Research Article
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Year 2022, Volume: 14 Issue: 1, 15 - 39, 02.09.2022

Vebil Yıldırım

https://doi.org/10.24107/ijeas.1071038

Abstract

References

  • Tang S. Elastic stresses in rotating anisotropic discs. Int J Mech Sci (IJMS), 11, 509–517, 1969.
  • Murthy D, Sherbourne A. Elastic stresses in anisotropic discs of variable thickness. Int J Mech Sci, 12, 627-640, 1970.
  • Reddy TY, Srinath H. Elastic stresses in a rotating anisotropic annular disc of variable thickness and variable density. Int J Mech Sci, 16(2), 85-89, 1974.
  • Chang CI. A closed-form solution for an orthotropic rotating disc. J Appl Mech, 41(4), 1122–1123, 1974.
  • Chang CI. The anisotropic rotating discs. Int J Mech Sci 1975; 17(6): 397-402.
  • Bert CW. Centrifugal stresses in arbitrarily laminated, rectangular-anisotropic circular discs. J Strain Anal Eng Des, 10, 84-92, 1975.
  • Gurushankar GV. Thermal stresses in a rotating nonhomogeneous, anisotropic disc of varying thickness and density. J Strain Anal Eng Des, 10, 137-142, 1975.
  • Christensen RM, Wu EM. Optimal design of anisotropic (fiber-reinforced) flywheels. J Compos Mater, 11, 395-404, 1977.
  • Belingardi G, Genta G, Gola M. A study of the stress distribution in rotating, orthotropic discs. Composites, 10(2), 77-80, 1979.
  • Genta G, Gola M. The stress distribution in orthotropic rotating discs. J Appl Mech, 48, 559-562, 1981.
  • Jain R, Ramachandra K, Simha KRY. Rotating anisotropic disk of uniform strength. Int J Mech Sci, 41, 639–648, 1999.
  • Tutuncu N. Effect of anisotropy on stresses in rotating discs. Int J Mech Sci, 37, 873–881, 2000.
  • Zhou F, Ogawa A. Elastic solutions for a solid rotating disc with cubic anisotropy. J Appl Mech, 69, 81-83, 2002. Callioglu H. Stress analysis of an orthotropic rotating disc under thermal loading. J Reinf Plast Compos, 23(17), 1857–1869, 2004.
  • Callioglu H, Topcu M, Altan G. Stress analysis of curvilinearly orthotropic rotating discs under mechanical and thermal loading. J Reinf Plast Compos, 24, 831-838, 2005.
  • Sayer M, Topcu M, Bektas NB, Tarakcilar AR. Thermoelastic stress analysis in a thermoplastic composite disc. Sci Eng Compos Mater, 12(4), 251–260, 2005.
  • Tahani M, Nosier A, Zebarjad SM. Deformation and stress analysis of circumferentially fiber-reinforced composite disks. Int J Solids Struct, 42(9-10), 2741–2754, 2005.
  • Zenkour AM, Allam NMN. On the rotating fiber-reinforced viskoelastic composite solid and annular disks of variable thickness. Int J Comput Methods Eng Sci Mech, 7, 21-31,2006.
  • Callioglu H, Topcu M, Tarakçılar AR. Elastic-plastic stress analysis of an orthotropic rotating disc. Int J Mech Sci, 48, 985-990, 2006.
  • Callioglu H. Thermal stress analysis of curvilinearly orthotropic rotating discs. J Thermoplast Compos Mater, 20, 357-369, 2007.
  • Alexandrova N, Vila Real PMM. Deformation and stress analysis of an anisotropic rotating annular disk. Int J Comput Methods Eng Sci Mech, 9(1), 43–50, 2008.
  • Sen F, Koruvatan T, Aldas K, Thermal residual stresses in thermoplastic composite disc with holes using 3D-FEM. Adv Compos Lett, 23(4), 79-87, 2014.
  • Eraslan AN, Kaya Y, Varlı E. Analytical solutions to orthotropic variable thickness disk problems. Pamukkale University Journal of Engineering Sciences, 22(1), 24–30, 2016.
  • Yıldırım V. The complementary functions method (CFM) solution to the elastic analysis of polar orthotropic rotating discs. Journal of Applied and Computational Mechanics (JACM), 4(3), 216-230, 2018. DOI: 10.22055/JACM.2017.23188.1150
  • Horgan C, Chan A. The pressurized hollow cylinder or disk problem for functionally graded isotropic linearly elastic materials. J Elasticity, 55, 43-59, 1999.
  • Horgan C, Chan A. The stress response of functionally graded isotropic linearly elastic rotating disks. J Elasticity, 55, 219-230, 1999.
  • Zenkour AM. Analytical solutions for rotating exponentially-graded annular disks with various boundary conditions. Int J Struct Stab Dy, 5, 557-577, 2005.
  • Eraslan AN, Akiş T. On the plane strain and plane stress solutions of functionally graded rotating solid shaft and solid disk problems. Acta Mechanica, 181(1–2), 43–63, 2006.
  • Zenkour AM. Elastic deformation of the rotating functionally graded annular disk with rigid casing. J Mater Sci, 42, 9717-9724, 2007.
  • You LH, You XY, Zhang JJ, Li J. On rotating circular disks with varying material properties. Zeitschrift für angewandte Mathematik und Physik ZAMP, 58, 1068–1084, 2007. Bayat M, Saleem M, Sahari B, Hamouda A, Mahdi E. Analysis of functionally graded rotating disks with variable thickness. Mech Res Commun, 35, 283-309, 2008.
  • Vivio F, Vullo V. Elastic stress analysis of rotating converging conical disks subjected to thermal load and having variable density along the radius. Int J Solids Struct, 44, 7767–7784, 2007.
