Effect of hygro-thermal loading on the two-dimensional response of a functionally graded piezomagnetic cylinder under asymmetric loads

Document Type : Article


Department of Mechanical Engineering, East China University of Science and Technology, Shanghai, China.


In this article, a semi-analytical solution is presented in order to analyze a functionally graded piezomagnetic (FGP) cylinder resting on an elastic foundation exposed to hygro-thermal loading. All mechanical, hygro-thermal and magnetic properties are considered to vary according to the power-law function through the thickness. The steady-state heat conduction and moisture diffusion equations are employed to attain the moisture concentration and temperature distributions in the FGP cylinder. The constitutive equations, and magnetic and mechanical equilibrium equations are combined in order to derive three second-order differential equations in terms of magnetic potential and mechanical displacements. The separation of variables and complex Fourier series method are utilized to solve governing equations. Numerical results reveal the effects of hygro-thermal loading, elastic foundation and non-homogeneity constants on hygro-thermo-magneto-elastic response of the functionally graded piezomagnetic cylinder. It is concluded that hygro-thermal loading has remarkable effects on the behavior of the cylinder leading to increase the absolute values of the radial magnetic induction, radial, circumferential and shear stresses.


Main Subjects

1. Koizumi, M. "FGM activities in Japan", Composites: Part B, 28, pp. 1-4 (1996).
2. Miyamoto, Y., Kaysser, W., Rabin, B., Kawasaki, A., and Ford, R., Functionally Graded Materials: Design, Processing and Appllications, Kluwer Academic Publishers (1999).
3. Mahamood, R.M.A., Esther, T., Shukla, M., and Pityana, S. "Functionally graded material: An overview", Proceedings of the World Congress on Engineering, 3, pp. 1-5 (2012).
4. Hosseini, M. and Dini, A. "Magneto-thermo-elastic response of a rotating functionally graded cylinder", Structural Engineering and Mechanics, 56(1), pp. 137- 156 (2015).
5. Mohsenizadeh, M., Gasbarri, F., Munther, M., Beheshti, A., and Davami, K. "Additively-manufactured lightweight metamaterials for energy absorption", Materials & Design, 139, pp. 521-530 (2018).
6. Rao, S.S. and Sunar, M. "Piezoelectricity and its use in disturbance sensing and control of  flexible structures: A survey", Applied Mechanics Reviews, 47(4), pp. 113-123 (1994).
7. Davami, K., Mohsenizadeh, M., Munther, M., Palma, T., Beheshti, A., and Momeni, K. "Dynamic energy absorption characteristics of additively-manufactured shape-recovering lattice structures", Mat. Res. Express., 6(4), p. 045302 (2018).
8. Chattopadhyay, S., Pressure Vessels: Design and Practice, CRC Press (2004).
9. Mita, A. and Kumagai, S.J.F. "An experimental study on soil-structure interaction effects", FAPIG (Tokyo), pp. 51-59 (1989).
10. Ahmadi, S.F. and Eskandari, M. "Rocking rotation of a rigid disk embedded in a transversely isotropic halfspace", Civil. Eng. Infrastruct. J., 47(1), pp. 125-138 (2014).
11. Ahmadi, S.F. and Eskandari, M. "Vibration analysis of a rigid circular disk embedded in a transversely isotropic solid", J. Eng. Mech., 140(7), p. 04014048 (2013).
12. Pak, R.Y. and Gobert, A.T. "Forced vertical vibration of rigid discs with arbitrary embedment", J. Eng. Mech., 117(11), pp. 2527-2548 (1991).
13. Khoshgoftar, M.J., Mirzaali, M.J., and Rahimi, G.H. "Thermoelastic analysis of non-uniform pressurized functionally graded cylinder with variable thickness using first order shear deformation theory (FSDT) and perturbation method", Chinese Journal of Mechanical Engineering, 28(6), pp. 1149-1156 (2015).
14. Atrian, A., Jafari Fesharaki, J., and Nourbakhsh, S.H. "Thermo-electromechanical behavior of functionally graded piezoelectric hollow cylinder under nonaxisymmetric loads", Applied Mathematics and Mechanics, 36(7), pp. 939-954 (2015).
15. Grigorenko, A.Y., Muller, W.H., Wille, R., and Loza, I.A. "Nonaxisymmetric electroelastic vibrations of a hollow sphere made of functionally gradient piezoelectric material", Continuum Mechanics and Thermodynamics, 26(6), pp. 771-781 (2014).
16. Hosseini, M., Dini, A., and Eftekhari, M. "Strain gradient effects on the thermoelastic analysis of a functionally graded micro-rotating cylinder using generalized differential quadrature method", Acta Mechanica, 228(5), pp. 1563-1580 (2017).
17. Meshkini, M., Firoozbakhsh, K., Jabbari, M., and Selkghafari, A. "Steady state thermal and mechanical stresses in two-dimensional functionally graded piezoelectric materials (2D-FGPMs) hollow cylinder", J. Scientia Iranica, 26(1), pp. 428-444 (2019).
