Smart Structures and Systems

  • 제13권4호
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  • Pages.637-657
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  • 2014
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  • 1738-1584(pISSN)
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  • 1738-1991(eISSN)
테크노프레스 (Techno-Press)
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DOI QR코드

DOI QR Code

A dynamic analysis of three-dimensional functionally graded beams by hierarchical models

  • 투고 : 2013.04.13
  • 심사 : 2013.11.30
  • 발행 : 2014.04.25
⟨ 이전 논문 다음 논문 ⟩

초록

This paper presents a dynamic analysis of three-dimensional beams. Structures made of functionally graded materials are considered. Several higher-order as well as classical theories are derived by means of a compact notation for the a-priori expansion order of the displacement field over the beam cross-section. The governing differential equations and boundary conditions are obtained in a condensed nuclear form that does not depend on the kinematic hypotheses. The problem is, then, exactly solved in space by means of a Navier-type solution, whereas time integration is performed by means of Newmark's solution scheme. Slender and short simply supported beams are investigated. Results are validated towards three-dimensional FEM results obtained via the commercial software ANSYS. Numerical investigations show that good accuracy can be obtained through the proposed formulation provided that the appropriate expansion order is considered.

키워드

참고문헌

  1. Aboudi, J. (1991), Mechanics of composite materials: a unified micromechanical approach, Elsevier, The Netherlands.
  2. Aboudi, J., Pindera, M.J. and Arnold, S.M. (1994), "Elastic response of metal matrix composites with tailored microstructures to thermal gradients", Int. J. Solids Struct., 31(10), 1393-1428. https://doi.org/10.1016/0020-7683(94)90184-8
  3. Aboudi, J., Pindera, M.J. and Arnold, S.M. (1996), "Thermoelastic theory for the response of materials functionally graded in two directions", Int. J. Solids Struct., 33(7), 931-966. https://doi.org/10.1016/0020-7683(95)00084-4
  4. Aboudi, J., Pindera, M.J. and Arnold, S.M. (1999), "Higher-order theory for functionally graded materials", Compos. Part B Eng., 30(8), 777-832. https://doi.org/10.1016/S1359-8368(99)00053-0
  5. Azadi, M. (2011), "Free and forced vibration analysis of FG beam considering temperature dependency of material properties", J. Mech. Sci. Technol., 25(1), 69-80. https://doi.org/10.1007/s12206-010-1015-y
  6. Bathe, K.J. (2006), Finite element procedures, Prentice hall.
  7. Birman, V. and Byrd, L.W. (2007), "Modeling and analysis of functionally graded materials and structures", Appl. Mech. Rev., 60(5), 195-216. https://doi.org/10.1115/1.2777164
  8. Bui, T. Q., Khosravifard, A., Zhang, Ch., Hematiyan, M.R. and Golub, M.V. (2013), "Dynamic analysis of sandwich beams with functionally graded core using a truly meshfree radial point interpolation method", Eng. Struct., 47, 90-104. https://doi.org/10.1016/j.engstruct.2012.03.041
  9. Carrera, E (2003), "Theories and finite elements for multilayered plates and shells: a unified compact formulation with numerical assessment and benchmarking", Arch. Comput. Method. E., 10(3), 215-296. https://doi.org/10.1007/BF02736224
  10. Carrera, E. and Brischetto, S. (2008a), "Analysis of thickness locking in classical, refined and mixed multilayered plate theories", Compos. Struct., 82(4), 549-562. https://doi.org/10.1016/j.compstruct.2007.02.002
  11. Carrera, E. and Brischetto, S. (2008b), "Analysis of thickness locking in classical, refined and mixed theories for layered shells", Compos. Struct., 85(1), 83-90. https://doi.org/10.1016/j.compstruct.2007.10.009
