Thermal Buckling of Functionally Graded Beams

Document Type : Research Paper

Authors

1 Amirkabir University of Technology

2 Mechanical Engineering Department, Islamic Azad University, Tehran Central Branch,

Abstract

In this article, thermal stability of beams made of functionally graded material (FGM) is considered. The derivations of equations are based on the one-dimensional theory of elasticity. The material properties vary continuously through the thickness direction. Tanigawa's model for the variation of Poisson's ratio, the modulus of shear stress, and the coefcient of thermal expansion is considered. The equilibrium and stability equations for the functionally graded beam under thermal loading are derived using the variational and force summation methods. A beam containing six different types of boundary conditions is considered and closed form solutions for the critical normalized thermal buckling loads related to the uniform temperature rise and axial temperature difference are obtained. The results are reduced to the buckling formula of beams made of pure isotropic materials.

References

[1] Roark, R.J., and Young,W.C., Formulas for Stress and Strain, 5th ed., McGraw-Hill, New
York, (1975).
[2] Forray, M.J., ” Formulas for the Determination of Thermal Stresses in Rings ”, Reader's
Forum, J. Aero/Space Sci., Vol. 27, No. 3, pp. 238-240, (1960).
[3] Forray, M.J., ” Thermal Stresses in Rings ”, Reader's Forum, J. Aero/Space Sci., Vol. 26,
No. 5, pp. 310-311, (1959).
[4] Flugge, W., Thermal Stresses, in Handbook of Engineering Mechanics, McGraw-Hill,
New York, (1962).
[5] Timoshenko, S., Strength of Material, Vol. 2, 3rd ed., Van Nostrand, Princeton, (1956).
[6] Langhaar, H.L., Energy Methods in Applied Mechanics, John Wiley, New York, (1962).
[7] Fettahlioglu, O.A., and Tabi, R., ” Consistent Treatment of Extensional Deformations for
the Bending of Arches, Curved Beams and Rings ”, Proc., Pressure Vessels and Piping
Conference, pp. 19-24, Mexico City, 1976; J. Pressure Vessel Technology, Vol. 99, No. 1,
pp. 2-11, (1977).
[8] Fettahlioglu, O.A., and Tabi, R., ” Effect of Transverse Shearing Deformations on the
Coupled Twist-bending of Curved Beams ”, Proc. of the Joint ASME/CSME Pressure
Vessels and Piping Conference, pp. 78-102, Montreal, Canada, (1978).
[9] Cheng, S., and Hoff, N.J., ” Bending of Thin Circular Ring ”, Int. J. Solids and Structures,
Vol. 2, pp. 139-152, (1975).
[10] Timoshenko, S., Theory of Elastic Stability, Engineering Societies Monograph, McGraw-
Hill, New York, (1936).
[11] Carter, W.O., and Gere, J.M., ” Critical Buckling Loads for Tapered Columns ”, Trans.
Am. Soc. Civil Eng., Vol. 128, pt. 2, (1963).
[12] Culver, C.G., and Preg, Jr S.M., ” Elastic Stability of Tapered Beam-Column ”, Proc. Am.
Soc. Civil Eng., Vol. 94, No. ST2, (1968).
[13] Kitipornchai, S., and Trahair, N.S., ” Elastic Stability of Tapered I-Beams ”, Proc. Am.
Soc. Civil Eng., Vol. 98, No. ST3, March (1972).
[14] Morrison, T.G., ” Lateral Buckling of Constrained Beams ”, Proc. Am. Soc. Civil Eng.,
Vol. 98, No. ST3, (1972).
[15] Massey, C., and McGuire, P.J., ” Lateral Stability of Nonuniform Cantilevers ”, Proc. Am.
Soc. Civil Eng., Vol. 97, No. EM3, (1971).
[16] Fowler, D.W., ” Design of Laterally Unsupported Timber Beams ”, Proc. Am. Soc. Civil
Eng., Vol. 97, No. ST3, (1971).
