One-Dimensional Transient Thermal and Mechanical Stresses in FGM Hollow Cylinder with Piezoelectric Layers

Document Type : Research Paper


Mechanical Engineering Department, South Tehran Branch, Islamic Azad University, Iran


In this paper, an analytical method is developed to obtain the solution for the one dimensional transient thermal and mechanical stresses in a hollow cylinder made of functionally graded material (FGM) and piezoelectric layers. The FGM properties are assumed to depend on the variable r and they are expressed as power functions of r but the Poisson’s ratio is assumed to be constant. Transient temperature distribution, as a function of radial direction and time with general thermal boundary conditions on the inside and outside surfaces, is analytically obtained for different layers, using the method of separation of variables and generalized Bessel function. A direct method is used to solve the Navier equations, using the Euler equation and complex Fourier series. This method of solution does not have the limitations of the potential function or numerical methods as to handle more general types of the mechanical and thermal boundary conditions.


[1] Miyamoto Y., Kaysser W.A., Rabin B.H., Kaeasaki A., Ford R.G.,1999, Functionally graded materials: design, Processing and Applications, Kluwer Academic Publishers.
[2] Tiersten H.F., 1969, Linear Piezoelectric Plate Vibrations, Plenum Press.
[3] Ootao Y., Akai T., Tanigawa Y., 1995, Three-dimensional transient thermal stress analysis of a nonhomogeneous hollow circular cylinder due to a moving heat source in the axial direction, Journal of Thermal Stress 18: 497-512.
[4] Obata Y., Noda N., 1993, Transient thermal stress in a plate of functionally gradient materials, Ceramic Transactions 34: 403.
[5] Jabbari M., Sohrabpour S., Eslami M.R., 2003, General solution for mechanical and thermal stresses in a functionally graded hollow cylinder due to non-axisymmetric steady-state loads, Journal of Applied Mechanics 70: 111-118.
[6] Jabbari M., Sohrabpour S., Eslami M.R., 2002, Mechanical and thermal stresses in a functionally graded hollow cylinder due to radially symmetric loads, International Journal of Pressure Vessels and Piping 79: 493-497.
[7] Poultangari R., Jabbari M., Eslami M.R., 2008, Functionally graded hollow spheres under non-axisymmetric thermo-mechanical loads, International Journal of Pressure Vessels and Piping 85: 295-305.
[8] He X.Q., Ng T.Y., Sivashanker S., Liew K.M., 2001, Active control of FGM plates with integrated piezoelectric sensors and actuators, International Journal of Solids and Structures 38: 1641-1655.
[9] JafariFesharaki J., JafariFesharaki V., Yazdipoor M., Razavian B., 2012, Two-dimensional solution for electro-mechanical behavior of functionally graded piezoelectric hollow cylinder, Applied Mathematical Modeling 36: 5521-5533.
[10] Hosseini S.M., Akhlaghi M., Shakeri M., 2007, Transient heat conduction in functionally graded thick hollow cylinders by analytical method, Heat and Mass Transfer 43: 669-675.
[11] Chu H.S., Tzou J.H., 1987, Transient response of a composite hollow cylinder heated by a moving line source, American Society of Mechanical Engineers 3: 677-682.
[12] Jabbari M., Vaghari A.R., Bahtui A., Eslami M.R., 2008, Exact solution for asymmetric transient thermal and mechanical stresses in FGM hollow cylinders with heat source, Structural Engineering and Mechanics 29: 551-565.
[13] Jabbari M., Mohazzab A.H., Bahtui A., 2009, One-dimensional moving heat source in a hollow FGM cylinder, Journal of Applied Mechanics 131: 12021-12027.
[14] Ashida F., Tauchert T.R., 2001, A general plane-stress solution in cylindrical coordinates for a piezo-thermoelastic plate, International Journal of Solids and Structures 38: 4969-4985.
[15] Jabbari M., Barati A.R., 2015, Analytical solution for the thermo-piezoelastic behavior of a smart functionally graded material hollow sphere under radially symmetric loadings, Journal of Pressure Vessel Technology 137(6): 061204.