  12. Carrera, E. and Giunta, G. (2009a), "Hierarchical evaluation of failure parameters in composite plates", AIAA J., 47(3), 692-702. https://doi.org/10.2514/1.38585
  13. Carrera, E. and Giunta, G. (2009b), "Exact, hierarchical solutions for localised loadings in isotropic, laminated and sandwich shells", J. Pressure Vessel Technol., 131(4), 041202. https://doi.org/10.1115/1.3141432
  14. Carrera, E. and Giunta, G. (2010), "Refined beam theories based on a unified formulation", Int. J. Appl. Mech., 2(1), 117-143. https://doi.org/10.1142/S1758825110000500
  15. Carrera, E., Giunta, G., Nali, P. and Petrolo, M. (2010), "Refined beam elements with arbitrary cross-section geometries", Comput. Struct., 88(5-6), 283-293. https://doi.org/10.1016/j.compstruc.2009.11.002
  16. Carrera, E., Giunta, G. and Petrolo, M. (2011), Beam structures: classical and advanced theories, Wiley-Blackwell.
  17. Carrera, E. and Petrolo, M. (2011), "On the effectiveness of higher-order terms in refined beam theories", J. Appl. Mech. - T ASME, 78(2), 021013-1-021013-17. https://doi.org/10.1115/1.4002207
  18. Carrera, E. and Varello, A. (2013), "Dynamic response of thin-walled structures by variable kinematic one-dimensional models", J. Sound Vib., 331(24), 5268-5282.
  19. Chakraborty, A., Gopalakrishnan, S. and Reddy, J.N. (2003), "A new beam finite element for the analysis of functionally graded materials", Int. J. Mech. Sci., 45(3), 519-539. https://doi.org/10.1016/S0020-7403(03)00058-4
  20. Cowper, G.R. (1966), "The shear co-efficient in Timoshenko beam theory", Int. J. Appl. Mech., 33(10), 335-340. https://doi.org/10.1115/1.3625046
  21. Giunta, G., Belouettar, S. and Carrera, E. (2010), "Analysis of FGM beams by means of classical and advanced theories", Mech. Adv. Mater. Struct., 17(8), 622-635. https://doi.org/10.1080/15376494.2010.518930
  22. Giunta, G., Biscani, F., Belouettar, S. and Carrera, E. (2011a), "Analysis of thin-walled beams via a one-dimensional unified formulation", Int. J. Appl. Mech., 3(3), 407-434. https://doi.org/10.1142/S1758825111001056
  23. Giunta, G., Biscani, F., Belouettar, S. and Carrera, E. (2011b), "Hierarchical modelling of doubly curved laminated composite shells under distributed and localised loadings", Compos. Part B: Eng., 42(4), 682-691. https://doi.org/10.1016/j.compositesb.2011.02.002
  24. Giunta, G., Crisafulli, D., Belouettar, S. and Carrera, E. (2011), "Hierarchical theories for the free vibration analysis of functionally graded beams", Compos. Struct., 94(1), 68-74. https://doi.org/10.1016/j.compstruct.2011.07.016
  25. Giunta, G., Biscani, F., Belouettar, S., Ferreira, A.J.M. and Carrera, E. (2013a), "Free vibration analysis of composite beams via refined theories", Compos. Part B: Eng., 44(1), 540-552. https://doi.org/10.1016/j.compositesb.2012.03.005
  26. Giunta, G., Crisafulli, D., Belouettar, S. and Carrera, E. (2013b), "A thermo-mechanical analysis of functionally graded beams via hierarchical modelling", Compos. Struct., 95, 676-690. https://doi.org/10.1016/j.compstruct.2012.08.013
  27. Hill, R. (1965), "A self-consistent mechanics of composite materials", J. Mech. Phys. Solids, 13(4), 213-222. https://doi.org/10.1016/0022-5096(65)90010-4
  28. Hughes, T.J.R. (2000), The finite element method, Dover.
  29. Khalili, S.M.R., Jafari, A.A. and Eftekhari, S.A. (2010), "A mixed Ritz-DQ method for forced vibration of functionally graded beams carrying moving loads", Compos. Struct., 92(10), 2497-2511. https://doi.org/10.1016/j.compstruct.2010.02.012
  30. Koizumi, M. (1997), "FGN activities in Japan", Compos. Part B - Eng., 28(1-2), 1-4.
  31. Miyamoto, Y., Kaysser, W. A., Rabin, B.H., Kawasaki, A. and Ford R.G. (1999), Functionally graded materials: design, Processing and Applications, Kluwer Academic, Boston, USA.