  • Vullo V, Vivio F. Elastic stress analysis of non-linear variable thickness rotating disks subjected to thermal load and having variable density along the radius. Int J Solids Struct, 45, 5337–5355, 2008.
  • Hojjati MH, Jafari. S Semi exact solution of elastic non uniform thickness and density rotating disks by Homotopy Perturbation and Adomian's decomposition methods Part I: Elastic solution. Int J Pres Ves Pip, 85, 871-878, 2008.
  • Hojjati MH, Hassani A. Theoretical and numerical analyses of rotating discs of nonuniform thickness and density. Int J Pres Ves Pip, 85, 694-700, 2008.
  • Nie GJ, Batra RC. Stress analysis and material tailoring in isotropic linear thermoelastic incompressible functionally graded rotating disks of variable thickness. Compos Struct, 92, 720-729, 2010.
  • Çallıoğlu H, Bektaş NB, Sayer M. Stress analysis of functionally graded rotating discs: Analytical and numerical solutions. Acta Mech Sinica, 27, 950-955, 2011.
  • Hassani A, Hojjati MH, Farrahi G, Alashti RA. Semi-exact elastic solutions for thermomechanical analysis of functionally graded rotating disks. Compos Struct, 93, 3239-3251, 2011.
  • Zenkour AM, Mashat DS. Stress function of a rotating variable-thickness annular disk using exact and numerical methods. Engineering, 3, 422-430, 2011.
  • Argeso H. Analytical solutions to variable thickness and variable material property rotating disks for a new three-parameter variation function. Mech Based Des Struc, 40, 133-152, 2012.
  • Nejad MZ, Abedi M, Lotfian MH, Ghannad M. Elastic analysis of exponential FGM disks subjected to internal and external pressure. Central European Journal of Engineering, 3, 459-465, 2013.
  • Nejad MZ, Rastgoo A, Hadi A. Exact elasto-plastic analysis of rotating disks made of functionally graded materials. Int J Eng Sci, 85, 47-57, 2014.
  • Eraslan AN, Arslan E. Analytical and numerical solutions to a rotating FGM disk. Journal of Multidisciplinary Engineering Science and Technology (JMEST), 2(10), 2843-2850, 2015.
  • Yıldırım V. Analytic solutions to power-law graded hyperbolic rotating discs subjected to different boundary conditions. International Journal of Engineering & Applied Sciences (IJEAS), 8(1), 38-52, 2016.
  • Yıldırım V, Kacar İ. Introducing a computer package program for elastic analysis of functionally graded rotating thick-walled annular structures. Digital Proceeding of ICOCEE – Cappadocia 2017, S. Sahinkaya and E. Kalıpcı (Editors), Nevsehir, TURKEY, May 8-10, 1733-1742, 2017.
  • Yıldırım V. Effects of inhomogeneity and thickness parameters on the elastic response of a pressurized hyperbolic annulus/disc made of functionally graded material. International Journal of Engineering & Applied Sciences (IJEAS), 9(3), 36-50, 2017. DOI: 10.24107/ijeas.329433
  • Gang M. Stress analysis of variable thickness rotating FG disc. International Journal of Pure and Applied Physics, 13(1), 158-161, 2017.
  • Yıldırım V. A parametric study on the centrifugal force-induced stress and displacements in power-law graded hyperbolic discs. Lati Am J Solids Stru (LAJSS), 15(4), 1-16, 2018.
  • Yıldırım V. Numerical elasticity solution for continuously tapered and arbitrarily functionally graded (FG) rotating disks via the transfer matrix approach. International Journal of Mathematics and Computational Science, 4(2), 48-73, 2018.
  • Khorsand M, Tang Y. Design functionally graded rotating disks under thermoelastic loads: Weight optimization. Int J Pres Ves Pip, 161, 33–40, 2018.
  • Durodola J, Attia O. Deformation and stresses in functionally graded rotating discs. Compos Sci Technol, 60, 987-995, 2000.
  • Chen J, Ding H, Chen W. Three-dimensional analytical solution for a rotating disc of functionally graded materials with transverse isotropy. Archive of Applied Mechanics, 77, 241-251, 2007.
  • Nie GJ, Zhong Z, Batra RC. Material tailoring for orthotropic rotating disks. Compos Sci Technol, 71, 406-414, 2011.
  • Kansal G, Parvez M. Thermal stress analysis of orthotropic graded rotating discs. International Journal of Modern Engineering Research (IJMER), 2(5), 3881-3885, 2012.
  • Lubarda VA. On pressurized curvilinearly orthotropic circular disc, cylinder and sphere made of radially nonuniform material. J Elasticity, 109, 103-133, 2012.
  • Peng XL, Li XF. Elastic analysis of rotating functionally graded polar orthotropic discs. Int J Mech Sci (IJMS), 60, 84-91, 2012.
  • Kacar I, Yıldırım V. Effect of the anisotropy ratios on the exact elastic behavior of functionally power-graded polar orthotropic rotating uniform discs under various boundary conditions. Digital Proceeding of ICOCEE – Cappadocia 2017, Nevsehir, Turkey, 1743-1752, 2017.
  • Essa S, Argeso H. Elastic analysis of variable profile and polar orthotropic FGM rotating disks for a variation function with three parameters. Acta Mechanica, 228, 3877–3899,2017.
