Steel and Composite Structures

  • 제15권2호
  • /
  • Pages.221-245
  • /
  • 2013
  • /
  • 1229-9367(pISSN)
  • /
  • 1598-6233(eISSN)
테크노프레스 (Techno-Press)
권호 표지
DOI QR코드

DOI QR Code

Thermo-mechanical bending response with stretching effect of functionally graded sandwich plates using a novel shear deformation theory

  • Saidi, Hayat (Laboratoire des Materiaux et Hydrologie, Universite de Sidi Bel Abbes, Faculte de Technologie) ;
  • Houari, Mohammed Sid Ahmed (Laboratoire des Structures et Materiaux Avances dans le Genie Civil et Travaux Publics, Universite de Sidi Bel Abbes, Faculte de Technologie) ;
  • Tounsi, Abdelouahed (Laboratoire des Materiaux et Hydrologie, Universite de Sidi Bel Abbes, Faculte de Technologie) ;
  • Bedia, El Abbas Adda (Laboratoire des Materiaux et Hydrologie, Universite de Sidi Bel Abbes, Faculte de Technologie)
  • 투고 : 2013.01.29
  • 심사 : 2013.07.11
  • 발행 : 2013.08.25
⟨ 이전 논문 다음 논문 ⟩

초록

This paper presents an analytical solution to the thermomechanical bending analysis of functionally graded sandwich plates by using a new hyperbolic shear deformation theory in which the stretching effect is included. The modulus of elasticity of plates is assumed to vary according to a power law distribution in terms of the volume fractions of the constituents. The core layer is still homogeneous and made of an isotropic ceramic material. The effects of functionally graded material (FGM) layer thickness, volume fraction index, layer thickness ratio, thickness ratio and aspect ratio on the deflections and stresses of functionally graded sandwich plates are investigated.

