Abstract
Compositional gradient exponents and grading direction in functionally graded materials designed for high-temperature applications play an important role in thermo-mechanical behavior. Herein, the effect of the material composition of both radial and angular directions on the thermo-mechanical behavior of the functionally graded circular plates adhesively bonded (FGCP-AB) and adhesive is investigated. The material composition varies along a plane direction, not in the plate thickness direction. Heat transfer and elasticity equations in polar coordinates are solved for plane stress and plane strain using the finite difference method. Herein, the coordinate-dependent change in material properties is taken into account in the partial differential equations. In the results obtained, it has been emphasized that the variation of the material composition is an important design criterion which must be taken into consideration both in the adhesive–adhesive interface and in the arrangement of the thermal residual stress regions occurring in the FGCP-AB. This study is an important source in determining the thermal stress behavior according to the material composition and grading direction of functionally graded circular plates adhesively bonded that have not yet been mass-produced.
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References
Ahlawat N, Lal R (2016) Buckling and vibrations of multi-directional functionally graded circular plate resting on elastic foundation. Proced Eng 144:85–93. https://doi.org/10.1016/j.proeng.2016.05.010
Alibeigloo A (2016) Thermo elasticity solution of sandwich circular plate with functionally graded core using generalized differential quadrature method. Compos Struct 136:229–240. https://doi.org/10.1016/j.compstruct.2015.10.012
Apalak MK, Demirbas MD (2012) Thermal residual stresses in adhesively bonded in-plane functionally graded clamped circular hollow plate. J Adhes Sci Technol 27(14):1590–1623. https://doi.org/10.1163/016942410X525768
Arefi M (2013) Nonlinear thermoelastic analysis of thick-walled functionally graded piezoelectric cylinder. Acta Mech 224(11):2771–2783. https://doi.org/10.1007/s00707-013-0888-0
Arefi M (2014) A complete set of equations for piezo-magneto-elastic analysis of a functionally graded thick shell of revolution. Latin Am J Solids Struct 11:2073–2098. https://doi.org/10.1590/S1679-78252014001100009
Arefi M, Nahas I (2014) Nonlinear electro thermo elastic analysis of a thick spherical functionally graded piezoelectric shell. Compos Struct 118:510–518. https://doi.org/10.1016/j.compstruct.2014.08.002
Arefi M, Rahimi GH (2012) Comprehensive thermoelastic analysis of a functionally graded cylinder with different boundary conditions under internal pressure using first order shear deformation theory. Mechanika 18(1):5–13. https://doi.org/10.5755/j01.mech.18.1.1273
Arefi M, Rahimi GH (2012) The effect of nonhomogeneity and end supports on the thermo elastic behavior of a clamped–clamped FG cylinder under mechanical and thermal loads. Int J Press Vessels Pip 96–97:30–37. https://doi.org/10.1016/j.ijpvp.2012.05.009
Arefi M, Rahimi GH (2014) Application of shear deformation theory for two dimensional electro-elastic analysis of a FGP cylinder. Smart Struct Syst 13(1):1–24. https://doi.org/10.12989/sss.2014.13.1.001
Arefi M, Abbasi AR, Vaziri Sereshk MR (2016) Two-dimensional thermoelastic analysis of FG cylindrical shell resting on the Pasternak foundation subjected to mechanical and thermal loads based on FSDT formulation. J Therm Stress 39(5):554–570. https://doi.org/10.1080/01495739.2016.1158607
Arefi M, Faegh RK, Loghman A (2016) The effect of axially variable thermal and mechanical loads on the 2D thermoelastic response of FG cylindrical shell. J Therm Stress 39(12):1539–1559. https://doi.org/10.1080/01495739.2016.1217178
Bergman TL, Lavine SA, Incropera FP, Dewitt DP (2011) Fundamentals of heat and mass transfer, 7th edn. Wiley, New York ISBN: 9781118137253
Burlayenko VN, Altenbach H, Sadowski T, Dimitrova SD, Bhaskar A (2017) Modelling functionally graded materials in heat transfer and thermal stress analysis by means of graded finite elements. Appl Math Model 45:422–438. https://doi.org/10.1016/j.apm.2017.01.005
Causon DM, Mingham CG (2010) Introductory finite difference methods for PDEs. Ventus Publishing ApS, London ISBN 978-87-7681-642-1