  • Zheng Y, Bahaloo H, Mousanezhad D, Vaziri A, Nayeb-Hashemi H. Displacement and stress fields in a functionally graded fiber-reinforced rotating disk with nonuniform thickness and variable angular velocity. J Eng Mater-T ASME, 39, 031010-1-9, 2017.
  • Yıldırım V. Unified exact solutions to the hyperbolically tapered pressurized/rotating disks made of nonhomogeneous isotropic/orthotropic materials. International Journal of Advanced Materials Research, 4(1), 1-23, 2018.
  • ournal of the Brazilian Society of Mechanical Sciences and Engineering (2018) 40:320 https://doi.org/10.1007/s40430-018-1216-3 (0123456789().,-volV)(01 ournal of the Brazilian Society of Mechanical Sciences and Engineering (2018) 40:320 https://doi.org/10.1007/s40430-018-1216-3 (0123456789().,-volV)(01 Numerical/analytical solutions to the elastic response of arbitrarily functionally graded polar orthotropic rotating discs Yıldırım V. Numerical/analytical solutions to the elastic response of arbitrarily functionally graded polar orthotropic rotating discs. J Braz Soc Mech Sci & Eng, 40, 1-21, 2018.
  • İnan M. The Method of Initial Values and the Carry-Over Matrix in Elastomechanics. ODTÜ M., Publication, Ankara, No: 20, 1968.
  • Haktanır V, Kiral E. Statical analysis of elastically and continuously supported helicoidal structures by the transfer and stiffness matrix methods. Computers and Structures,49(4), 663-677, 1993.
  • Chen YZ, Lin XY. An alternative numerical solution of thick-walled cylinders and spheres made of functionally graded materials. Comp Mater Sci, 48, 640–647, 2010. Arici M, Granata MF. Generalized curved beam on elastic foundation solved by Transfer Matrix Method. Structural Engineering & Mechanics, 40(2), 279-295, 2011.
  • Garus S, Sochacki W. One dimensional phononic FDTD algorithm and transfer matrix method implementation for severin aperiodic multilayer. Journal of Applied Mathematics and Computational Mechanics, 16(4), 17-27, 2017.
  • Wimmer H, Nachbagauer K. Exact transfer- and stiffness matrix for the composite beam-column with refined zigzag kinematics. Compos Struct,189, 700-706, 2018.
  • Zhong H, Liu Z, Qin H, Liu Y. Static analysis of thin-walled space frame structures with arbitrary closed cross-sections using transfer matrix method. Thin Wall Struct, 123, 255-269, 2018.
  • Yıldırım V. Several stress resultant and deflection formulas for Euler-Bernoulli beams under concentrated and generalized power/sinusoidal distributed loads. International Journal of Engineering & Applied Sciences (IJEAS), 10(2), 35-632018. DOI: 10.24107/ijeas.430666
  • Aktas Z. Numerical Solutions of Two-Point Boundary Value Problems. Ankara, Turkey, METU, Dept of Computer Eng, 1972.
  • Roberts S, Shipman J. Fundamental matrix and two-point boundary-value problems. J Optimiz Theory App, 28(1), 77-88, 1979.
  • Haktanir V, Kıral E. Direct application of complementary functions method to axisymmetrical shells and cylindrical vaults (barrels). Journal of Isparta Eng Faculty of Akdeniz Un., 6, 220-239, 1991.
  • Haktanır V. The complementary functions method for the element stiffness matrix of arbitrary spatial bars of helicoidal axes. Int J Numer Meth Eng, 38(6), 1031–1056, 1995. Doi:10.1002/nme.1620380611
  • Yıldırım V. Free vibration analysis of non-cylindrical coil springs by combined use of the transfer matrix and the complementary functions methods. Commun Numer Meth Eng, 13(6), 487–494, 1997.
  • Yıldırım V. A parametric study on the natural frequencies of unidirectional composite conical springs. Commun Numer Meth Eng, 20(3), 207–227, 2004.
  • Eraslan AN, Orcan Y. Elastic–plastic deformation of a rotating solid disk of exponentially varying thickness. Mech Mater, 34, 423-432, 2002.
  • Yıldırım, V. The best grading pattern selection for the axisymmetric elastic response of pressurized inhomogeneous annular structures (sphere/ cylinder/annulus) including rotation. Journal of the Brazilian Society of Mechanical Sciences and Engineering. 42:109, 2020. https://doi.org/10.1007/s40430-020-2193-x
  • Avcar M., Hadji L., Civalek Ö. Natural frequency analysis of sigmoid functionally graded sandwich beams in the framework of high order shear deformation theory. Composite Structures, 276, 114564, 2021. https://doi.org/10.1016/j.compstruct.2021.114564.
  • Hadji L., Avcar M., Zouatnia N. Natural frequency analysis of imperfect FG sandwich plates resting on Winkler-Pasternak foundation. Materials Today: Proceedings, 53(1), 153-160, 2022. https://doi.org/10.1016/j.matpr.2021.12.485.
  • Civalek, Ö., Avcar, M. Free vibration and buckling analyses of CNT reinforced laminated non-rectangular plates by discrete singular convolution method. Engineering with Computers. 2020. https://doi.org/10.1007/s00366-020-01168-8
  • Arslan E., Mack W., Apatay T. Thermo-mechanically loaded steel/aluminum functionally graded spherical containers and pressure vessels. International Journal of Pressure Vessels and Piping. 191, 104334, 2021. https://doi.org/10.1016/j.ijpvp.2021.104334