키워드

참고문헌

  1. Abdelaziz, H.H., Atmane, H.A., Mechab, I., Boumia, L., Tounsi, A. and Adda Bedia, E.A. (2011), "Static analysis of functionally graded sandwich plates using an efficient and simple refined theory", Chinese J. Aeronaut., 24(4), 434-448. https://doi.org/10.1016/S1000-9361(11)60051-4
  2. Atmane, H.A., Tounsi, A., Mechab, I. and Adda Bedia, E.A. (2010), "Free vibration analysis of functionally graded plates resting on Winkler-Pasternak elastic foundations using a new shear deformation theory", Int. J. Mech. Mater. in Design, 6(2), 113-121. https://doi.org/10.1007/s10999-010-9110-x
  3. Bert, C.W. (1984), "A critical evaluation of new plate theories applied to laminated composites", Compos. Struct., 2(4), 794-805.
  4. Bian, Z.G., Chen, W.Q., Lim, C.W. and Zhang, N. (2005), "Analytical solutions for single- and multi-span functionally graded plates in cylindrical bending", Int. J. Solid. Struct., 42(24-25), 6433-6456. https://doi.org/10.1016/j.ijsolstr.2005.04.032
  5. Bouderba, B., Houari, M.S.A. and Tounsi, A. (2013), "Thermomechanical bending response of FGM thick plates resting on Winkler-Pasternak elastic foundations", Steel Compos. Struct., Int. J., 14(1), 85-104. https://doi.org/10.12989/scs.2013.14.1.085
  6. Bourada, M., Tounsi, A., Houari, M.S.A. and Adda Bedia, E.A. (2012), "A new four-variable refined plate theory for thermal buckling analysis of functionally graded sandwich plates", J. Sandwich Struct. Mater., 14(1), 5-33. https://doi.org/10.1177/1099636211426386
  7. Cheng, Z.Q. and Batra, R.C. (2000a), "Deflection relationships between the homogeneous kirchhoff plate theory and different functionally graded plate theories", Arch. Mech., 52(1), 143-158.
  8. Cheng, Z.Q. and Batra, R.C. (2000b), "Exact correspondence between eigenvalues of membranes and functionally graded simply supported polygonal plates", J. Sound Vib., 229(4), 879-895. https://doi.org/10.1006/jsvi.1999.2525
  9. Cheng, Z.Q. and Batra, R.C. (2000c), "Three-dimensional thermoelastic deformations of a functionally graded elliptic plate", Compos. Part B: Eng., 31(2), 97-106.
  10. Delale, F. and Erdogan, F. (1983), "The crack problem for a nonhomogeneous plane", J. Appl. Mech., 50(3), 609-614. https://doi.org/10.1115/1.3167098
  11. Hadji, L., Atmane, H.A., Tounsi, A., Mechab, I. and Adda Bedia, E.A. (2011), "Free vibration of functionally graded sandwich plates using four variable refined plate theory", Applied Mathematics and Mechanics, 32(7), 925-942. https://doi.org/10.1007/s10483-011-1470-9
  12. Hamidi, A., Zidi, M., Houari, M.S.A. and Tounsi, A. (2013), "A new four variable refined plate theory for bending response of functionally graded sandwich plates under thermomechanical loading", Compos. Part B:Eng. (In press).
  13. Houari, M.S.A, Benyoucef, S., Mechab, I., Tounsi, A. and Adda bedia, E.A. (2011), "Two variable refined plate theory for thermoelastic bending analysis of functionally graded sandwich plates", J. Thermal Stresses, 34(4), 315-334. https://doi.org/10.1080/01495739.2010.550806
  14. Karama, M., Afaq, K.S. and Mistou, S. (2003), "Mechanical behavior of laminated composite beam by the new multilayered laminated composite structures model with transverse shear stress continuity", Int. J. Solid. Struct., 40(6), 1525-1546. https://doi.org/10.1016/S0020-7683(02)00647-9
  15. Levinson, M. (1980), "An accurate simple theory of the statics and dynamics of elastic plates", Mech. Res. Commun., 7, 343-350. https://doi.org/10.1016/0093-6413(80)90049-X
  16. Lim, C.W., Yang, Q. and Lu, C.F. (2009), "Two-dimensional elasticity solutions for temperature-dependent in-plane vibration of FGM circular arches", Compos. Struct., 90(3), 323-329. https://doi.org/10.1016/j.compstruct.2009.03.014
  17. Lo, K.H., Chiristensen, R.M. and Wu, E.M. (1977), "A higher-order theory of plate deformation, part 2: laminated plates", J. Appl. Mech., 44(4), 669-676. https://doi.org/10.1115/1.3424155
  18. Lu, C.F., Lim, C.W. and Chen, W.Q. (2009a), "Semi-analytical analysis for multi-directional functionally graded plates: 3-D elasticity solutions", Int. J. Numer. Method. Eng., 79(1), 25-44. https://doi.org/10.1002/nme.2555