Cengel YA (2011) Heat and mass transfer. McGraw-Hill Education, New York ISBN: 9780071077866
Chaabane N, Rivire B (2017) A splitting-based finite element method for the Biot poroelasticity system. Comput Math Appl. https://doi.org/10.1016/j.camwa.2017.12.009
Choules BD, Kokini K (1996) Architecture of functionally graded ceramic coatings against surface thermal fracture. J Eng Mater Technol 118(4):522–528. https://doi.org/10.1115/1.2805951
Cinefra M, Carrera E, Brischetto S, Belouettar S (2010) Thermo-mechanical analysis of functionally graded shells. J Therm Stress 33(10):942–963. https://doi.org/10.1016/j.actamat.2004.06.008
Demirbas MD (2017) Thermal stress analysis of functionally graded plates with temperature-dependent material properties using theory of elasticity. Compos Part B Eng 131:100–124. https://doi.org/10.1016/j.compositesb.2017.08.005
Demirbas MD, Apalak MK (2011) Thermal residual stresses in one-directional functionally graded plates subjected to in-plane heat flux. Numer Heat Transf Part A Appl 60:50–83. https://doi.org/10.1177/1464420713509699
Donatelli M, Dorostkar A, Mazza M, Neytcheva M, Serra-Capizzano S (2017) Function-based block multigrid strategy for a two-dimensional linear elasticity-type problem. Comput Math Appl 74(5):1015–1028. https://doi.org/10.1016/j.camwa.2017.05.024
Fazzolari FA, Carrera E (2014) Thermal stability of FGM sandwich plates under various through-the-thickness temperature distributions. J Therm Stress 37(12):1449–1481. https://doi.org/10.1080/01495739.2014.937251
Ghannad M, Parhizkar Yaghoobi M (2017) 2D thermo elastic behavior of a FG cylinder under thermomechanical loads using a first order temperature theory. Int J Press Vessels Pip 149:75–92. https://doi.org/10.1016/j.ijpvp.2016.12.002
Hatta H, Taya M (1985) Effective thermal conductivity of a misoriented short fiber composite. J Appl Phys 58(7):2478–2486. https://doi.org/10.1063/1.335924
Jaskowiec J, Milewski S (2015) The effective interface approach for coupling of the FE and meshless FD methods and applying essential boundary conditions. Comput Math Appl 70(5):962–979. https://doi.org/10.1016/j.camwa.2015.06.020
Jaskowiec J, Milewski S (2016) Coupling finite element method with meshless finite difference method in thermomechanical problems. Comput Math Appl 72(9):2259–2279. https://doi.org/10.1016/j.camwa.2016.08.020
Khoshgoftara MJ, Rahimi GH, Arefi M (2013) Exact solution of functionally graded thick cylinder with finite length under longitudinally non-uniform pressure. Mech Res Commun 51:61–66. https://doi.org/10.1016/j.mechrescom.2013.05.001
Lal R, Ahlawat N (2015) Buckling and vibration of functionally graded non-uniform circular plates resting on winkler foundation. Latin Am J Solids Struct 12(12):2231–2258. https://doi.org/10.1590/1679-78251595
Lal R, Ahlawat N (2017) Buckling and vibrations of two-directional FGM Mindlin circular plates under hydrostatic peripheral loading. Mech Adv Mater Struct. https://doi.org/10.1080/15376494.2017.1341576
Ma J, Zhou Z, Cui Z (2017) Hybrid Laplace transform and finite difference methods for pricing American options under complex models. Comput Math Appl 74(3):369–384. https://doi.org/10.1016/j.camwa.2017.04.018
Mahdavi E, Ghasemi A, Akbari Alashti R (2016) Elastic-plastic analysis of functionally graded rotating disks with variable thickness and temperature-dependent material properties under mechanical loading and unloading. Aerosp Sci Technol 59:57–68. https://doi.org/10.1016/j.ast.2016.10.011
MATLAB (2006) (Ver R2006b) The language of technical computing. http://www.mathworks.com. Accessed 26 June 2006
MatWeb (2017) Online materials information resource database. http://www.matweb.com. Accessed 26 June 2018
Moosaie A (2014) A nonlinear analysis of thermal stresses in an incompressible functionally graded hollow cylinder with temperature-dependent material properties. Eur J Mech A Solids 55:212–220. https://doi.org/10.1016/j.euromechsol.2015.09.005
Mori T, Tanaka K (1973) Average stress in matrix and average elastic energy of materials with misfittings inclusions. Acta Metall 21(5):517–574. https://doi.org/10.1016/0001-6160(73)90064-3
Najibi A, Talebitooti R (2017) Nonlinear transient thermo-elastic analysis of a 2D-FGM thick hollow finite length cylinder. Compos Part B Eng 111:211–227. https://doi.org/10.1016/j.compositesb.2016.11.055
