Journal of Theoretical
and Applied Mechanics

56, 4, pp. 1097-1108, Warsaw 2018
DOI: 10.15632/jtam-pl.56.4.1097

Finite element study on thermal buckling of functionally graded piezoelectric beams considering inverse effects

Reza Nasirzadeh, Bashir Behjat, Mahsa Kharazi
In this article, the buckling behavior and bifurcation point of Functionally Graded Piezoelec-
tric (FGP) beams are investigated based on Euler-Bernoulli beam theory. The finite element
method is employed to model the beam in thermal environment. The material properties
of the beam are considered to vary gradually in the thickness direction and the beam is
subjected to electrical and thermal loading. In this paper, direct and inverse piezoelectric
effects are considered and buckling of the beam in the sensor state is investigated. By solving
the eigenvalue problem, the buckling load of the FGP beam is obtained and the effect of
various parameters such as power law index, temperature, applied voltage and beam aspect
ratio on the buckling load are investigated. The results show that the boundary conditions
are the main factor that affects the buckling load of the FGP beam.
Keywords: FGPM beam, buckling load, inverse piezoelectric effect, thermal environment


Bathe K.J., 1996, Finite Element Procedures, Prentice Hall, New York

Chen D., Yang J., Kitipornchai S., 2015, Elastic buckling and static bending of shear defor-

mable functionally graded porous beam, Composite Structures, 133, 54-61

Esfahani S.E., Kiani Y., Eslami M.R., 2013, Non-linear thermal stability analysis of tempera-

ture dependent FGM beams supported on non-linear hardening elastic foundations, International

Journal of Mechanical Sciences, 69, 10-20

Fallah A., Aghdam M.M., 2011, Nonlinear free vibration and post-buckling analysis of functio-

nally graded beams on nonlinear elastic foundation, European Journal of Mechanics-A/Solids, 30, 571-583

Fu Y., Wang J., Mao Y., 2012, Nonlinear analysis of buckling, free vibration and dynamic stabi-

lity for the piezoelectric functionally graded beams in thermal environment, Applied Mathematical

Modelling, 36, 4324-4340

Ghiasian S.E., Kiani Y., Eslami M.R., 2015, Nonlinear thermal dynamic buckling of FGM

beams, European Journal of Mechanics A/Solids, 54, 232-242

Jerome R., Ganesan N., 2010, New generalized plane strain FE formulation for the buckling

analysis of piezocomposite beam, Finite Elements in Analysis and Design, 46, 896-904

Kapuria S., Alam N., 2004, Zigzag theory for buckling of hybrid piezoelectric beams under

electromechanical loads, International Journal of Mechanical Sciences, 46, 1-25

Kiani Y., Eslami M., 2010, Thermal buckling analysis of functionally graded material beams,

International Journal of Mechanics and Materials in Design, 6, 229-238

Kiani Y., Rezaei M., Taheri S., Eslami M., 2011, Thermo-electrical buckling of piezoelectric

functionally graded material Timoshenko beams, International Journal of Mechanics and Materials

in Design, 7, 185-197

Komijani M., Esfahani S.E., Reddy J.N., Liu Y.P., Eslami M.R., 2014, Nonlinear thermal

stability and vibration of pre/post-buckled temperature- and microstructure-dependent functional-

ly graded beams resting on elastic foundation, Composite Structures, 112, 292-307

Komijani M., Kiani Y., Eslami M., 2012, Non-linear thermoelectrical stability analysis of func-

tionally graded piezoelectric material beams, Journal of Intelligent Material Systems and Structures, 24, 399-410

Komijani M., Reddy J.N., Ferreira A.J.M., 2013, Nonlinear stability and vibration of

pre/post-buckled microstructure-dependent FGPM actuators, Meccanica, 49, 1-17

Li S.R., Batra R.C., 2013, Relations between buckling loads of functionally graded Timoshenko

and homogeneous Euler-Bernoulli beams, Composite Structures, 95, 5-9

Li S,-R., Zhang J.-H., Zhao Y.-G., 2006, Thermal post-buckling of functionally graded material

Timoshenko beams, Applied Mathematics and Mechanics (English Edition), 27, 803-810

Li Z.-M., Qiao P., 2015, Buckling and postbuckling behavior of shear deformable anisotropic

laminated beams with initial geometric imperfections subjected to axial compression, Engineering

Structures, 85, 277-292

Nasirzadeh R., Behjat B., Kharazi M., 2014, Stability of FGP beams under thermo-

electromechanical loading, International Journal of Material Science Innovations, 2, 164-177

Rafiee M., Yang J., Kitipornchai S., 2013, Thermal bifurcation buckling of piezoelectric

carbon nanotube reinforced composite beams, Computers and Mathematics with Applications, 66, 1147-1160

Rahimi G., Gazor M., Hemmatnezhad M., Toorani H., 2013, On the postbuckling and free

vibrations of FG Timoshenko beams, Composite Structures, 95, 247-253

Takagi K., Li J.F., Yokoyama S., Watanabe R., 2003, Fabrication and evaluation of PZT/PT

piezoelectric composites and functionally graded actuators, Journal of the European Ceramic Society, 23, 1577-1583

Wattanasakulpong N., Gangadhara Prusty B., Kelly D.W., 2011, Thermal buckling and

elastic vibration of third-order shear deformable functionally graded beams, International Journal

of Mechanical Sciences, 53, 734-743