18. Pourhamid, R., Ahmadian, M.T., Mahdavy Moghaddam, H., and Mohammadzadeh, A.R. "Mechanical analysis of a functionally graded cylinder-piston under internal pressure due to a combustion engine using a cylindrical super element and considering thermal loading", J. Scientia Iranica, Transactions B, Mechanical Engineering, 22(2), pp. 493-503 (2015).
19. Jabbari, M., Mohazzab, A.H., Bahtui, A., and Eslami, M.R. "Analytical solution for three-dimensional stresses in a short length FGM hollow cylinder",Zamm, 87(6), pp. 413-429 (2007).
20. Ghorbanpour Arani, A., Khoddami Maraghi, Z., Mozdianfard,  M.R., and Shajari, A.R. "Thermo-piezomagneto- mechanical stresses analysis of FGPM hollow rotating thin disk", Int. J. Mech. Mater. Des., 6(4), pp. 341-349 (2011).
21. Zenkour, A.M. "On the magneto-thermo-elastic responses of FG annular sandwich disks", International Journal of Engineering Science, 75, pp. 54-66 (2014).
22. Almasi, A., Baghani, M., Moallemi, A., Baniassadi, M., and Faraji, G. "Investigation on thermal stresses in FGM hyperelastic thick-walled cylinders", Journal of Thermal Stresses, 41(2), pp. 204-221 (2018/02/01 2018).
23. Shokrollahi, H. "Elastic-plastic analysis of functionally graded spherical pressure vessels using strain gradient plasticity", International Journal of Applied Mechanics, 9(8), p. 1750118 (2017).
24. Barati, A.R. and Jabbari, M. "Two-dimensional piezothermoelastic analysis of a smart FGM hollow sphere", Acta Mechanica, 226(7), pp. 2195-2224 (2015).
25. Sayman, O. "Analysis of multi-layered composite cylinders under hygrothermal loading", Composites Part A: Applied Science and Manufacturing, 36(7), pp. 923-933 (2005).
26. Dai, H.-L., Zheng, Z.-Q., and Dai, T. "Investigation on a rotating FGPM circular disk under a coupled hygrothermal field", Applied Mathematical Modelling, 46, pp. 28-47 (2017).
27. Ebrahimi, F. and Barati, M.R. "Hygrothermal effects on vibration characteristics of viscoelastic FG nanobeams based on nonlocal strain gradient theory", Composite Structures, 159, pp. 433-444 (2017).
28. Smittakorn, W. and Heyliger, P.R. "A discrete-layer model of laminated hygrothermopiezoelectric plates", Mechanics of Advanced Materials and Structures, 7(1), pp. 79-104 (2000).
29. Keles, I. and Tutuncu, N. "Exact analysis of axisymmetric dynamic response of functionally graded cylinders (or disks) and spheres", Journal of Applied Mechanics, 78(6), p. 061014 (2011).
30. Akbarzadeh, A.H. and Pasini, D. "Multiphysics of multilayered and functionally graded cylinders under prescribed hygrothermomagnetoelectromechanical loading", Journal of Applied Mechanics, 81(4), p. 041018 (2013).
31. Vinyas, M. and Kattimani, S.C. "Hygrothermal analysis of magneto-electro-elastic plate using 3D finite element analysis", Composite Structures, 180, pp. 617-637 (2017).
32. Akbarzadeh, A.H. and Chen, Z.T. "Hygrothermal stresses in one-dimensional functionally graded piezoelectric media in constant magnetic field", Composite Structures, 97, pp. 317-331 (2013).
33. Jafari Fesharaki, J., Jafari Fesharaki, V., Yazdipoor, M., and Razavian, B. "Two-dimensional solution for electro-mechanical behavior of functionally graded piezoelectric hollow cylinder", Applied Mathematical Modelling, 36(11), pp. 5521-5533 (2012).
34. Alashti, R.A. and Khorsand, M. "Three-dimensional thermo-elastic analysis of a functionally graded cylindrical shell with piezoelectric layers by differential quadrature method", International Journal of Pressure Vessels and Piping, 88(5-7), pp. 167-180 (2011).
35. Saadatfar, M. and Aghaie-Khafri, M. "Hygrothermomagnetoelectroelastic analysis of a functionally graded magnetoelectroelastic hollow sphere resting on an  elastic foundation", Smart Materials and Structures, 23(3), p. 035004 (2014).
36. Saadatfar, M. and Aghaie-Khafri, M. "Hygrothermal analysis of a rotating smart exponentially graded cylindrical shell with imperfect bonding supported by an elastic foundation", Aerospace Science and Technology, 43, pp. 37-50 (2015).
37. Akbarzadeh, A.H. and Chen, Z.T. "Magnetoelectroelastic behavior of rotating cylinders resting on an elastic foundation under hygrothermal loading", Smart Materials and Structures, 21(12), p. 125013 (2012).
38. Sih, G.C., Michopoulos, J., and Chou, S.C., Hygrothermoelasticity, Dordrecht: Martinus Nijhoff Publishers (1986).
39. Zenkour, A.M. "Hygrothermoelastic responses of inhomogeneous piezoelectric and exponentially graded cylinders", International Journal of Pressure Vessels and Piping, 119, pp. 8-18 (2014).
40. Badrieh, F. "Complex Fourier series", In Spectral, Convolution and Numerical Techniques in Circuit Theory, Springer, pp. 125-134 (2018).
41. Samea, P., Eskandari, M., and Ahmadi, S.F. "Displacement potentials for functionally graded piezoelectric solids", 52, pp. 458-469 (2017).
42. Hou, P.F. and Leung, A.Y.T. "The transient responses of magneto-electro-elastic hollow cylinders", Smart Materials and Structures, 13(4), pp. 762-776 (2004).