mechanics, vol. 32(1), pp. 35-46, 2016.

Exact Axisymmetric Thermal Analysis of Functionally Graded Disks with Continuously Hyperbolically Varying Thickness

Year 2020, Volume: 6 Issue: 1, 1 - 12, 31.03.2020

Vebil Yıldırım

https://doi.org/10.19072/ijet.689703

Abstract

An exact thermal analysis of radially functionally graded (FG) disks with continuously varying thickness is performed by steady-state 1-D Fourier heat conduction equation at specific surface temperatures. By employing a simple-power material grading pattern together with the convergent/divergent hyperbolic disk profiles, the differential equation is obtained in the form of Euler-Cauchy type. Analytical solution of the differential equation gives the temperature field and heat flux distributions in the radial direction in a closed form. A numerical study is conducted to visualize both the temperature and heat flux variations with respect to the disk profile parameter for hyperbolic disks made of SUS-304 /ZrO2 (Stainless steel/Zirconium oxide) metal-ceramic pairs. Those exact expressions are also used to study parametrically the effects of both the inhomogeneity and profile parameters on the temperature field of the disks made of hypothetic FG metal-ceramic pairs. It is revealed that heat conduction behavior of such disks is strictly affected from the variation of both inhomogeneity and disk profile parameters.

Keywords

Thermal analysis functionally graded exact solution variable thickness hyperbolic disk

