Structural Engineering and Mechanics

  • 제41권6호
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  • Pages.775-789
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  • 2012
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  • 1225-4568(pISSN)
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  • 1598-6217(eISSN)
테크노프레스 (Techno-Press)
권호 표지
DOI QR코드

DOI QR Code

Post-buckling analysis of Timoshenko beams made of functionally graded material under thermal loading

  • Kocaturk, Turgut (Department of Civil Engineering, Yildiz Technical University, Davutpasa Campus) ;
  • Akbas, Seref Doguscan (Department of Civil Engineering, Yildiz Technical University, Davutpasa Campus)
  • 투고 : 2011.09.12
  • 심사 : 2012.02.21
  • 발행 : 2012.03.25
⟨ 이전 논문 다음 논문 ⟩

초록

This paper focuses on post-buckling analysis of functionally graded Timoshenko beam subjected to thermal loading by using the total Lagrangian Timoshenko beam element approximation. Material properties of the beam change in the thickness direction according to a power-law function. The beam is clamped at both ends. The considered highly non-linear problem is solved by using incremental displacement-based finite element method in conjunction with Newton-Raphson iteration method. As far as the authors know, there is no study on the post-buckling analysis of functionally graded Timoshenko beams under thermal loading considering full geometric non-linearity investigated by using finite element method. The convergence studies are made and the obtained results are compared with the published results. In the study, with the effects of material gradient property and thermal load, the relationships between deflections, end constraint forces, thermal buckling configuration and stress distributions through the thickness of the beams are illustrated in detail in post-buckling case.