[17] Clark, J.W., and Hill, H.N., ” Lateral Buckling of Beams ”, Proc. Am. Soc. Civil Eng.,
Vol. 86, No. ST7, (1960).
[18] Trahair, N.S., and Anderson, J.M., ” Stability of Monosymmetric Beams and Cantilevers
”, Proc. Am. Soc. Civil Eng., Vol. 98, No. ST1, (1972).
[19] Roorda, J., ” Some Thoughts on the Southwell Plot ”, Proc. Am. Soc. Civil Eng., Vol. 93,
No. EM6, (1967).
[20] Burgreen, D., and Manitt, P.J., ” Thermal Buckling of a Bimetallic Beam ”, Proc. Am.
Civil Eng., Vol. 95, No. EM2, (1969).
[21] Burgreen, D., and Regal, D., ” Higher Mode Buckling of Bimetallic Beam ”, Proc. Am.
Soc. Civil Eng., Vol. 97, No. EM4, (1971).
[22] Austin, W.J., ” In-plane Bending and Buckling of Arches ”, Proc. Am. Soc. Civil Eng.,
Vol. 97, No. ST5, 1971. Discussion by Schmidt, R., DaDeppo, D.A., and Forrester, K.,
ibid., Vol. 98, No. ST1, (1972).
[23] Chicurel, R., ” Shrink Buckling of Thin Circular Rings ”, ASME J. Appl. Mech., Vol. 35,
No. 3, (1968).
[24] Birman, V., ” Buckling of Functionally Graded Hybrid Composite Plates ”, Proc. 10th
Conference on Engineering Mechanics, Vol. 2, pp. 1199-1202, (1995).
[25] Ng, T.Y., Lam, Y.K., Liew, K.M., and Reddy, J.N., ” Dynamic Stability Analysis of Functionally
Graded Cylindrical Shell under Periodic Axial Loading ”, Int. J. Solids and Structures,
Vol. 38, pp. 1295-1300, (2001).
[26] Shahsiah, R., and Eslami, M.R., ” Thermal Buckling of Functionally Graded Cylindrical
Shell ”, J. Thermal Stresses, Vol. 26, No. 3, pp. 277-294, (2003).
[27] Shahsiah, R., and Eslami, M.R., ” Functionally Graded Cylindrical Shell Thermal Instability
Based on Improved Donnell Equations ”, J. AIAA, Vol. 41, No. 9, pp.1819-1826,
(2003).
[28] Najazadeh, M.M., and Eslami, M.R., ” First Order Theory Based Thermoelastic Stability
of Functionally Graded Material Circular Plates ”, J. AIAA, Vol. 40, No. 7, pp. 444-450,
(2002).
[29] Javaheri, R., and Eslami, M.R., ” Thermoelastic Buckling of Rectangular Plates made of
Functionally Graded Materials ”, J. AIAA, Vol. 40, No. 1, pp. 162-169, (2002).
[30] Javaheri, R., and Eslami, M.R., ” Buckling of Functionally Graded Plates under In-plane
Compressive Loading ”, J. ZAMM, Vol. 82, No. 4, pp. 277-283, (2002).
[31] Javaheri, R., and Eslami, M.R., ” Buckling of Functionally Graded Plates under In-plane
Compressive Loading Based on Various Plate Theories ”, Trans., Iranian Society of Mechanical
Engineers, Vol. 6, No. 1, pp. 76-93, March, (2005).
[32] Javaheri, R., and Eslami, M.R., ” Thermal Buckling of Functionally Graded Plates Based
on Higher Order Theory ”, J. Thermal Stresses, Vol. 25, No. 7, pp. 603-625, (2002).
[33] Shahsiah, R., and Eslami, M.R., ” Thermal Instability of Rings made of Functionally
Graded Materials ”, Proc. ASME-ESDA Conf., Istanbul, Turkey, July 2002.
[34] Shai, H., Naii, M.H., and Eslami, M.R., ” Mechanical Buckling of Curved Beams made
of FGM ”, Int. J. Mechanical Sciences, Vol. 48, Issue 8, pp. 907-915, (2006).
[35] Tanigawa, O., ” Optimization of Material Composition of Nonhomogeneous Hollow Circular
Cylinder for Thermal Stress Relaxation Making use of Neural Network ”, J. Thermal
Stresses, Vol. 22, No. 1, pp. 1-22, (1999).
 
Iranian Journal of Mechanical Engineering Transactions of the ISME
Volume 10, Issue 2 - Serial Number 13
September 2009
Pages 65-81

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