Structural Engineering and Mechanics

  • 제55권3호
  • /
  • Pages.473-494
  • /
  • 2015
  • /
  • 1225-4568(pISSN)
  • /
  • 1598-6217(eISSN)
테크노프레스 (Techno-Press)
권호 표지
DOI QR코드

DOI QR Code

Application of graded harmonic FE in the analysis of 2D-FGM axisymmetric structures

  • Karakas, Ali I. (Department of Civil Engineering, Karadeniz Technical University) ;
  • Daloglu, Ayse T. (Department of Civil Engineering, Karadeniz Technical University)
  • 투고 : 2014.11.29
  • 심사 : 2015.04.27
  • 발행 : 2015.08.10
⟨ 이전 논문 다음 논문 ⟩

초록

A graded harmonic finite element formulation based on three-dimensional elasticity theory is developed for the structural analysis of 2D functionally graded axisymmetric structures. The mechanical properties of the axisymmetric solid structures composed of two different metals and ceramics are assumed to vary in radial and axial directions according to power law variations as a function of the volume fractions of the constituents. The material properties of the graded element are calculated at the integration points. Effects of material distribution profile on the static deformation, natural frequency and dynamic response analyses of particular axisymmetric solid structures are investigated by changing the power law exponents. It is observed that the displacements, stresses and natural frequencies are severely affected by the variation of axial and radial power law exponents. Good accuracy is obtained with fewer elements in the present study since Fourier series expansion eliminates the need of finite element mesh in circumferential direction and continuous material property distribution within the elements improves accuracy without refining the mesh size in axial and radial directions.