  32. Mori, T. and Tanaka, K. (1973), "Average stress in matrix and average elastic energy of materials with misfitting inclusions", Acta Metallurgica, 21(5), 571-574. https://doi.org/10.1016/0001-6160(73)90064-3
  33. Murty, A.V. K. (1970), "Analysis of short beams", AIAA J., 8, 2098-2100. https://doi.org/10.2514/3.6067
  34. Na, S., Kim, K.W. Lee, B.H. and Marzocca, P. (2009), "Dynamic response analysis of rotating functionally graded thin-walled blades exposed to steady temperature and external excitation", J. Therm. Stresses, 32(3), 209-225. https://doi.org/10.1080/01495730802507956
  35. Nemat-Nasser, S. and Hori, M. (1993), Micromechanics: overall properties of heterogeneous materials. North-Holland, New York.
  36. Newmark, N.M. (1959), "A method of computation for structural dynamics", J. Eng. Mech. - ASCE, 85(7), 67-94.
  37. Philips, G.M. (2003), Interpolation and approximation by polynomials, Springer-Verlag.
  38. Pindera, M. J., Aboudi, J. and Arnold, S.M. (1995), "Limitations of the uncoupled RVE-based micromechanical approach in the analysis of functional graded composites", Mech. Mater., 20(1), 77-94. https://doi.org/10.1016/0167-6636(94)00052-2
  39. Praveen, G.N. and Reddy, J.N. (1998), "Nonlinear transient thermoelastic analysis of functionally graded ceramic-metal plates", Int. J. Solids Struct., 35(33), 4457-4476. https://doi.org/10.1016/S0020-7683(97)00253-9
  40. Reddy, J. N. (2002), Energy principles and variational methods in applied mechanics, John Wiley and Sons.
  41. Shooshtari, A. and Rafiee, M. (2011), "Nonlinear forced vibration analysis of clamped functionally graded beams", Acta Mech., 221(1-2), 23-38. https://doi.org/10.1007/s00707-011-0491-1
  42. Simsek, M., and Kocaturk, T. (2009), "Free and forced vibration of a functionally graded beam subjected to a concentrated moving harmonic load", Compos. Struct., 90(4), 465-473. https://doi.org/10.1016/j.compstruct.2009.04.024
  43. 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
  44. Simsek, M. and Cansiz, S. (2012), "Dynamics of elastically connected double-functionally graded beam systems with different boundary conditions under action of a moving harmonic load", Compos. Struct., 94(9), 2861-2878. https://doi.org/10.1016/j.compstruct.2012.03.016
  45. Simsek, M., Kocaturk, T. and Akbas, S.D. (2012), "Dynamic behavior of an axially functionally graded beam under action of a moving harmonic load", Compos. Struct., 94(8), 2358-2364. https://doi.org/10.1016/j.compstruct.2012.03.020
  46. Suresh, S. and Mortensen, A. (1998), Fundamentals of functional graded materials, IOM Communications Limited, London, UK.
  47. Wakashima, H. T. and Tsukamoto, H. (1990), "Micromechanical approach to the thermomechanics of ceramic-metal gradient materials", Proceedings of the 1st Symposium on Functionally Gradient Materials, The Functionally Gradient Materials Forum, Sendai, Japan.
  48. Watanabe, R., Nishida, T. and Hirai, T. (2003), "Present status of research on design and processing of functionally graded materials", Metal. Mater. Int., 9(6), 513-519. https://doi.org/10.1007/BF03027249
  49. Yang, J., Chen, Y., Xiang, Y. and Jia. X.L. (2008), "Free and forced vibration of cracked inhomogeneous beams under an axial force and a moving load", J. Sound Vib., 312(1-2), 166-181. https://doi.org/10.1016/j.jsv.2007.10.034
  50. Zienkiewicz, O.C., Taylor, R.L. and Zhu, J.Z. (2005), The finite element method: its basis and fundamentals, Elsevier.
  51. Zuiker, J.R. and Dvorak, G.J. (1994), "The effective properties of functionally graded composites - i extension of the Mori-Tanaka method to linearly varying fields", Compos. Eng., 4(1), 19-35. https://doi.org/10.1016/0961-9526(94)90004-3

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