Instability of Curved Beams Made of Functionally Graded Material Under Thermal Loading

  • A. Rastgo
  • H. Shafie
  • A. Allahverdizadeh


In this paper the thermal buckling load of a curved beam made of functionally graded material (FGM) with doubly symmetric cross section is considered. By instability conditions we mean the in-plane and out-of-plane buckling. The stability equations are derived using the variational principles. The curved beam is under temperature rise for thermal loading. The solution for critical thermal buckling load is obtained using the stability equations and the Galerkin method. The critical thermal buckling load is obtained.


buckling FGM instability thermal load 


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  1. Brush, D.O., Almroth, B.O. 1975Buckling of Bars, Plates and Shells McGraw-HillNew YorkGoogle Scholar
  2. Eslami, M.R., Javaheri, R. 2002Thermo elastic buckling of rectangular plates made of functionally graded materialsAIAA Journal40162169Google Scholar
  3. Eslami, M.R., Shahsiyah, R. 2000Thermal buckling of imperfect cylindrical shellsJournal of Thermal Stresses247190Google Scholar
  4. Fettahlioglu, O.A. and Tabi, R. (1976). Consistent treatment of extensional deformation for the bending of arches, curved beams and rings, in Proceedings of the Petroleum Mechanical Engineering and Pressure Vessels and Piping Conference, Mexico ,September 19–24, 1976, Journal of Pressure Vessel Technology 99 Series J. No. 1, pp. 2–11, 1977.Google Scholar
  5. Fettahlioglu, O.A. and Tabi, R. (1987). Effect of Transverse shearing deformation on the coupled twist–bending of curved beams, in Proceedings of the joint ASME/CSME Pressure Vessels and Piping Conference, Montreal, Canada, June 25–30, 1987, Paper no. 78-PVP-102.Google Scholar
  6. Kang, Y.J., Yoo, C.H. 1994Thin-walled curved beams I: formulation of nonlinear equationsJournal of Engineering Mechanics ASCE12020722010Google Scholar
  7. Kim,  M.-Y, Min, B., Suh, M.W. 2000Spatial stability of non symmetric thin-walled curved beamsJournal of Engineering Mechanics ASCE126497505Google Scholar
  8. Love, A.E.H. 1934A treatise on the Mathematical Theory of Elasticity. Dover Books on Physics & ChemistryDover PublicationsNew YorkGoogle Scholar
  9. Papangelis, T.P., Trahair, N.S. 1987aFlexural–torsional buckling of archesJournal of Structural Engineering ASCE113889906Google Scholar
  10. Praveen, G.N., Reddy, J.N. 1998Nonlinear transient thermo elastic analysis of functionally graded ceramic metal platesInternational Journal of Solids and Structures3544574476CrossRefGoogle Scholar
  11. Rajasencaran, S., Padmanbhan, S. 1989Equations of curved beamsJournal of Engineering Mechanics ASCE11510941111Google Scholar
  12. Roark, R.J., Young, W.C. 1975Formulas for Stress and Strain5McGraw-HillNew YorkGoogle Scholar
  13. Timoshenko, S.P., Gere, J.M. 1961Theory of Elastic Stability2McGraw-HillNew YorkGoogle Scholar
  14. Valso, V.Z. 1961Thin Walled Elastic Beams2National science foundationWashington DCGoogle Scholar
  15. Yang, Y.B., Kuo, S.R. 1987Effect of curvature on stability of curved beamsJournal of Structural Engineering ASCE11311851202Google Scholar
  16. Yang, Y.B., Kou, S.R., Yau, J.D. 1991Use of straight beam approach to study buckling of curved beamsJournal of Structural Engineering ASCE11719631978Google Scholar
  17. Yoo, Chai Hong 1982Flexural–tensional stability of curved beamsJournal of Engineering Mechanical Division ASCE10813511369Google Scholar

Copyright information

© Springer 2006

Authors and Affiliations

  1. 1.Department of Mechanical Engineering, Faculty of EngineeringTehran UniversityTehranIran

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