Structural Engineering and Mechanics

  • 제36권5호
  • /
  • Pages.545-560
  • /
  • 2010
  • /
  • 1225-4568(pISSN)
  • /
  • 1598-6217(eISSN)
테크노프레스 (Techno-Press)
권호 표지
DOI QR코드

DOI QR Code

Thermal post-buckling analysis of uniform slender functionally graded material beams

  • Anandrao, K. Sanjay (Advanced Systems Laboratory, Kanchanbagh) ;
  • Gupta, R.K. (Advanced Systems Laboratory, Kanchanbagh) ;
  • Ramchandran, P. (Defense Research and Development Laboratory, Kanchanbagh) ;
  • Rao, G. Venkateswara (School of Mechanical Engineering, Sreenidhi Institute of Science and Technology)
  • 투고 : 2010.02.22
  • 심사 : 2010.07.16
  • 발행 : 2010.11.30
⟨ 이전 논문 다음 논문 ⟩

초록

Two or more distinct materials are combined into a single functionally graded material (FGM) where the microstructural composition and properties change gradually. Thermal post-buckling behavior of uniform slender FGM beams is investigated independently using the classical Rayleigh-Ritz (RR) formulation and the versatile Finite Element Analysis (FEA) formulation developed in this paper. The von-Karman strain-displacement relations are used to account for moderately large deflections of FGM beams. Bending-extension coupling arising due to heterogeneity of material through the thickness is included. Simply supported and clamped beams with axially immovable ends are considered in the present study. Post-buckling load versus deflection curves and buckled mode shapes obtained from both the RR and FEA formulations for different volume fraction exponents show an excellent agreement with the available literature results for simply supported ends. Response of the FGM beam with clamped ends is studied for the first time and the results from both the RR and FEA formulations show a very good agreement. Though the response of the FGM beam could have been studied more accurately by FEA formulation alone, the authors aim to apply the RR formulation is to find an approximate closed form post-buckling solutions for the FGM beams. Further, the use of the RR formulation clearly demonstrates the effect of bending-extension coupling on the post-buckling response of the FGM beams.

키워드

참고문헌

  1. Deschilder, M., Eslami, H. and Zhao, Y. (2006), "Non-linear static analysis of a beam made of functionally graded material", Proceedings of the 47th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, Newport, Rhode Island, May.
  2. Han, S.C., Lomboy, G.R. and Kim, K.D. (2008), "Mechanical vibration and buckling analysis of FGM plates and shells using a four node quasi conforming shell element", Int. J. Struct. Stabil. Dyn., 8(2), 203-229. https://doi.org/10.1142/S0219455408002624
  3. Ibrahim, H.H. (2007), "Thermal buckling and nonlinear flutter behavior of functionally graded material panels", J. Aircraft, 44(5), 1610-1618. https://doi.org/10.2514/1.27866
  4. Jabbari, M., Vaghari, A.R., Bahtui, A. and Eslami, M.R. (2008), "Exact solution for asymmetric transient thermal and mechanical stresses in FGM hollow cylinders with heat source", Struct. Eng. Mech., 29(5), 551-565. https://doi.org/10.12989/sem.2008.29.5.551
  5. Julien, T., Eslami, H. and Zhao, Y. (2008), "Thermal post buckling analysis of FGM beams", Proceedings of the 47th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, Newport, Rhode Island, May..
  6. Kitipornchai, S., Ke, L.L., Yang, J. and Xiang, Y. (2009), "Nonlinear vibration of edge cracked functionally graded Timoshenko beams", J. Sound Vib., 324, 962-982. https://doi.org/10.1016/j.jsv.2009.02.023
  7. Lee, S.L. and Kim, J.H. (2007), "Thermal stability boundary of FG panel under aerodynamic load", Int. J. Mech. Syst. Sci. Eng., 1(2), 105-110.
  8. Li, X.F. (2008), "A unified approach for analyzing static and dynamic behaviors of functionally graded Timoshenko and Euler-Bernoulli beams", J. Sound Vib., 318, 1210-1229. https://doi.org/10.1016/j.jsv.2008.04.056
  9. Prakash, T. and Ganapathi, M. (2006), "Asymmetric flexural vibration and thermoelastic stability of FGM plates using finite element method", Composites: Part B, 37, 642-649. https://doi.org/10.1016/j.compositesb.2006.03.005
  10. Prakash, T., Singh, M.K. and Ganapathi, M. (2006), "Vibrations and thermal stability of functionally graded spherical caps", Struct. Eng. Mech., 24(4), 447-462. https://doi.org/10.12989/sem.2006.24.4.447
  11. Raju, K.K. and Rao Venkateswara, G. (2005), "Towards improved evaluation of large amplitude free vibration behavior of uniform beams using multi-term admissible functions", J. Sound Vib., 282, 1238-1246. https://doi.org/10.1016/j.jsv.2004.04.036
  12. Rao Venkateswara, G. (2003), "A simple energy method to predict the thermal post buckling behavior of columns", J. Aeros. Sci. Technol., 55(2), 141-143.
  13. Rao Venkateswara, G. and Kanaka Raju, K. (1984), "Thermal post buckling of columns", AIAA J., 22(6), 850-851. https://doi.org/10.2514/3.8695
  14. Rao Venkateswara, G. and Kanaka Raju, K. (2002), "Thermal post buckling of uniform Columns: A simple intuitive method", AIAA J., 40(10), 2138-2140. https://doi.org/10.2514/2.1553
  15. Rao Venkateswara, G. and Kanaka Raju, K. (2003), "A simple method to predict the thermal post-buckling behavior of columns on Pasternak foundation", Ind. J. Eng. Mater. Sci., 10, 177-182.
  16. Rao Venkateswara, G. and Raju, P.C. (1977), "Post-buckling of uniform cantilever columns – Galerkin finite element formulation", Eng. Fract. Mech., 9, 1-4. https://doi.org/10.1016/0013-7944(77)90046-7
  17. Sankar, B.V. (2001), "An elasticity solution for functionally graded beams", Compos. Sci. Technol., 61, 689-696. https://doi.org/10.1016/S0266-3538(01)00007-0
  18. Timoshenko, S.P. and Gere, J.M. (1970), Theory of Elastic Stability, McGraw-Hill.
  19. Turvey, G.J. and Lih, M. (1995), Buckling and Postbuckling of Composite Plates, Chapman and Hall, London.
  20. Zhong, Z. and Yu, T. (2007), "Analytical solution of a cantilever functionally graded beam", Compos. Sci. Technol., 67, 481-488. https://doi.org/10.1016/j.compscitech.2006.08.023