Numerical Elastic Analysis of Functionally Graded (FG) Polar Orthotropic and Exponentially Varying-Thickness Rotating Disks via Combined Complementary Functions and the Transfer Matrix Methods

Year 2022, Volume: 14 Issue: 1, 15 - 39, 02.09.2022

Vebil Yıldırım

https://doi.org/10.24107/ijeas.1071038

Abstract

In the present paper, the transfer matrix method (TMM) is to be employed for the first time in the open literature for the elastic analysis of variable-thickness disks made of functionally graded (FG) two orthotropic materials. Those materials are assumed to be continuously radially functionally graded (FG) based on the Voigt rule of mixture with two models. An exponential disk profile with two parameters is considered. Effects of the different boundary conditions (free-free, fixed-free, and fixed-fixed) and inhomogeneity indexes on the elastic response of the disk rotating at a constant angular speed are also examined. Additionally, direct numerical solutions of the problem with the complementary functions method (CFM) are presented in tabular forms together with the transfer matrix method solutions in which CFM was used as an assistant tool. It was observed that both location and amplitude of the maximum equivalent stress are affected by the grading models chosen. Such differences become more obvious for small values of the inhomogeneity indexes. The maximum relative error may reach 18% for the two material grading models in fixed-free disks. Consequently, Model-I may be recommended for just the inhomogeneity indexes equal to or greater than 0.5.