References

  • U. Güven, and O. Altay, “Elastic–plastic solid disk with nonuniform heat source subjected to external pressure”, International Journal of Mechanical Sciences, vol. 42(5), pp. 831-842, 2000.
  • H. Jahed, and R. Shirazi, “Loading and unloading behaviour of a thermoplastic disc”, International Journal of Pressure Vessels and Piping, vol. 78, pp. 637–645, 2001.
  • V.S. Gogulwar, and K.C. Deshmukh, “An inverse quasi-static thermal stresses in an annular disc”, Proceeding of ICADS, Narosa Publishing House, New Delhi, 2002.
  • V.S. Kulkarni, and K.C. Deshmukh, “Thermal stresses in a thick annular disc, Journal of Thermal Stresses, vol. 31(4), pp. 331-342, 2008.
  • M.S. Genç, G. Özşik, and H. Yapıcı, “A numerical study of the thermally induced stress distribution in a rotating hollow disc heated by a moving heat source acting on one of the side surfaces”, Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, vol. 223(8), pp. 1877-1887, 2009.
  • M.Z. Nejad, and A. Afshin, “Transient thermoelastic analysis of pressurized rotating disks subjected to arbitrary boundary and initial conditions”, Chinese Journal of Engineering, Article ID 894902, 13 pages, 2014. http://dx.doi.org/10.1155/2014/894902
  • M. Rattan, A. Kaushik, and N. Chamoli, “Steady state creep behavior of thermally graded isotropic rotating disc of composite taking into account the thermal residual stress”, European Journal of Mechanics A/Solids, vol. 60, pp. 315-326, 2016.
  • J. Kaur, P. Thakur, and S.B. Singh, “Steady thermal stresses in a thin rotating disc of finitesimal deformation with mechanical load”, Journal of Solid Mechanics, vol. 8(1), pp. 204-211, 2016.
  • P. Nayak, K. Saha, “Elastic limit angular speed of solid and annular disks under thermomechanical loading”, International Journal of Engineering, Science and Technology, vol. 8(2), pp. 30-45, 2016.
  • V. Yıldırım, “Heat-induced, pressure-induced and centrifugal-force-induced exact axisymmetric thermo-mechanical analyses in a thick-walled spherical vessel, an infinite cylindrical vessel, and a uniform disc made of an isotropic and homogeneous material”, International Journal of Engineering & Applied Sciences (IJEAS), vol. 9 (2), pp. 66-87, 2017.
  • F. Vivio, and V. Vullo, “Elastic stress analysis of rotating converging conical disks subjected to thermal load and having variable density along the radius”, International Journal of Solids and Structures, vol. 44, pp. 7767–7784, 2007.
  • V. Vullo, and F. Vivio, “Elastic stress analysis of non-linear variable thickness rotating disks subjected to thermal load and having variable density along the radius”, International Journal of Solids and Structures, vol. 45, pp. 5337–5355, 2008.
  • G.J. Nie, and R.C. Batra, “Stress analysis and material tailoring in isotropic linear thermoelastic incompressible functionally graded rotating disks of variable thickness”, Compos. Struct., vol. 92, pp. 720–729, 2010.
  • M. Garg, B.S. Salaria, and V.K. Gupta, “Effect of thermal gradient on steady state creep in a rotating disc of variable thickness”, Procedia Eng., vol. 55, 542e547. 2013.
  • E. Çetin, A. Kurşun, Ş. Aksoy, and M.T. Çetin, “Elastic stress analysis of annular bi-material discs with variable thickness under mechanical and thermomechanical loads”, World Academy of Science, Engineering and Technology, International Journal of Mechanical, Aerospace, Industrial, Mechatronic and Manufacturing Engineering, vol. 8(2), pp. 288-292, 2014.
  • O. Sayman, “Thermal stress analysis in an aluminum metal-matrix orthotropic disc”, Journal of Reinforced Plastics and Composites, vol. 23, pp. 1473-1479, 2004.
  • H. Çallıoğlu, M. Topçu, and G. Altan, “Stress analysis of curvilinearly orthotropic rotating discs under mechanical and thermal loading”, Journal of Reinforced Plastics and Composites, vol. 24(8), pp. 831-838, 2005.
  • H. Çallıoğlu, “Thermal stress analysis of curvilinear orthotropic rotating disks”, Journal of Thermoplastic Composite Materials, vol. 20, pp. 357-369, 2007.
  • F. Sen, and M. Sayer, “Elasto-plastic thermal stress analysis in a thermoplastic composite disc under uniform temperature using FEM”, Mathematical and Computational Applications, vol. 11(1), pp. 31-39, 2006.
  • G. Altan, M. Topçu, N.B. Bektaş, and B.D. Altan, “Elastic-plastic thermal stress analysis of an aluminum composite disc under parabolic thermal load distribution”, J. Mech. Sci. Technol., 22(12), pp. 2318–2327, 2008.
  • F. Mohammadi, A. Hadadian, and G.J. Singh, “Analytical solution of pressurized rotating composite disk under thermal loading”, Proceedings of the World Congress on Engineering II: WCE 2010, London, U.K. (4 pages) 2010.
  • M.T. Mustafa, S.M. Zubair, and A.F.M. Arif, “Thermal analysis of orthotropic annular fins with contact resistance: A closed-form analytical solution”, Appl. Therm. Eng., vol. 31, pp. 937–945, 2011.
  • G. Kansal, and M. Parvez, “Thermal stress analysis of orthotropic graded rotating discs”, International Journal of Modern Engineering Research (IJMER), vol. 2(5), pp. 3381-3885, 2012.
  • I.H. Stampouloglou, and E.E. Theotokoglou, “The radially nonhomogeneous thermoelastic axisymmetric problem”, International Journal of Mechanical Sciences, vol. 120, pp. 311–321, 2017.