키워드

참고문헌

  1. Aboudi, J., Pindera, M.J. and Arnold, S.M. (1999), "Higher- order theory for functionally graded materials", Compos. Part B, 30, 777-832. https://doi.org/10.1016/S1359-8368(99)00053-0
  2. Asgari, M. and Akhlaghi, M. (2011), "Natural frequency analysis of 2D-FGM thick hollow cylinder based on three-dimensional elasticity equations", Eur. J. Mech. A Solid., 30, 72-81. https://doi.org/10.1016/j.euromechsol.2010.10.002
  3. Asgari, M., Akhlaghi, M. and Hosseini, S.M. (2009), "Dynamic analysis of two-dimensional functionally graded thick hollow cylinder with finite length under impact loading", Acta Mech., 208, 163-180. https://doi.org/10.1007/s00707-008-0133-4
  4. Birman, V. and Byrd, L.W. (2007), "Modeling and analysis of functionally graded materials and structures", Appl. Mech. Rev., 60, 195-215. https://doi.org/10.1115/1.2777164
  5. Buttlar, W.G., Paulino, H.H. and Song, S.H. (2006), "Application of graded finite elements for asphalt pavements", J. Eng. Mech., 132, 240-249. https://doi.org/10.1061/(ASCE)0733-9399(2006)132:3(240)
  6. Cook, R.D., Malkus, D.S. and Plesha, M.E. (1989), Concepts and Applications of Finite Element Analysis, 3rd Edition, Wiley&Sons.
  7. Foroutan, M. and Moradi-Dastjerdi, R. (2011), "Dynamic analysis of functionally graded material cylinders under an impact load by a mesh-free method", Acta Mech., 219, 281-290. https://doi.org/10.1007/s00707-011-0448-4
  8. Goldberg, R.K. and Hopkins, D.A. (1995), "Thermal analysis of a functionally graded material subject to a thermal gradient using the boundary element method", Compos. Meth. Appl. Mech. Eng., 5(7), 793-806.
  9. Han, X., Liu, G.R., Xi, Z.C. and Lam, K.Y. (2001), "Transient waves in a functionally graded cylinder", Int. J. Solid. Struct., 38, 3021-3037. https://doi.org/10.1016/S0020-7683(00)00219-5
  10. Hosseini, S.M., Akhlaghi, M. and Shakeri, M. (2007), "Dynamic response and radial wave propagation velocity in thick hollow cylinder made of functionally graded materials", Int. J. Comput. Aid. Eng. Softw., 24, 288-303. https://doi.org/10.1108/02644400710735043
  11. Karakas, A.I. (2012), "Static and dynamic analyses of axisymmetric structures using Harmonic Solid Ring Finite Element Modeling", Master dissertation, Karadeniz Technical University, Turkey.
  12. Kim, J.H. and Paulino, G.H. (2002), "Isoparametric graded finite elements for nonhomogeneous isotropic and orthotropic materials", J. Appl. Mech., 69, 502-514. https://doi.org/10.1115/1.1467094
  13. Koizumi, M. (1993), "The concept of FGM.", Ceram. Tran. Funct. Gradient Mater., 51, 28-32.
  14. Li, Y., Ramesh, K.T. and Chin, E.S.C. (2001), "Dynamic characterization of layered and graded structures under impulsive loading", Int. J. Solid. Struct., 38, 6045-6061. https://doi.org/10.1016/S0020-7683(00)00364-4
  15. Loy, C.T., Lam, K.Y. and Reddy, J.N. (1999), "Vibration of functionally graded cylindrical shells", Int. J. Mech. Sci., 41, 309-324. https://doi.org/10.1016/S0020-7403(98)00054-X
  16. Marur, P.R. and Tippur, H.V. (2000), "Numerical analysis of crack-tip fields in functionally graded materials with a crack normal to the elastic gradient", Int. J. Solid. Struct., 37, 5353-5370. https://doi.org/10.1016/S0020-7683(99)00207-3
  17. Paulino, G.H. and Jin, Z.H. (2000), "Viscoelastic functionally graded materials subjected to antiplane shear fracture", ASME J. Appl. Mech., 68(1), 284-293.
  18. Pindera, M.J. and Dunn, P. (1997), "Evaluation of the higher-order theory for functionally graded materials via the finite element method", Compos. Part B, 28, 109-119. https://doi.org/10.1016/S1359-8368(96)00035-2
  19. Praveen, G.N. and Reddy, J.N. (1998), "Nonlinear transient thermoelastic analysis of functionally graded ceramic-metal plates", Int. J. Solid. Struct., 35, 4457-4476. https://doi.org/10.1016/S0020-7683(97)00253-9
  20. Pradhan, S.C., Loy, C.T., Lam, K.Y. and Reddy, J.N. (2000), "Vibration characteristics functionally graded cylindrical shells under various boundary conditions", Appl. Acoust., 61, 111-129. https://doi.org/10.1016/S0003-682X(99)00063-8
  21. Shakeri, M., Akhlaghi, M. and Hosseini, S.M. (2006), "Vibration and radial wave propagation velocity in functionally graded thick hollow cylinder", Compos. Struct., 76, 174-181. https://doi.org/10.1016/j.compstruct.2006.06.022
  22. Santare, M.H. and Lambros, J. (2000), "Use of graded finite elements to model the behavior of nonhomogeneous materials", J. Appl. Mech., 67, 819-822. https://doi.org/10.1115/1.1328089
  23. Santare, M.H., Thamburaj, P. and Gazonas, G.A. (2003), "The use of graded finite elements in the study of elastic wave propagation in continuously nonhomogeneous materials" Int. J. Solid. Struct., 40, 5621-5634. https://doi.org/10.1016/S0020-7683(03)00315-9
  24. Sutradhar, S., Paulino, G.H. and Gray, L.J. (2002), "Transient heat conduction in homogenous and non-homogeneous materials by the laplace transform Galerkin boundary element method", Eng. Anal. Bound. Elem., 26, 119-132. https://doi.org/10.1016/S0955-7997(01)00090-X
  25. Taghvaeipour, A., Bonakdar, M. and Ahmadian, M.T. (2012), "Application of a new cylindrical element formulation in finite element structural analysis of FGM hollow cylinders", Finite Elem. Anal. Des., 50, 1-7. https://doi.org/10.1016/j.finel.2011.08.006