Keywords

Rotating disk Functionally graded Polar orthotropic Variable thickness Transfer matrix method Complementary functions method Initial value problem

References

  • Tang S. Elastic stresses in rotating anisotropic discs. Int J Mech Sci (IJMS), 11, 509–517, 1969.
  • Murthy D, Sherbourne A. Elastic stresses in anisotropic discs of variable thickness. Int J Mech Sci, 12, 627-640, 1970.
  • Reddy TY, Srinath H. Elastic stresses in a rotating anisotropic annular disc of variable thickness and variable density. Int J Mech Sci, 16(2), 85-89, 1974.
  • Chang CI. A closed-form solution for an orthotropic rotating disc. J Appl Mech, 41(4), 1122–1123, 1974.
  • Chang CI. The anisotropic rotating discs. Int J Mech Sci 1975; 17(6): 397-402.
  • Bert CW. Centrifugal stresses in arbitrarily laminated, rectangular-anisotropic circular discs. J Strain Anal Eng Des, 10, 84-92, 1975.
  • Gurushankar GV. Thermal stresses in a rotating nonhomogeneous, anisotropic disc of varying thickness and density. J Strain Anal Eng Des, 10, 137-142, 1975.
  • Christensen RM, Wu EM. Optimal design of anisotropic (fiber-reinforced) flywheels. J Compos Mater, 11, 395-404, 1977.
  • Belingardi G, Genta G, Gola M. A study of the stress distribution in rotating, orthotropic discs. Composites, 10(2), 77-80, 1979.
  • Genta G, Gola M. The stress distribution in orthotropic rotating discs. J Appl Mech, 48, 559-562, 1981.
  • Jain R, Ramachandra K, Simha KRY. Rotating anisotropic disk of uniform strength. Int J Mech Sci, 41, 639–648, 1999.
  • Tutuncu N. Effect of anisotropy on stresses in rotating discs. Int J Mech Sci, 37, 873–881, 2000.
  • Zhou F, Ogawa A. Elastic solutions for a solid rotating disc with cubic anisotropy. J Appl Mech, 69, 81-83, 2002. Callioglu H. Stress analysis of an orthotropic rotating disc under thermal loading. J Reinf Plast Compos, 23(17), 1857–1869, 2004.
  • Callioglu H, Topcu M, Altan G. Stress analysis of curvilinearly orthotropic rotating discs under mechanical and thermal loading. J Reinf Plast Compos, 24, 831-838, 2005.
  • Sayer M, Topcu M, Bektas NB, Tarakcilar AR. Thermoelastic stress analysis in a thermoplastic composite disc. Sci Eng Compos Mater, 12(4), 251–260, 2005.
  • Tahani M, Nosier A, Zebarjad SM. Deformation and stress analysis of circumferentially fiber-reinforced composite disks. Int J Solids Struct, 42(9-10), 2741–2754, 2005.
  • Zenkour AM, Allam NMN. On the rotating fiber-reinforced viskoelastic composite solid and annular disks of variable thickness. Int J Comput Methods Eng Sci Mech, 7, 21-31,2006.
  • Callioglu H, Topcu M, Tarakçılar AR. Elastic-plastic stress analysis of an orthotropic rotating disc. Int J Mech Sci, 48, 985-990, 2006.
  • Callioglu H. Thermal stress analysis of curvilinearly orthotropic rotating discs. J Thermoplast Compos Mater, 20, 357-369, 2007.
  • Alexandrova N, Vila Real PMM. Deformation and stress analysis of an anisotropic rotating annular disk. Int J Comput Methods Eng Sci Mech, 9(1), 43–50, 2008.
  • Sen F, Koruvatan T, Aldas K, Thermal residual stresses in thermoplastic composite disc with holes using 3D-FEM. Adv Compos Lett, 23(4), 79-87, 2014.
  • Eraslan AN, Kaya Y, Varlı E. Analytical solutions to orthotropic variable thickness disk problems. Pamukkale University Journal of Engineering Sciences, 22(1), 24–30, 2016.
  • Yıldırım V. The complementary functions method (CFM) solution to the elastic analysis of polar orthotropic rotating discs. Journal of Applied and Computational Mechanics (JACM), 4(3), 216-230, 2018. DOI: 10.22055/JACM.2017.23188.1150
  • Horgan C, Chan A. The pressurized hollow cylinder or disk problem for functionally graded isotropic linearly elastic materials. J Elasticity, 55, 43-59, 1999.
  • Horgan C, Chan A. The stress response of functionally graded isotropic linearly elastic rotating disks. J Elasticity, 55, 219-230, 1999.
  • Zenkour AM. Analytical solutions for rotating exponentially-graded annular disks with various boundary conditions. Int J Struct Stab Dy, 5, 557-577, 2005.
  • Eraslan AN, Akiş T. On the plane strain and plane stress solutions of functionally graded rotating solid shaft and solid disk problems. Acta Mechanica, 181(1–2), 43–63, 2006.
  • Zenkour AM. Elastic deformation of the rotating functionally graded annular disk with rigid casing. J Mater Sci, 42, 9717-9724, 2007.
