Two-dimensional Axisymmetric Electromechanical Response of Piezoelectric, Functionally Graded and Layered Composite Cylinders

Document Type : Research Paper


1 Institute Chair Professor, Department of Civil Engineering, Indian Institute of Technology Bombay

2 Manager (Design), S N Bhobe and Associates, Navi Mumbai


A mixed semi-analytical cum numerical approach is presented in this paper which accounts for the coupled mechanical and electrical response of piezoelectric, functionally graded (FG) and layered composite hollow circular cylinders of finite length. Under axisymmetric mechanical and electrical loadings, the three-dimensional problem (3D) gets reduced to a two-dimensional (2D) plane strain problem of elasticity. The 2D problem is further simplified and reduced to a one-dimensional (1D) by assuming an analytical solution in longitudinal direction (z) in terms of Fourier series expansion which satisfies the simply (diaphragm) supported boundary conditions exactly at the two ends z = 0, l. Fundamental (basic) dependent variables are chosen in the radial direction (thickness coordinate) of the cylinder. The resulting mathematical model is cast in the form of first order simultaneous ordinary differential equations which are integrated through an effective numerical integration technique by first transforming the BVP into a set of initial value problems (IVPs). The cylinder is subjected to internal/external pressurized mechanical and an electrical loading. Finally, numerical results are obtained which govern the active and sensory response of piezoelectric and FG cylinders. Numerical results are compared for their accuracy with available results. New results of finite length cylinders are generated and presented for future reference.


[1] Heyliger P. R., Pan E., 2004, Static fields in magnetoelectroelastic laminates, AIAA Journal 42 (7): 1435-1443.
[2] Kapuria S., Sengupta S., Dumir P.C., 1997, Three-dimensional solution for a hybrid cylindrical shell under axisymmetric thermoelectric load, Archive of Applied Mechanics 67: 320-330.
[3] Heyliger P. R., 1997, A note on the static behaviour of simply supported laminated piezoelectric cylinders, International Journal of Solids and Structures 34 (29): 3781-3794.
[4] Timoshenko S., Goodier J., 1951, Theory of Elasticity, New York, McGraw- Hill.
[5] Misovec A., Kempner J., 1970, Approximate elasticity solution for orthotropic cylinder under hydrostatic pressure and band loads, ASME Journal of Applied Mechanics 37(1): 101–108.
[6] Chandrashekhara K., Kumar B. S., 1993, Static analysis of a thick laminated circular cylindrical shell subjected to axisymmetric load, Composite Structures 23: 1-9.
[7] Horgan C., Chan A., 1999, The pressurized hollow cylinder or disk problem for functionally graded isotropic linearly elastic materials, Journal of Elasticity 55: 43–59.
[8] Galic D., Horgan C., 2002, Internally pressurized radially polarized piezoelectric cylinders, Journal of Elasticity 66: 257–272.
[9] Galic D., Horgan C., 2003, The stress response of radially polarized rotating piezoelectric cylinders, ASME Journal of Applied Mechanics 70: 426-435.
[10] Kapuria S. S., Dumir P., 1997, Three-dimensional solution for a hybrid cylindrical shell under axisymmetric thermoelectric load, Archive of Applied Mechanics 67: 320–330.
[11] Ye W G., Chen R., Cai J., 2001, A uniformly heated functionally graded cylindrical shell with transverse isotropy, Mechanics Research Communication 28(5): 535–542.
[12] Cady W. G., 1946, Piezoelectricity: an introduction to the theory and applications of electromechanical phenomena in crystals, New York: McGraw-Hill Book.
[13] Kant T., Ramesh C., 1981, Numerical integration of linear boundary value problems in solid mechanics by segmentation method, International Journal of Numerical Methods in Engineering 17: 1233-1256.
[14] Kangming X., Noor A. K., 1996, Three-dimensional analytical solutions for coupled thermoelectroelastic response of multilayered cylindrical shells, AIAA Journal 34(4): 802-812.
[15] Kollar L. P., Springer G. S., 2003, Mechanics of Composite Structures, first edition. New York: Cambridge University Press.
[16] Pagano N. J., 1969, Exact solutions for composite laminates in cylindrical bending, Journal of Composite Materials 3: 398-411.
[17] Lekhnitskii S., 1968, Anisotropic Plates, Gordon and Breach Science, New York.