15. Hygrothermal analysis of heterogeneous piezoelectric elastic cylinders

Ashraf M. Zenkour

Department of Mathematics, Faculty of Science, King Abdulaziz University,
P.O. Box 80203, Jeddah 21589, Saudi Arabia

Department of Mathematics, Faculty of Science, Kafrelsheikh University, Kafr El-Sheikh 33516, Egypt

E-mail: zenkour@gmail.com

(Received 2 August 2015; received in revised form 14 January 2016; accepted 20 January 2016)

Abstract. The analytical solutions of hygrothermal effects in heterogeneous piezoelectric solid and hollow cylinders are obtained. The interaction of electric displacement, electric potentials, and elastic deformations is discussed. The present cylinder is subjected to a mechanical load at its lateral surfaces as well as an electric potential. The displacement, stresses and electric potentials in the heterogeneous piezoelectric cylinders are determined. The material properties coefficients of the present cylinder are assumed to be changed in the radial direction. The hygrothermoelastic responses of piezoelectric heterogeneous hollow and solid circular cylinders are presented. Numerical application examples for both cylinders are displayed. The significant of influence of material inhomogeneity, initial temperature, final moisture, and the pressure load and electric potential ratios are investigated. Suitable discussions and conclusions are presented.

Keywords: heterogeneous, piezoelectric material, hygrothermal effect, hollow and solid cylinders.


[1]        Petroski H. J. On the finite torsion and radial heating of thermoelastic cylinders. International Journal of Solids and Structures, Vol. 11, Issue 6, 1975, p. 741‑749.

[2]        Reddy J. N., Chin C. D. Thermomechanical analysis of functionally graded cylinders and plates. Journal of Thermal Stresses, Vol. 21, Issue 6, 1998, p. 593‑626.

[3]        Ponnusamy P. Wave propagation in a generalized thermoelastic solid cylinder of arbitrary cross‑section. International Journal of Solids and Structures, Vol. 44, Issue 16, 2007, p. 5336‑5348.

[4]        Zenkour A. M. Thermoelastic analysis of an annular sandwich disk with metal/ceramic faces and functionally graded core. Journal of Thermoplastic Composite Materials, Vol. 22, Issue 2, 2009, p. 163‑181.

[5]        Chitikireddy R., Datta S. K., Shah A. H., Bai H. Transient thermoelastic waves in an anisotropic hollow cylinder due to localized heating. International Journal of Solids and Structures, Vol. 48, Issue 21, 2011, p. 3063‑3074.

[6]        Sharma J. N., Sharma P. K., Mishra K. C. Analysis of free vibrations in axisymmetric functionally graded thermoelastic cylinders. Acta Mechanica, Vol. 225, Issue 6, 2014, p. 1581‑1594.

[7]        Kollár L. P., Patterson J. M., Springer G. S. Composite cylinders subjected to hygrothermal and mechanical loads. International Journal of Solids and Structures, Vol. 29, Issue 12, 1992, p. 1519‑1534.

[8]        Kollár L. P. Three-dimensional analysis of composite cylinders under axially varying hygrothermal and mechanical loads. Computers and Structures, Vol. 50, Issue 4, 1994, p. 525‑540.

[9]        Yang Yu-C., Chu S-S., Lee H.-L., Lin S.-L. Hybrid numerical method applied to transient hygrothermal analysis in an annular cylinder. International Communications in Heat and Mass Transfer, Vol. 33, Issue 1, 2006, p. 102‑111.

[10]     Wang B. L. Transient thermal fracture of a piezoelectric cylinder. Journal of Thermal Stresses, Vol. 28, Issue 2, 2005, p. 197‑212.

[11]     Dai H.-L., Wang X., Dai Q. H. Thermoelectroelastic responses in orthotropic piezoelectric hollow cylinders subjected to thermal shock and electric excitation. Journal of Reinforced Plastics and Composites, Vol. 24, Issue 10, 2005, p. 1085‑1103.

[12]     Dai H. L., Wang X. Magneto‑thermo‑electro‑elastic transient response in a piezoelectric hollow cylinder subjected to complex loadings. International Journal of Solids and Structures, Vol. 43, Issues 18‑19, 2006, p. 5628‑5646.

[13]     Arani A. G., Barzoki A. A. M., Kolahchi R., Mozdianfard M. R., Loghman A. Semi-analytical solution of time-dependent electro-thermo-mechanical creep for radially polarized piezoelectric cylinder. Computers and Structures, Vol. 89, Issues 15‑16, 2011, p. 1494‑1502.

[14]     Dai H. L., Fu Y. M., Yang J. H. Electromagnetoelastic behaviors of functionally graded piezoelectric solid cylinder and sphere. Acta Mechanica Sinica, Vol. 23, Issue 1, 2007, p. 55‑63.

[15]     Fesharaki J. J., Fesharaki V. J., Yazdipoor M., Razavian B. Two-dimensional solution for electro‑mechanical behavior of functionally graded piezoelectric hollow cylinder. Applied Mathematical Modelling, Vol. 36, Issue 11, 2012, p. 5521‑5533.

[16]     Zenkour A. M. Piezoelectric behavior of an inhomogeneous hollow cylinder with thermal gradient, International Journal of Thermophysics, Vol. 33, Issue 7, 2012, p. 1288‑1301.

[17]     Arefi M. Nonlinear thermoelastic analysis of thick-walled functionally graded piezoelectric cylinder. Acta Mechanica, Vol. 224, Issue 11, 2013, p. 2771‑2783.

[18]     Dai H.-L., Jiang H.-J. Analytical study for electromagnetothermoelastic behavior of a functionally graded piezoelectric solid cylinder. Mechanics of Advanced Materials and Structures, Vol. 20, Issue 10, 2013, p. 811‑818.

[19]     Allam M. N. M., Zenkour A. M., Tantawy R. Analysis of functionally graded piezoelectric cylinders in a hygrothermal environment. The Advances in Applied Mathematics and Mechanics, Vol. 6, Issue 2, 2014, p. 233‑246.

[20]     Zenkour A. M. Hygrothermoelastic responses of inhomogeneous piezoelectric and exponentially graded cylinders. International Journal of Pressure Vessels and Piping, Vol. 119, 2014, p. 8‑18.

[21]     Zenkour A. M. Exact solution of thermal stress problem of an inhomogeneous hygrothermal piezoelectric hollow cylinder. Applied Mathematical Modelling, Vol. 38, Issue 24, 2014, p. 6133‑6143.

Cite this article

Zenkour Ashraf M. Hygrothermal analysis of heterogeneous piezoelectric elastic cylinders. Mathematical Models in Engineering, Vol. 2, Issue 1, 2016, p. 1‑17.


Mathematical Models in Engineering. June 2016, Volume 2, Issue 1

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