  • You LH, You XY, Zhang JJ, Li J. On rotating circular disks with varying material properties. Zeitschrift für angewandte Mathematik und Physik ZAMP, 58, 1068–1084, 2007. Bayat M, Saleem M, Sahari B, Hamouda A, Mahdi E. Analysis of functionally graded rotating disks with variable thickness. Mech Res Commun, 35, 283-309, 2008.
  • Vivio F, Vullo V. Elastic stress analysis of rotating converging conical disks subjected to thermal load and having variable density along the radius. Int J Solids Struct, 44, 7767–7784, 2007.
  • Vullo V, Vivio F. Elastic stress analysis of non-linear variable thickness rotating disks subjected to thermal load and having variable density along the radius. Int J Solids Struct, 45, 5337–5355, 2008.
  • Hojjati MH, Jafari. S Semi exact solution of elastic non uniform thickness and density rotating disks by Homotopy Perturbation and Adomian's decomposition methods Part I: Elastic solution. Int J Pres Ves Pip, 85, 871-878, 2008.
  • Hojjati MH, Hassani A. Theoretical and numerical analyses of rotating discs of nonuniform thickness and density. Int J Pres Ves Pip, 85, 694-700, 2008.
  • Nie GJ, Batra RC. Stress analysis and material tailoring in isotropic linear thermoelastic incompressible functionally graded rotating disks of variable thickness. Compos Struct, 92, 720-729, 2010.
  • Çallıoğlu H, Bektaş NB, Sayer M. Stress analysis of functionally graded rotating discs: Analytical and numerical solutions. Acta Mech Sinica, 27, 950-955, 2011.
  • Hassani A, Hojjati MH, Farrahi G, Alashti RA. Semi-exact elastic solutions for thermomechanical analysis of functionally graded rotating disks. Compos Struct, 93, 3239-3251, 2011.
  • Zenkour AM, Mashat DS. Stress function of a rotating variable-thickness annular disk using exact and numerical methods. Engineering, 3, 422-430, 2011.
  • Argeso H. Analytical solutions to variable thickness and variable material property rotating disks for a new three-parameter variation function. Mech Based Des Struc, 40, 133-152, 2012.
  • Nejad MZ, Abedi M, Lotfian MH, Ghannad M. Elastic analysis of exponential FGM disks subjected to internal and external pressure. Central European Journal of Engineering, 3, 459-465, 2013.
  • Nejad MZ, Rastgoo A, Hadi A. Exact elasto-plastic analysis of rotating disks made of functionally graded materials. Int J Eng Sci, 85, 47-57, 2014.
  • Eraslan AN, Arslan E. Analytical and numerical solutions to a rotating FGM disk. Journal of Multidisciplinary Engineering Science and Technology (JMEST), 2(10), 2843-2850, 2015.
  • Yıldırım V. Analytic solutions to power-law graded hyperbolic rotating discs subjected to different boundary conditions. International Journal of Engineering & Applied Sciences (IJEAS), 8(1), 38-52, 2016.
  • Yıldırım V, Kacar İ. Introducing a computer package program for elastic analysis of functionally graded rotating thick-walled annular structures. Digital Proceeding of ICOCEE – Cappadocia 2017, S. Sahinkaya and E. Kalıpcı (Editors), Nevsehir, TURKEY, May 8-10, 1733-1742, 2017.
  • Yıldırım V. Effects of inhomogeneity and thickness parameters on the elastic response of a pressurized hyperbolic annulus/disc made of functionally graded material. International Journal of Engineering & Applied Sciences (IJEAS), 9(3), 36-50, 2017. DOI: 10.24107/ijeas.329433
  • Gang M. Stress analysis of variable thickness rotating FG disc. International Journal of Pure and Applied Physics, 13(1), 158-161, 2017.
  • Yıldırım V. A parametric study on the centrifugal force-induced stress and displacements in power-law graded hyperbolic discs. Lati Am J Solids Stru (LAJSS), 15(4), 1-16, 2018.
  • Yıldırım V. Numerical elasticity solution for continuously tapered and arbitrarily functionally graded (FG) rotating disks via the transfer matrix approach. International Journal of Mathematics and Computational Science, 4(2), 48-73, 2018.
  • Khorsand M, Tang Y. Design functionally graded rotating disks under thermoelastic loads: Weight optimization. Int J Pres Ves Pip, 161, 33–40, 2018.
  • Durodola J, Attia O. Deformation and stresses in functionally graded rotating discs. Compos Sci Technol, 60, 987-995, 2000.
  • Chen J, Ding H, Chen W. Three-dimensional analytical solution for a rotating disc of functionally graded materials with transverse isotropy. Archive of Applied Mechanics, 77, 241-251, 2007.
  • Nie GJ, Zhong Z, Batra RC. Material tailoring for orthotropic rotating disks. Compos Sci Technol, 71, 406-414, 2011.