  19. Lu, C.F., Lim, C.W. and Chen, W.Q. (2009b), "Exact solutions for free vibrations of functionally graded thick plates on elastic foundations", Mech. Adv. Mater. Struct., 16(8), 576-584. https://doi.org/10.1080/15376490903138888
  20. Matsunaga, H. (2000), "Vibration and stability of cross-ply laminated composite plates according to a global higher-order plate theory", Compos. Struct., 48(4), 231-244. https://doi.org/10.1016/S0263-8223(99)00110-5
  21. Matsunaga, H. (2009), "Thermal buckling of functionally graded plates according to a 2 D higher-order deformation theory", Compos. Struct., 90(1), 76-86. https://doi.org/10.1016/j.compstruct.2009.02.004
  22. Merdaci, S., Tounsi, A., Houari, M.S.A., Mechab, I., Hebali, H. and Benyoucef, S. (2011), "Two new refined shear displacement models for functionally graded sandwich plates", Arch. Appl. Mech., 81(11), 1507-1522. https://doi.org/10.1007/s00419-010-0497-5
  23. Mindlin, R.D. (1951), "Influence of rotatory inertia and shear on flexural vibrations of isotropic elastic plates", J. Appl. Mech., 73, 31-38.
  24. Murthy, M.V. (1981), "An improved transverse shear deformation theory for laminated anisotropic plates", NASA Technical Paper 1903.
  25. Reddy, J.N. (1984), "A simple higher-order theory for laminated composite plates", J. Appl. Mech., 51(4), 745-752. https://doi.org/10.1115/1.3167719
  26. Reddy, J.N. (2000), "Analysis of functionally graded plates", Int. J. Num. Method. Eng., 47(1-3), 663-684. https://doi.org/10.1002/(SICI)1097-0207(20000110/30)47:1/3<663::AID-NME787>3.0.CO;2-8
  27. Reissner, E. (1945), "The Effect of transverse shear deformation on the bending of elastic plates", J. Appl. Mech., 12, 69-77.
  28. Simsek, M. (2009), Static analysis of a functionally graded beam under a uniformly distributed load by Ritz method, Int. J. Eng. Appl. Sci., 1(3), 1-11.
  29. Simsek, M. (2010), "Vibration analysis of a functionally graded beam under a moving mass by using different beam theories", Compos. Struct., 92(4), 904-917. https://doi.org/10.1016/j.compstruct.2009.09.030
  30. Tounsi, A., Houari, M.S.A., Benyoucef, S. and Adda Bedia, E.A. (2013), "A refined trigonometric shear deformation theory for thermoelastic bending of functionally graded sandwich plates", Aerosp. Sci. Tech., 24(1), 209-220. https://doi.org/10.1016/j.ast.2011.11.009
  31. Uymaz, B. and Aydogdu, M. (2013), "Three dimensional shear buckling of FG plates with various boundary conditions", Composite Structures, 96, 670-682. https://doi.org/10.1016/j.compstruct.2012.08.031
  32. Vel, S.S. and Batra, R.C. (2002), "Exact Solution for Thermoelastic Deformations of Functionally Graded Thick Rectangular Plates", AIAA J., 40(7), 1421-1433. https://doi.org/10.2514/2.1805
  33. Yaghoobi, H. and Yaghoobi, P. (2013), "Buckling analysis of sandwich plates with FGM face sheets resting on elastic foundation with various boundary conditions: An analytical approach", Meccanica, March. (In press).
  34. Ying, J., Lu, C.F. and Lim, C.W. (2009), "3D thermoelasticity solutions for functionally graded thick plates", J Zhejiang Univ Sci A, 10(3), 327-336. https://doi.org/10.1631/jzus.A0820406
  35. Zhang, X.Z., Kitipornchai, S., Liew, K.M., Lim, C.W. and Peng, L.X. (2003), "Thermal stresses around a circular hole in a functionally graded plate", J. Therm. Stresses, 26(4), 379-390. https://doi.org/10.1080/713855900
  36. Zenkour, A.M. and Alghamdi, N. (2008), "Thermoelastic bending analysis of functionally graded sandwich plates", J. Mater. Sci., 43(8), 2574-2589. https://doi.org/10.1007/s10853-008-2476-6
  37. Zenkour, A.M. and Alghamdi, N. (2010), "Bending analysis of functionally graded sandwich plates under the effect of mechanical and thermal loads", Mech. Adv. Mater. Struct., 17(6), 419-432. https://doi.org/10.1080/15376494.2010.483323
  38. Zeng, Q.C., Lim, C.W., Lu, C.F. and Yang, Q. (2012), "Asymptotic two-dimensional elasticity approach for free vibration of FGM circular arches", Mech. Adv. Mater. Struct., 19(1-3), 29-38. https://doi.org/10.1080/15376494.2011.572235