  • W. Shang-Sheng, “Analysis on transient thermal stresses in an annular fin”, Journal of Thermal Stresses, vol. 20, pp. 591–615, 1997.
  • C.H. Chiu, and O.K.C. Chen, “Thermal stresses in annular fins with temperature dependent conductivity under periodic boundary condition”, Journal of Thermal Stresses, vol. 25(5), pp. 475–492, 2002.
  • M. Bayat, M. Saleem, B.B. Sahari, A.M.S. Hamouda, and E. Mahdi, “Thermo elastic analysis of a functionally graded rotating disk with small and large deflections”, Thin-Wall Struct, vol. 45, pp. 677–691, 2007.
  • S.A.H. Kordkheili, and R. Naghdabadi, “Thermoelastic analysis of a functionally graded rotating disk”, Composite Structures, vol. 79, pp. 508–516, 2007.
  • A.G. Arani, M.R. Mozdianfard, Z.K. Maraghi, and A.R. Shajari, “Thermo-piezo-magneto-mechanical stresses analysis of FGPM hollow rotating thin disk”, Int. J. Mech. Mater. Des., vol. 6, pp. 341–349, 2010.
  • A.M. Afsar, J. Go, “Finite element analysis of thermoelastic feld in a rotating FGM circular disk”, Appl. Math. Model, vol. 34, pp. 3309–3320, 2010.
  • X.L. Peng, and X.F. Li, “Thermal stress in rotating functionally graded hollow circular discs”, Composite Structures, vol. 92 (8), pp. 1896–1904, 2010.
  • A. Kursun, M. Topçu, and T. Tetik, “Stress analysis of functionally graded disc under thermal and mechanical loads”, ICM11, Engineering Procedia, vol. 10, pp. 2949–2954, 2011.
  • J.F. Gong, P.J. Ming, L.K. Xuan, and W.P. Zhang, “Thermoelastic analysis of three-dimensional functionally graded rotating disks based on finite volume method”, Proceedings of the Institution of Mechanical Engineers Part C., Journal of Mechanical Engineering Science, vol. 228(4), pp. 583–598, 2014.
  • D. Gonczi, and I. Ecsedi, “Thermoelasic analysis of functionally graded hollow circular disk”, Arch Mech Eng, vol. LXII, pp. 5–18, 2015.
  • V. Yıldırım, “Thermomechanical characteristics of a functionally graded mounted uniform disc with/without rigid casing”, The Journal of Aerospace Technology and Management (JATM), vol. 11: e2919 (25 pages), 2019.
  • R. Chiba, “Stochastic thermal stresses in an FGM annular disc of variable thickness with spatially random heat transfer coefficients”, Meccanica, vol. 44, pp. 159–176, 2009.
  • M. Bayat, M. Saleem, B.B. Sahari, A.M.S Hamouda, and E. Mahdi, “Mechanical and thermal stresses in a functionally graded rotating disk with variable thickness due to radially symmetry loads”, Int. Journal of Pressure Vessels and Piping, vol. 86, pp. 357–372, 2009.
  • M. Bayat, B.B. Sahari, M. Saleem, A. Ali, and S.V. Wong, “Thermoelastic solution of a functionally graded variable thickness rotating disk with bending based on the first-order shear deformation theory”, Thin-Wall Struct., vol. 47, pp. 568–582, 2009.
  • M. Bayat, B.B. Sahari, M. Saleem, A.M.S. Hamouda, and J.N. Reddy, “Thermo elastic analysis of functionally graded rotating disks with temperature-dependent material properties: uniform and variable thickness”, Journal of Mechanics and Materials in Design, vol. 5(3), pp. 263–279, 2009.
  • M. Bayat, A.H. Mohazzab, B.B. Sahari, and M. Saleem, “Exact solution for functionally graded variable-thickness rotating disc with heat source, Proceedings of the Institution of Mechanical Engineers-Part C., Journal of Mechanical Engineering Science, vol. 224(11), pp. 2316–2331, 2010.
  • G. Arani, A. Loghman, A. Shajari, and S.A.R. Amir, “Semi-analytical solution of magneto-thermo-elastic stresses for functionally graded variable thickness rotating disks”, J. Mech. Sci. Technol., vol. 24(10), pp. 2107–2117, 2010.
  • M. Damircheli, and M. Azadi, “Temperature and thickness effects on thermal and mechanical stresses of rotating FG-disks”, Journal of Mechanical Science and Technology, vol. 25(3), pp. 827-836, 2011.
  • A. Hassani, M.H. Hojjati, G. Farrahi, and R.A. Alashti, “Semi-exact elastic solutions for thermo-mechanical analysis of functionally graded rotating disks”, Composite Structures, vol. 93(12), pp. 3239–3251, 2011.
  • N. Tutuncu, and B. Temel, “An efficient unified method for thermoelastic analysis of functionally graded rotating disks of variable thickness”, Mechanics of Advanced Materials and Structures, vol. 20(1), pp. 38-46, 2013.
  • M.E. Golmakani, “Large deflection thermoelastic analysis of shear deformable functionally graded variable thickness rotating disk”, Composites: Part B, vol. 45, pp. 1143-1155, 2013.
  • A. Kurşun, and M. Topçu, “Thermal stress analysis of functionally graded disc with variable thickness due to linearly increasing temperature load”, Arab J Sci Eng, vol. 38, pp. 3531–3549, 2013.
  • E. Mahdavi, R. AkbariAlashti, A.C. Darabi, and M. Alizadeh, “Linear thermoplastic analysis of FGM rotating discs with variable thickness”, Iranian Journal Of Mechanical Engineering, vol. 14(2), pp. 73-87, 2013.
  • M. Jabbari, M. Ghannad, and M.Z. Nejad, “Effect of thickness profile and FG function on rotating disks under thermal and mechanical loading”, Journal of Mechanics, vol. 32(1), pp. 35-46, 2016.
There are 48 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Articles
Authors