  • Kansal G, Parvez M. Thermal stress analysis of orthotropic graded rotating discs. International Journal of Modern Engineering Research (IJMER), 2(5), 3881-3885, 2012.
  • Lubarda VA. On pressurized curvilinearly orthotropic circular disc, cylinder and sphere made of radially nonuniform material. J Elasticity, 109, 103-133, 2012.
  • Peng XL, Li XF. Elastic analysis of rotating functionally graded polar orthotropic discs. Int J Mech Sci (IJMS), 60, 84-91, 2012.
  • Kacar I, Yıldırım V. Effect of the anisotropy ratios on the exact elastic behavior of functionally power-graded polar orthotropic rotating uniform discs under various boundary conditions. Digital Proceeding of ICOCEE – Cappadocia 2017, Nevsehir, Turkey, 1743-1752, 2017.
  • Essa S, Argeso H. Elastic analysis of variable profile and polar orthotropic FGM rotating disks for a variation function with three parameters. Acta Mechanica, 228, 3877–3899,2017.
  • Zheng Y, Bahaloo H, Mousanezhad D, Vaziri A, Nayeb-Hashemi H. Displacement and stress fields in a functionally graded fiber-reinforced rotating disk with nonuniform thickness and variable angular velocity. J Eng Mater-T ASME, 39, 031010-1-9, 2017.
  • Yıldırım V. Unified exact solutions to the hyperbolically tapered pressurized/rotating disks made of nonhomogeneous isotropic/orthotropic materials. International Journal of Advanced Materials Research, 4(1), 1-23, 2018.
  • ournal of the Brazilian Society of Mechanical Sciences and Engineering (2018) 40:320 https://doi.org/10.1007/s40430-018-1216-3 (0123456789().,-volV)(01 ournal of the Brazilian Society of Mechanical Sciences and Engineering (2018) 40:320 https://doi.org/10.1007/s40430-018-1216-3 (0123456789().,-volV)(01 Numerical/analytical solutions to the elastic response of arbitrarily functionally graded polar orthotropic rotating discs Yıldırım V. Numerical/analytical solutions to the elastic response of arbitrarily functionally graded polar orthotropic rotating discs. J Braz Soc Mech Sci & Eng, 40, 1-21, 2018.
  • İnan M. The Method of Initial Values and the Carry-Over Matrix in Elastomechanics. ODTÜ M., Publication, Ankara, No: 20, 1968.
  • Haktanır V, Kiral E. Statical analysis of elastically and continuously supported helicoidal structures by the transfer and stiffness matrix methods. Computers and Structures,49(4), 663-677, 1993.
  • Chen YZ, Lin XY. An alternative numerical solution of thick-walled cylinders and spheres made of functionally graded materials. Comp Mater Sci, 48, 640–647, 2010. Arici M, Granata MF. Generalized curved beam on elastic foundation solved by Transfer Matrix Method. Structural Engineering & Mechanics, 40(2), 279-295, 2011.
  • Garus S, Sochacki W. One dimensional phononic FDTD algorithm and transfer matrix method implementation for severin aperiodic multilayer. Journal of Applied Mathematics and Computational Mechanics, 16(4), 17-27, 2017.
  • Wimmer H, Nachbagauer K. Exact transfer- and stiffness matrix for the composite beam-column with refined zigzag kinematics. Compos Struct,189, 700-706, 2018.
  • Zhong H, Liu Z, Qin H, Liu Y. Static analysis of thin-walled space frame structures with arbitrary closed cross-sections using transfer matrix method. Thin Wall Struct, 123, 255-269, 2018.
  • Yıldırım V. Several stress resultant and deflection formulas for Euler-Bernoulli beams under concentrated and generalized power/sinusoidal distributed loads. International Journal of Engineering & Applied Sciences (IJEAS), 10(2), 35-632018. DOI: 10.24107/ijeas.430666
  • Aktas Z. Numerical Solutions of Two-Point Boundary Value Problems. Ankara, Turkey, METU, Dept of Computer Eng, 1972.
  • Roberts S, Shipman J. Fundamental matrix and two-point boundary-value problems. J Optimiz Theory App, 28(1), 77-88, 1979.
  • Haktanir V, Kıral E. Direct application of complementary functions method to axisymmetrical shells and cylindrical vaults (barrels). Journal of Isparta Eng Faculty of Akdeniz Un., 6, 220-239, 1991.
  • Haktanır V. The complementary functions method for the element stiffness matrix of arbitrary spatial bars of helicoidal axes. Int J Numer Meth Eng, 38(6), 1031–1056, 1995. Doi:10.1002/nme.1620380611
  • Yıldırım V. Free vibration analysis of non-cylindrical coil springs by combined use of the transfer matrix and the complementary functions methods. Commun Numer Meth Eng, 13(6), 487–494, 1997.
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There are 78 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Articles
Authors