피인용 문헌

  1. Analytical solution for bending analysis of functionally graded beam vol.19, pp.4, 2015, https://doi.org/10.12989/scs.2015.19.4.829
  2. Flexure of power law governed functionally graded plates using ABAQUS UMAT vol.46, 2015, https://doi.org/10.1016/j.ast.2015.06.021
  3. A numerical tool for thermo-mechanical analysis of multilayer stepped structures vol.48, pp.6, 2013, https://doi.org/10.12989/sem.2013.48.6.757
  4. Nonlinear dynamic response and vibration of shear deformable imperfect eccentrically stiffened S-FGM circular cylindrical shells surrounded on elastic foundations vol.40, 2015, https://doi.org/10.1016/j.ast.2014.11.005
  5. On vibration properties of functionally graded nano-plate using a new nonlocal refined four variable model vol.18, pp.4, 2015, https://doi.org/10.12989/scs.2015.18.4.1063
  6. A new simple shear and normal deformations theory for functionally graded beams vol.18, pp.2, 2015, https://doi.org/10.12989/scs.2015.18.2.409
  7. A computational shear displacement model for vibrational analysis of functionally graded beams with porosities vol.19, pp.2, 2015, https://doi.org/10.12989/scs.2015.19.2.369
  8. Mathematical Modeling and Optimization of Functionally Graded Structures vol.2013, 2013, https://doi.org/10.1155/2013/536867
  9. Non-linear multi-mode buckling of non-symmetric FML/FGM thin-walled columns with open cross-sections under compression vol.167, 2017, https://doi.org/10.1016/j.compstruct.2017.01.072
  10. Size-dependent nonlinear vibration of beam-type porous materials with an initial geometrical curvature vol.184, 2018, https://doi.org/10.1016/j.compstruct.2017.10.052
  11. On bending, buckling and vibration responses of functionally graded carbon nanotube-reinforced composite beams vol.19, pp.5, 2015, https://doi.org/10.12989/scs.2015.19.5.1259
  12. Numerical simulation and experiments of titanium alloy engine blades based on laser shock processing vol.40, 2015, https://doi.org/10.1016/j.ast.2014.10.017
  13. A simple shear deformation theory for thermo-mechanical behaviour of functionally graded sandwich plates on elastic foundations vol.17, pp.2, 2015, https://doi.org/10.1177/1099636214554904
  14. A new higher order shear and normal deformation theory for functionally graded beams vol.18, pp.3, 2015, https://doi.org/10.12989/scs.2015.18.3.793
  15. Hygro-thermo-mechanical bending of S-FGM plates resting on variable elastic foundations using a four-variable trigonometric plate theory vol.18, pp.4, 2016, https://doi.org/10.12989/sss.2016.18.4.755
  16. On thermal stability of plates with functionally graded coefficient of thermal expansion vol.60, pp.2, 2016, https://doi.org/10.12989/sem.2016.60.2.313
  17. Thermoelastic behavior of advanced composite sandwich plates by using a new 6 unknown quasi-3D hybrid type HSDT vol.126, 2015, https://doi.org/10.1016/j.compstruct.2015.01.055
  18. Wave propagation in functionally graded plates with porosities using various higher-order shear deformation plate theories vol.53, pp.6, 2015, https://doi.org/10.12989/sem.2015.53.6.1143
  19. Analytical solution of nonlinear cylindrical bending for functionally graded plates vol.9, pp.5, 2015, https://doi.org/10.12989/gae.2015.9.5.631
  20. Bending analysis of FGM plates under hygro-thermo-mechanical loading using a four variable refined plate theory vol.34, 2014, https://doi.org/10.1016/j.ast.2014.02.001
  21. Hygrothermal analysis of a rotating smart exponentially graded cylindrical shell with imperfect bonding supported by an elastic foundation vol.43, 2015, https://doi.org/10.1016/j.ast.2015.02.012
  22. A new nonlocal hyperbolic shear deformation theory for nanobeams embedded in an elastic medium vol.55, pp.4, 2015, https://doi.org/10.12989/sem.2015.55.4.743
  23. Free vibration analysis of a rotating non-uniform functionally graded beam vol.19, pp.5, 2015, https://doi.org/10.12989/scs.2015.19.5.1279
  24. Buckling analysis of isotropic and orthotropic plates using a novel four variable refined plate theory vol.21, pp.6, 2016, https://doi.org/10.12989/scs.2016.21.6.1287
  25. Small-scale effects on the dynamic response of inhomogeneous nanobeams on elastic substrate under uniform dynamic load vol.132, pp.4, 2017, https://doi.org/10.1140/epjp/i2017-11441-9
  26. A new higher-order shear and normal deformation theory for functionally graded sandwich beams vol.19, pp.3, 2015, https://doi.org/10.12989/scs.2015.19.3.521
  27. Higher order refined computational models for the stability analysis of FGM plates – Analytical solutions vol.47, 2014, https://doi.org/10.1016/j.euromechsol.2014.06.003