Vebil Yıldırım 0000-0001-9955-8423

Publication Date March 31, 2020
Acceptance Date September 18, 2020
Published in Issue Year 2020 Volume: 6 Issue: 1

Cite

APA Yıldırım, V. (2020). Exact Axisymmetric Thermal Analysis of Functionally Graded Disks with Continuously Hyperbolically Varying Thickness. International Journal of Engineering Technologies IJET, 6(1), 1-12. https://doi.org/10.19072/ijet.689703
AMA Yıldırım V. Exact Axisymmetric Thermal Analysis of Functionally Graded Disks with Continuously Hyperbolically Varying Thickness. IJET. March 2020;6(1):1-12. doi:10.19072/ijet.689703
Chicago Yıldırım, Vebil. “Exact Axisymmetric Thermal Analysis of Functionally Graded Disks With Continuously Hyperbolically Varying Thickness”. International Journal of Engineering Technologies IJET 6, no. 1 (March 2020): 1-12. https://doi.org/10.19072/ijet.689703.
EndNote Yıldırım V (March 1, 2020) Exact Axisymmetric Thermal Analysis of Functionally Graded Disks with Continuously Hyperbolically Varying Thickness. International Journal of Engineering Technologies IJET 6 1 1–12.
IEEE V. Yıldırım, “Exact Axisymmetric Thermal Analysis of Functionally Graded Disks with Continuously Hyperbolically Varying Thickness”, IJET, vol. 6, no. 1, pp. 1–12, 2020, doi: 10.19072/ijet.689703.
ISNAD Yıldırım, Vebil. “Exact Axisymmetric Thermal Analysis of Functionally Graded Disks With Continuously Hyperbolically Varying Thickness”. International Journal of Engineering Technologies IJET 6/1 (March 2020), 1-12. https://doi.org/10.19072/ijet.689703.
JAMA Yıldırım V. Exact Axisymmetric Thermal Analysis of Functionally Graded Disks with Continuously Hyperbolically Varying Thickness. IJET. 2020;6:1–12.
MLA Yıldırım, Vebil. “Exact Axisymmetric Thermal Analysis of Functionally Graded Disks With Continuously Hyperbolically Varying Thickness”. International Journal of Engineering Technologies IJET, vol. 6, no. 1, 2020, pp. 1-12, doi:10.19072/ijet.689703.
Vancouver Yıldırım V. Exact Axisymmetric Thermal Analysis of Functionally Graded Disks with Continuously Hyperbolically Varying Thickness. IJET. 2020;6(1):1-12.

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