키워드

참고문헌

  1. Akbas, S.D. and Kocatürk, T. (2011), "Post-buckling analysis of a simply supported beam under uniform thermal loading", Sci. Res. Essay., 6(4), 1135-1142.
  2. Akbas, S.D. (2011), "Thermal post-buckling analysis of functionally graded beams", PhD Thesis Term Report on May and November, Institute of Science at Yildiz Technical University ( stanbul).
  3. Akbas, S.D. and Kocaturk, T. (2011), "Eksenel Dogrultuda Fonksiyonel derecelendirilmi Timoshenko kirisinin sicaklik etkisi alt ndaki burkulma sonrasi davranisinin incelenmesi (Post-buckling behavior of axially functionally graded Timoshenko beam under the influence of temperature)", XVII. Turkish National Mechanic Congress, Elazig, Turkey, In Print (in Turkish).
  4. Alibeigloo, A. (2010), "Thermoelasticity analysis of functionally graded beam with integrated surface piezoelectric layers", Compos. Struct., 92, 1535-1543. https://doi.org/10.1016/j.compstruct.2009.10.030
  5. Anandrao, K.S., Gupta, R.K., Ramchandran, P. and Rao, V. (2010), "Thermal post-buckling analysis of uniform slender functionally graded material beams", Struct. Eng. Mech., 36(5), 545-560. https://doi.org/10.12989/sem.2010.36.5.545
  6. Bhangale, R.K. and Ganesan, N. (2006), "Thermoelastic buckling and vibration behavior of a functionally graded sandwich beam with constrained viscoelastic core", J. Sound Vib., 295, 294-316. https://doi.org/10.1016/j.jsv.2006.01.026
  7. Carpinteri, A. and Paggi, M. (2008), "Thermo-elastic mismatch in nonhomogeneous beams", J. Eng. Mat., 61(2-4), 371-384. https://doi.org/10.1007/s10665-008-9212-8
  8. Ching, H.K. and Yen, S.C. (2005), "Meshless local Petrov-Galerkin analysis for 2D functionally graded elastic solids under mechanical and thermal loads", Composites: Part B, 36, 223-240. https://doi.org/10.1016/j.compositesb.2004.09.007
  9. Ching, H.K. and Yen, S.C. (2005), "Transient thermoelastic deformations of 2-D functionally graded beams under nonuniformly convective heat supply", Compos. Struct., 73, 381-393.
  10. Farid, M., Zahedinejad, P. and 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", Struct. Eng. Mech., 31(1), 2-13.
  11. Felippa, C.A., Retrieved May (2011), "Notes on nonlinear finite element methods", http://www.colorado.edu/ engineering/cas/courses.d/NFEM.d/NFEM.Ch09.d/NFEM.Ch09.pdf
  12. Inan, O., Dag, S. and Erdogan, F. (2005), "Three dimensional fracture analysis of FGM coatings", Mater. Sci. Forum, 492-493, 373-378.
  13. Kapuria, S., Bhattacharyya, M. and Kumar, A.N. (2008), "Theoretical modeling and experimental validation of thermal response of metal-ceramic functionally graded beams", J. Therm. Stresses, 31, 759-787. https://doi.org/10.1080/01495730802194292
  14. Ke, L.L., Yang, J. and Kitipornchai, S. (2009), "Postbuckling analysis of edge cracked functionally graded Timoshenko beams under end shortening", Compos. Struct., 90(2), 152-160. https://doi.org/10.1016/j.compstruct.2009.03.003
  15. Khdeir, A.A. (2001), "Thermal buclding of cross-ply laminated composite beams", Acta Mechanica, 149, 201-213. https://doi.org/10.1007/BF01261672
  16. Kiani, Y. and Eslami, M.R. (2010), "Thermal buckling analysis of functionally graded material beams, Int. J. Mech. Mater. Des., 6(3), 229-238. https://doi.org/10.1007/s10999-010-9132-4
  17. Kocatürk, T., im ek M. and Akba , .D. (2011), "Large displacement static analysis of a cantilever Timoshenko beam composed of functionally graded material", Sci. Eng. Compos. Mater., 18, 21-34.
  18. Kocatürk, T. and Akba , S.D. (2011), "Post-buckling analysis of Timoshenko beams with various boundary conditions under non-uniform thermal loading", Struct. Eng. Mech., 40(3), 347-371. https://doi.org/10.12989/sem.2011.40.3.347
  19. Librescua, L., Oha, S.Y. and Songb, O. (2005), "Thin-walled beams made of functionally graded materials and operating in a high temperature environment: vibration and stability", J. Therm. Stresses, 28, 649-712. https://doi.org/10.1080/01495730590934038
  20. Li, S.R., Zhang, J.H. and Zhao, Y.G. (2006), "Thermal Post-Buckling of functionally graded material Timoshenko beams", Appl. Math. Mech., 26(6), 803-810.
  21. Li, S.R., Su, H.D. and Cheng, C.J. (2009), "Free vibration of functionally graded material beams with surfacebonded piezoelectric layers in thermal environment", Appl. Math. Mech., 30(8), 969-982. https://doi.org/10.1007/s10483-009-0803-7
  22. Lim, C.W., Yang, Q. and Lu, C.F. (2009), "Two-dimensional elasticity solutions for temperature dependent inplane vibration of FGM circular arches", Compos. Struct., 90, 323-329. https://doi.org/10.1016/j.compstruct.2009.03.014
  23. Lu, C., Chen, W. and Zhong, Z. (2006), Two-dimensional thermoelasticity solution for functionally graded thick beams", Science in China Series G: Physics, Mechanics & Astronomy 49(4), 451-460. https://doi.org/10.1007/s11433-006-0451-2
  24. Malekzadeh, P., Haghighi, M.R.G. and Atashi, M.M. (2010), "Out-of-plane free vibration of functionally graded circular curved beams in thermal environment", Compos. Struct. 92(2), 541-552. https://doi.org/10.1016/j.compstruct.2009.08.040
  25. Mohammadia, M. and Drydena, J.R. (2008), "Thermal stress in a nonhomogeneous curved beam", J. Therm. Stresses, 31(7), 587-598. https://doi.org/10.1080/01495730801978471
  26. Na, K.S. and Kim, J.H. (2006), "Thermal postbuckling investigations of functionally graded plates using 3-D finite element method", Finite Elem. Analy. Des., 42(8-9), 749-756. https://doi.org/10.1016/j.finel.2005.11.005
  27. Nirmula, K., Upadhyay, P.C., Prucz, J. and Lyons, D. (2006), "Thermo-elastic Stresses in Composite Beams with Functionally Graded Layer", J. Reinf. Plast. Compos., 25(12), 1241-1254. https://doi.org/10.1177/0731684406059787
  28. Pradhan, S.C. and Murmu, T. (2009), "Thermo-mechanical vibration of FGM sandwich beam under variable elastic foundations using differential quadrature method", J. Sound Vib., 321, 342-362. https://doi.org/10.1016/j.jsv.2008.09.018
  29. Rahimi, G.H. and Davoodinik, A.R. (2008), "Thermal behavior analysis of the functionally graded Timoshenko's beam", IUST Int. J. Eng. Sci., 19(5-1), 105-113.
  30. Rastgo, A., Shafie, H. and Allahverdizadeh, A. (2005), "Instability of curved beams made of functionally graded material under thermal loading, International", J. Mech. Mater. Des., 2, 117-128. https://doi.org/10.1007/s10999-005-4446-3
  31. Reddy, J.N. (2004), An Introduction to Non-linear Finite Element Analysis, Oxford University Press Inc., New York.
  32. Sankar, B.V. and Tzeng, J.T. (2002), "Thermal stresses in functionally graded beams", AIAA J., 40(6), 1228-1232. https://doi.org/10.2514/2.1775
  33. Song, X. and Li, S. (2008), "Nonlinear stability of fixed-fixed FGM arches subjected to mechanical and thermal load", Adv. Mater. Res., 33-37, 699-706. https://doi.org/10.4028/www.scientific.net/AMR.33-37.699
  34. Xiang, H.J. and Yang, J. (2008), "Free and forced vibration of a laminated FGM Timoshenko beam of variable thickness under heat conduction", Composites: Part B, 39, 292-303. https://doi.org/10.1016/j.compositesb.2007.01.005
  35. Wakashima, K., Hirano, T. and Niino, M. (1990), "Space applications of advanced structural materials", ESA, SP: 303-397.
  36. Zienkiewichz, O.C. and Taylor, R.L. (2000), The Finite Element Method, Fifth Edition, Volume 2, Solid Mechanics, Butterworth-Heinemann, Oxford.

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