Abstract
In this article, buckling analysis of functionally graded material (FGM) beams with or without surface-bonded piezoelectric layers subjected to both thermal loading and constant voltage is studied. Thermal and mechanical properties of FGM layer is assumed to follow the power law distribution in thickness direction, except Poisson’s ratio which is considered constant. The Timoshenko beam theory and nonlinear strain-displacement relations are used to obtain the governing equations of piezoelectric FGM beam. Beam is assumed under three types of thermal loading and various types of boundary conditions. For each case of boundary conditions, existence of bifurcation-type buckling is examined and for each case of thermal loading and boundary conditions, closed-form solutions are obtained which are easily usable for engineers and designers. The effects of the applied actuator voltage, beam geometry, boundary conditions, and power law index of FGM beam on critical buckling temperature difference are examined.
Similar content being viewed by others
References
Abbasi, M., Sabbaghian, M., Eslami, M.R.: Exact closed-form solution of the dynamic coupled thermoelastic response of a functionally graded Timoshenko beam. J. Mech. Mater. Struct. 5(1), 79–94 (2010)
Alibeigloo, A.: Thermoelasticity analysis of functionally graded beam with integrated surface piezoelectric layers. Compos. Struct. 92(6), 1535–1543 (2010)
Anandrao, K.S., Gupta, R.K., Ramchandran, P., Rao, G.V.: Thermal post-buckling analysis of uniform slender functionally graded material beams. Eng. Mech. 36(5), 545–560 (2010)
Aydoglu, M.: Thermal buckling analysis of cross-ply laminated composite beams with general boundary conditions. Compos. Sci. Technol. 67(6), 1096–1104 (2007)
Aydoglu, M., Taskin, V.: Free vibration analysis of functionally graded beams with simply supported edges. Mater. Des. 28(5), 1651–1656 (2007)
Bian, Z.G., Lim, C.W., Chen, W.Q.: On functionally graded beams with integrated surface piezoelectric layers. Compos. Struct. 72(3), 339–351 (2006)
Brush, D.O., Almorth, B.O.: Buckling of Bars, Plates, and Shells. McGraw-Hill, New York (1975)
Chen, L.W., Lin, C.Y., Wang, C.C.: Dynamic stability analysis and control of a composite beam with piezoelectric layers. Compos. Struct. 56(1), 97–109 (2002)
Gharib, A., Salehi, M., Fazeli, S.: Deflection control of functionally graded material beams with bonded piezoelectric sensors and actuators. Mat. Sci. Eng. A 498(1–2), 110–114 (2008)
Huang, D., Ding, H., Chen, W.: Analytical solution for functionally graded anisotropic cantilever beam under thermal and uniformly distributed load. J. Zhejiang Univ. Sci. A 8(9), 1351–1355 (2007)
Kang, Y.A., Li, X.F.: Large deflections of a non-linear cantilever functionally graded beam. J. Reinf. Plast. Comp. 29(12), 1761–1774 (2010)
Kapuria, S., Ahmed, A., Dumir, P.C.: Static and dynamic thermo-electro-mechanical analysis of angle-ply hybrid piezoelectric beams using an efficient coupled zigzag theory. Compos. Sci. Technol. 64(16), 2463–2475 (2004)
Kapuria, S., Bhattacharyya, M., Kumar, A.N.: Bending and free vibration response of layered functionally graded beams: a theoretical model and its experimental validation. Compos. Struct. 82(3), 390–402 (2008)
Khdeir, A.A.: Thermal buckling of cross-ply laminated composite beams. J. Acta Mech. 149(1-4), 201–213 (2001)
Kiani, Y., Eslami M., R.: Thermal buckling analysis of functionally graded material beams. Int. J. Mech. Mater. Des. 6(3), 229–238 (2010)
Li, S.R., Zhang, J.H., Zhao, Y.G.: Thermal post-buckling of functionally graded material Timoshenko beams. Appl. Math. Mech. 27(6), 803–810 (2006)
Li, S.R., Su, H.D., Cheng, C.J.: Free vibration of functionally graded material beams with surface-bonded piezoelectric layers in thermal environment. Appl. Math. Mech. 30(8), 969–982 (2009)
Liew, K.M., Yang, J., Kitipornchai, S.: Postbuckling of piezoelectric FGM plates subject to thermo-electro-mechanical loading. Int. J. Solids Struct. 40(15), 3869–3892 (2003)
Ma, L.S., Lee, D.W.: A further discussion of nonlinear mechanical behavior for FGM beams under in-plane thermal loading. Compos. Struct. 93(2), 831–842 (2011)
Mirzavand, B., Eslami, M.R.: Thermal buckling of simply supported piezoelectric FGM cylindrical shells. J. Therm. Stress. 30(11), 1117–1135 (2007)
Nirmala, K., Upadhyay, P.C., Prucz, J., Lyons, D.: Thermo-elastic stresses in composite beams with functionally graded layer. J. Reinf. Plast. Compos. 25(12), 1241–1254 (2006)
Praveen, G.N., Reddy, J.N.: Nonlinear transient thermoelastic analysis of functionally graded ceramic-metal plates. Int. J. Solids Struct. 35(33), 4457–4476 (1998)
Rastgo, A., Shafie, H., Allahverdizadeh, A.: Instability of curved beams made of functionally graded material under thermal loading. Int. J. Mech. Mater. Des. 2(1-2), 117–128 (2005)
Sankar, B.V.: An elasticity solution for functionally graded beams. Compos. Sci. Technol. 61(5), 689–696 (2001)
Shen, H.S.: Postbuckling of FGM plates with piezoelectric actuators under thermo-electro-mechanical loadings. Int. J. Solids Struct. 42(23), 6101–6121 (2005a)
Shen, H.S.: Postbuckling of axially loaded FGM hybrid cylindrical shells in thermal environments. Compos. Sci. Technol. 65(11-12), 1675–1690 (2005b)
Shen, H.S., Noda, N.: Postbuckling of pressure-loaded FGM hybrid cylindrical shells in thermal environments. Compos. Struct. 77(4), 546–560 (2007)
Sina, S.A., Navazi, H.M., Haddadpour, H.: An analytical method for free vibration analysis of functionally graded beams. Mater. Des. 30(3), 741–747 (2009)
Suresh, S., Mortensen, A.: Fundamentals of Functionally Graded Materials. IOM Communications Ltd., London (1998)
Wang, C.M., Wang, C.Y., Reddy, J.N.: Exact Solutions for Buckling of Structural Members. CRC Press, Boca Raton (2004)
Acknowledgements
The financial support of the National Elite Foundation is gratefully acknowledged.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Kiani, Y., Rezaei, M., Taheri, S. et al. Thermo-electrical buckling of piezoelectric functionally graded material Timoshenko beams. Int J Mech Mater Des 7, 185–197 (2011). https://doi.org/10.1007/s10999-011-9158-2
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10999-011-9158-2