Nemat-Alla M (2003) Reduction of thermal stresses by developing two-dimensional functionally graded materials. Int J Solids Struct 40(26):7339–7356. https://doi.org/10.1016/j.ijsolstr.2003.08.017
Noda N (1997) Thermal stresses intensity factor for functionally gradient plate with an edge crack. J Therm Stress 20(3–4):373–387. https://doi.org/10.1080/01495739708956108
Qin F, Chen J, Li Z, Cai M (2017) A Cartesian grid nonconforming immersed finite element method for planar elasticity interface problems. Comput Math Appl 73(3):404–418
Rahimi GH, Arefi M, Khoshgoftar MJ (2012) Electro elastic analysis of a pressurized thick-walled functionally graded piezoelectric cylinder using the first order shear deformation theory and energy method. Mechanika 18(3):292–300. https://doi.org/10.5755/j01.mech.18.3.1875
Rosen BW, Hashin Z (1970) Effective thermal expansion coefficients and specific heats of composite materials. Int J Eng Sci 8(2):157–173. https://doi.org/10.1016/0020-7225(70)90066-2
Saada AD (2013) Elasticity: theory and applications, Pergamon unified engineering series, vol 16, Elsevier. ISBN:1483159531, 9781483159539
Saied M, Ahmed K, Ahmed M, Nemat-Alla M, El-Sebaie M (2017) Investigations of solid oxide fuel cells with functionally graded electrodes for high performance and safe thermal stress. Int J Hydrog Energy 42(24):15887–15902. https://doi.org/10.1016/j.ijhydene.2017.05.071
Shariyat M, Behzad H, Shaterzadeh AR (2018) 3D thermomechanical buckling analysis of perforated annular sector plates with multiaxial material heterogeneities based on curved B-spline elements. Compos Struct 188:89–103. https://doi.org/10.1016/j.compstruct.2017.12.065
Shweta K, Santwana M (2013) Study of a problem of functionally graded hollow disk under different thermoelasticity theories. An analysis of phase-lag effects. Comput Math Appl 66(7):1306–1321. https://doi.org/10.1016/j.camwa.2013.07.029
Swaminathan K, Sangeetha DM (2017) Thermal analysis of FGM plates: a critical review of various modeling techniques and solution methods. Compos Struct 160:43–60. https://doi.org/10.1016/j.compstruct.2016.10.047
Taher HRD, Omidi M, Zadpoor AA, Nikooyan AA (2006) Free vibration of circular and annular plates with variable thickness and different combinations of boundary conditions. J Sound Vib 296(4–5):1084–1092. https://doi.org/10.1016/j.aej.2017.03.006
Wang L, Mai YW, Zhang XH (2004) Thermal shock resistance of functionally graded materials. Acta Mater 52(17):4961–4972
Wang Y, Chen KS, Mishler J, Cho SC, Adroher SC (2017) A review of polymer electrolyte membrane fuel cells: technology applications and needs on fundamental research. Appl Energy 88(4):981–1007. https://doi.org/10.1016/j.apenergy.2010.09.030
Wilmanski K (2010) Fundamentals of solid mechanics. IUSS Press, Pavia ISBN 978-88- 6198-047-1
Xie J, Hao W, Wang F (2017) Analysis of anode functional layer for minimizing thermal stress in solid oxide fuel cell. Appl Phys A Mater Sci Process 123:656. https://doi.org/10.1007/s00339-017-1266-x
Zur KK (2015) Green’s function in frequency analysis of circular thin plates of variable thickness. J Theor Appl Mech 53(4):873–884. https://doi.org/10.15632/jtam-pl.53.4.873
Zur KK (2016) Green’s function for frequency analysis of thin annular plates with nonlinear variable thickness. Appl Math Model 40(5–6):3601–3619. https://doi.org/10.1016/j.apm.2015.10.014
Zur KK (2018a) Quasi-Greens function approach to free vibration analysis of elastically supported functionally graded circular plates. Compos Struct 183:600–610. https://doi.org/10.1016/j.compstruct.2017.07.012
Zur KK (2018b) Free vibration analysis of elastically supported functionally graded annular plates via quasi-Green’s function method. Compos Part B 144:37–55. https://doi.org/10.1016/j.compositesb.2018.02.019
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Demirbas, M.D., Apalak, M.K. Investigation of the Thermo-elastic Response of Adhesively Bonded Two-Dimensional Functionally Graded Circular Plates Based on Theory of Elasticity. Iran J Sci Technol Trans Mech Eng 42, 415–433 (2018). https://doi.org/10.1007/s40997-018-0261-y
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DOI: https://doi.org/10.1007/s40997-018-0261-y