  28. A new hyperbolic shear deformation plate theory for static analysis of FGM plate based on neutral surface position vol.8, pp.3, 2015, https://doi.org/10.12989/gae.2015.8.3.305
  29. Influence of the porosities on the free vibration of FGM beams vol.21, pp.3, 2015, https://doi.org/10.12989/was.2015.21.3.273
  30. Stress, vibration and buckling analyses of FGM plates—A state-of-the-art review vol.120, 2015, https://doi.org/10.1016/j.compstruct.2014.09.070
  31. Bending and buckling analyses of functionally graded material (FGM) size-dependent nanoscale beams including the thickness stretching effect vol.18, pp.2, 2015, https://doi.org/10.12989/scs.2015.18.2.425
  32. Thermomechanical effects on the bending of antisymmetric cross-ply composite plates using a four variable sinusoidal theory vol.19, pp.1, 2015, https://doi.org/10.12989/scs.2015.19.1.093
  33. A sinusoidal plate theory with 5-unknowns and stretching effect for thermomechanical bending of functionally graded sandwich plates vol.18, pp.1, 2015, https://doi.org/10.12989/scs.2015.18.1.235
  34. Thermal Buckling Response of Functionally Graded Plates with Clamped Boundary Conditions vol.38, pp.6, 2015, https://doi.org/10.1080/01495739.2015.1015900
  35. Thermo-mechanical postbuckling of symmetric S-FGM plates resting on Pasternak elastic foundations using hyperbolic shear deformation theory vol.57, pp.4, 2016, https://doi.org/10.12989/sem.2016.57.4.617
  36. Transverse vibration analysis of single-layered graphene sheet under magneto-thermal environment based on nonlocal plate theory vol.116, pp.16, 2014, https://doi.org/10.1063/1.4898759
  37. A simple hyperbolic shear deformation theory for vibration analysis of thick functionally graded rectangular plates resting on elastic foundations vol.11, pp.2, 2016, https://doi.org/10.12989/gae.2016.11.2.289
  38. A mechanical response of functionally graded nanoscale beam: an assessment of a refined nonlocal shear deformation theory beam theory vol.54, pp.4, 2015, https://doi.org/10.12989/sem.2015.54.4.693
  39. A refined theory with stretching effect for the flexure analysis of laminated composite plates vol.11, pp.5, 2016, https://doi.org/10.12989/gae.2016.11.5.671
  40. Effects of nonlinear hygrothermomechanical loading on bending of FGM rectangular plates resting on two-parameter elastic foundation using four-unknown plate theory pp.1521-074X, 2018, https://doi.org/10.1080/01495739.2018.1469962
  41. A new five unknown quasi-3D type HSDT for thermomechanical bending analysis of FGM sandwich plates vol.22, pp.5, 2013, https://doi.org/10.12989/scs.2016.22.5.975
  42. A four variable refined nth-order shear deformation theory for mechanical and thermal buckling analysis of functionally graded plates vol.13, pp.3, 2013, https://doi.org/10.12989/gae.2017.13.3.385
  43. Analysis of non symmetric FG sandwich plates under Thermo-mechanical loading using a novel shear deformation theory with stretching effect vol.241, pp.None, 2013, https://doi.org/10.1051/matecconf/201824101018
  44. Assessing the Effects of Porosity on the Bending, Buckling, and Vibrations of Functionally Graded Beams Resting on an Elastic Foundation by Using a New Refined Quasi-3D Theory vol.55, pp.2, 2013, https://doi.org/10.1007/s11029-019-09805-0
  45. A refined quasi-3D shear deformation theory for thermo-mechanical behavior of functionally graded sandwich plates on elastic foundations vol.21, pp.6, 2013, https://doi.org/10.1177/1099636217727577
  46. Bending analysis of anti-symmetric cross-ply laminated plates under nonlinear thermal and mechanical loadings vol.33, pp.1, 2013, https://doi.org/10.12989/scs.2019.33.1.081
  47. Static stability analysis of axially functionally graded tapered micro columns with different boundary conditions vol.33, pp.1, 2019, https://doi.org/10.12989/scs.2019.33.1.133
  48. Buckling response of functionally graded nanoplates under combined thermal and mechanical loadings vol.22, pp.4, 2020, https://doi.org/10.1007/s11051-020-04815-9
  49. Vibration behavior of trapezoidal sandwich plate with functionally graded-porous core and graphene platelet-reinforced layers vol.36, pp.1, 2013, https://doi.org/10.12989/scs.2020.36.1.047
  50. Vibration analysis of sandwich sector plate with porous core and functionally graded wavy carbon nanotube-reinforced layers vol.37, pp.6, 2013, https://doi.org/10.12989/scs.2020.37.6.711
  51. Thermomechanical Bending Analysis of FG Sandwich Plates Using a Quasi-Three-Dimensional Theory vol.34, pp.3, 2013, https://doi.org/10.1061/(asce)as.1943-5525.0001249