피인용 문헌

  1. Dynamic behavior of an axially functionally graded beam under action of a moving harmonic load vol.94, pp.8, 2012, https://doi.org/10.1016/j.compstruct.2012.03.020
  2. Nonlinear thermal dynamic buckling of FGM beams vol.54, 2015, https://doi.org/10.1016/j.euromechsol.2015.07.004
  3. Effect of Temperature-Dependent Material Properties on Nonlinear Flexural Response and Thermal Postbuckling of Shear Flexible FGM Beams: A Study Using FEM vol.15, pp.2, 2014, https://doi.org/10.1080/15502287.2013.845623
  4. Nonlinear thermal stability and vibration of pre/post-buckled temperature- and microstructure-dependent functionally graded beams resting on elastic foundation vol.112, 2014, https://doi.org/10.1016/j.compstruct.2014.01.041
  5. Thermo-electrical buckling of piezoelectric functionally graded material Timoshenko beams vol.7, pp.3, 2011, https://doi.org/10.1007/s10999-011-9158-2
  6. On Post-Buckling Behavior of Edge Cracked Functionally Graded Beams Under Axial Loads vol.15, pp.04, 2015, https://doi.org/10.1142/S0219455414500655
  7. Non-linear thermal stability analysis of temperature dependent FGM beams supported on non-linear hardening elastic foundations vol.69, 2013, https://doi.org/10.1016/j.ijmecsci.2013.01.007
  8. A study on thermal buckling load of clamped functionally graded beams under linear and nonlinear thermal gradient across thickness 2016, https://doi.org/10.1177/1464420716649213
  9. Dynamic buckling of suddenly heated or compressed FGM beams resting on nonlinear elastic foundation vol.106, 2013, https://doi.org/10.1016/j.compstruct.2013.06.001
  10. Thermal post-buckling analysis of functionally graded beams with temperature-dependent physical properties vol.15, pp.5, 2013, https://doi.org/10.12989/scs.2013.15.5.481
  11. Three-dimensional biaxial post-buckling analysis of heterogeneous auxetic rectangular plates on elastic foundations by new criteria vol.302, 2016, https://doi.org/10.1016/j.cma.2015.12.026
  12. Size-dependent three-dimensional free vibration of rotating functionally graded microbeams based on a modified couple stress theory vol.136, 2018, https://doi.org/10.1016/j.ijmecsci.2017.12.028
  13. Exact Solution for Nonlinear Stability of Piezoelectric FGM Timoshenko Beams Under Thermo-Electrical Loads vol.36, pp.10, 2013, https://doi.org/10.1080/01495739.2013.818888
  14. Thermomechanical buckling oftemperature-dependent FGM beams vol.10, pp.2, 2013, https://doi.org/10.1590/S1679-78252013000200001
  15. Non-linear thermo-elastic and buckling analysis of FGM shallow arches vol.109, 2014, https://doi.org/10.1016/j.compstruct.2013.10.045
  16. In-plane free vibrations of circular beams made of functionally graded material in thermal environment: Beam theory approach vol.122, 2015, https://doi.org/10.1016/j.compstruct.2014.11.051
  17. Post-Buckling Analysis of Functionally Graded Three-Dimensional Beams Under the Influence of Temperature vol.36, pp.12, 2013, https://doi.org/10.1080/01495739.2013.788397
  18. Thermal effect on the dynamic response of axially functionally graded beam subjected to a moving harmonic load vol.127, 2016, https://doi.org/10.1016/j.actaastro.2016.05.030
  19. Thermoelastic buckling analysis of pre-twisted functionally graded beams with temperature-dependent material properties vol.133, 2017, https://doi.org/10.1016/j.actaastro.2017.01.007
  20. Geometrically Nonlinear Static Analysis of Edge Cracked Timoshenko Beams Composed of Functionally Graded Material vol.2013, 2013, https://doi.org/10.1155/2013/871815