Vebil Yıldırım 0000-0001-9955-8423

Publication Date September 2, 2022
Acceptance Date May 31, 2022
Published in Issue Year 2022 Volume: 14 Issue: 1

Cite

APA Yıldırım, V. (2022). Numerical Elastic Analysis of Functionally Graded (FG) Polar Orthotropic and Exponentially Varying-Thickness Rotating Disks via Combined Complementary Functions and the Transfer Matrix Methods. International Journal of Engineering and Applied Sciences, 14(1), 15-39. https://doi.org/10.24107/ijeas.1071038
AMA Yıldırım V. Numerical Elastic Analysis of Functionally Graded (FG) Polar Orthotropic and Exponentially Varying-Thickness Rotating Disks via Combined Complementary Functions and the Transfer Matrix Methods. IJEAS. September 2022;14(1):15-39. doi:10.24107/ijeas.1071038
Chicago Yıldırım, Vebil. “Numerical Elastic Analysis of Functionally Graded (FG) Polar Orthotropic and Exponentially Varying-Thickness Rotating Disks via Combined Complementary Functions and the Transfer Matrix Methods”. International Journal of Engineering and Applied Sciences 14, no. 1 (September 2022): 15-39. https://doi.org/10.24107/ijeas.1071038.
EndNote Yıldırım V (September 1, 2022) Numerical Elastic Analysis of Functionally Graded (FG) Polar Orthotropic and Exponentially Varying-Thickness Rotating Disks via Combined Complementary Functions and the Transfer Matrix Methods. International Journal of Engineering and Applied Sciences 14 1 15–39.
IEEE V. Yıldırım, “Numerical Elastic Analysis of Functionally Graded (FG) Polar Orthotropic and Exponentially Varying-Thickness Rotating Disks via Combined Complementary Functions and the Transfer Matrix Methods”, IJEAS, vol. 14, no. 1, pp. 15–39, 2022, doi: 10.24107/ijeas.1071038.
ISNAD Yıldırım, Vebil. “Numerical Elastic Analysis of Functionally Graded (FG) Polar Orthotropic and Exponentially Varying-Thickness Rotating Disks via Combined Complementary Functions and the Transfer Matrix Methods”. International Journal of Engineering and Applied Sciences 14/1 (September 2022), 15-39. https://doi.org/10.24107/ijeas.1071038.
JAMA Yıldırım V. Numerical Elastic Analysis of Functionally Graded (FG) Polar Orthotropic and Exponentially Varying-Thickness Rotating Disks via Combined Complementary Functions and the Transfer Matrix Methods. IJEAS. 2022;14:15–39.
MLA Yıldırım, Vebil. “Numerical Elastic Analysis of Functionally Graded (FG) Polar Orthotropic and Exponentially Varying-Thickness Rotating Disks via Combined Complementary Functions and the Transfer Matrix Methods”. International Journal of Engineering and Applied Sciences, vol. 14, no. 1, 2022, pp. 15-39, doi:10.24107/ijeas.1071038.
Vancouver Yıldırım V. Numerical Elastic Analysis of Functionally Graded (FG) Polar Orthotropic and Exponentially Varying-Thickness Rotating Disks via Combined Complementary Functions and the Transfer Matrix Methods. IJEAS. 2022;14(1):15-39.
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