  21. Analytical Approximate Prediction of Thermal Post-Buckling Behavior of the Spring-Hinged Beam vol.08, pp.03, 2016, https://doi.org/10.1142/S1758825116500289
  22. Postbuckling of FGM rings vol.85, 2014, https://doi.org/10.1016/j.ijmecsci.2014.05.021
  23. Thermoelectromechanically induced stochastic post buckling response of piezoelectric functionally graded beam vol.10, pp.3, 2014, https://doi.org/10.1007/s10999-014-9246-1
  24. Post-Buckling Analysis of Axially Functionally Graded Three-Dimensional Beams vol.07, pp.03, 2015, https://doi.org/10.1142/S1758825115500477
  25. Flexural stress analysis of uniform slender functionally graded material beams using non-linear finite element method vol.5, pp.4, 2012, https://doi.org/10.1080/19373260.2012.688362
  26. Post-buckling finite strip analysis of thick functionally graded plates vol.49, pp.5, 2014, https://doi.org/10.12989/sem.2014.49.5.569
  27. Thermal buckling and post-buckling of FGM Timoshenko beams on nonlinear elastic foundation vol.39, pp.1, 2016, https://doi.org/10.1080/01495739.2015.1120627
  28. Vibration of a Temperature-Dependent Thermally Pre/Postbuckled FGM Beam Over a Nonlinear Hardening Elastic Foundation vol.81, pp.1, 2013, https://doi.org/10.1115/1.4023975
  29. Modeling and analysis of functionally graded sandwich beams: A review pp.1537-6532, 2018, https://doi.org/10.1080/15376494.2018.1447178
  30. Mathematical solution for free vibration of sigmoid functionally graded beams with varying cross-section vol.11, pp.6, 2010, https://doi.org/10.12989/scs.2011.11.6.489
  31. Free vibration of an axially functionally graded pile with pinned ends embedded in Winkler-Pasternak elastic medium vol.40, pp.4, 2010, https://doi.org/10.12989/sem.2011.40.4.583
  32. Post-buckling analysis of Timoshenko beams made of functionally graded material under thermal loading vol.41, pp.6, 2010, https://doi.org/10.12989/sem.2012.41.6.775
  33. Analytical approximate solutions for large post-buckling response of a hygrothermal beam vol.43, pp.2, 2010, https://doi.org/10.12989/sem.2012.43.2.211
  34. Non-linear free vibrations and post-buckling analysis of shear flexible functionally graded beams vol.44, pp.3, 2010, https://doi.org/10.12989/sem.2012.44.3.339
  35. Thermal post-buckling of slender composite and FGM columns through a simple and novel FE formulation vol.41, pp.8, 2010, https://doi.org/10.1007/s12046-016-0516-5
  36. Thermo-mechanical analysis of carbon nanotube-reinforced composite sandwich beams vol.6, pp.2, 2010, https://doi.org/10.12989/csm.2017.6.2.207
  37. Post-buckling responses of functionally graded beams with porosities vol.24, pp.5, 2017, https://doi.org/10.12989/scs.2017.24.5.579
  38. Nonlinear static analysis of functionally graded porous beams under thermal effect vol.6, pp.4, 2017, https://doi.org/10.12989/csm.2017.6.4.399
  39. Geometrically nonlinear analysis of functionally graded porous beams vol.27, pp.1, 2010, https://doi.org/10.12989/was.2018.27.1.059
  40. Symplectic Method-Based Analysis of Axisymmetric Dynamic Thermal Buckling of Functionally Graded Circular Plates vol.55, pp.4, 2010, https://doi.org/10.1007/s11029-019-09825-w
  41. 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
  42. A review of size-dependent continuum mechanics models for micro- and nano-structures vol.170, pp.None, 2022, https://doi.org/10.1016/j.tws.2021.108562