Effect of Porosity and Hygrothermal Environment on FGP ‎Hollow Spheres under Electromechanical Loads

Document Type : Research Paper

Authors

1 Department of Mathematics, Faculty of Science, Damietta University, P.O. Box 34517, Egypt‎

2 Department of Mathematics, Faculty of Science, Kafrelsheikh University, Kafrelsheikh 33516, Egypt‎

Abstract

Semi-analytical studies for the porosity action of a hollow sphere made of functionally graded piezoelectric material are presented. A semi-analytical technique for radial displacement is presented. A combination of internal and external pressures, temperature distribution, uniform hygrothermal distribution, and an electric potential variation has been discussed between the inner and outer surfaces of the sphere. The material physical properties for the present porous hollow sphere are varying through the thickness due to the power functions of the radius. Numerical outcomes are validated for radial displacement, electric potential, and stresses for the perfect and porous functionally graded hollow sphere. The effect of different mechanical, piezoelectric, and hygrothermal are investigated.

Keywords

Main Subjects

Publisher’s Note Shahid Chamran University of Ahvaz remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. 

‎[1] Zhang, Y., Wang, J., Fabrication of functionally graded porous polymer structures using thermal bonding lamination techniques, ‎Procedia Manufacturing, 10, 2017, 866–875.‎
‎[2] Wang, Y., Wan, Y., Zhang, Y., Vibrations of longitudinally traveling functionally graded material plates with porosities, European Journal of Mechanics - A/Solids, 66, 2017, 55–68.‎
‎[3] Gupta, A., Talha, M., Influence of initial geometric imperfections and porosity on the stability of functionally graded material plates, Mechanics Based Design of Structures and Machines, 46, 2017, 693–711.‎
‎[4] Zhou, K., Lin, Z., Huang, X., Hua, H., Vibration and sound radiation analysis of temperature-dependent porous functionally graded ‎material plates with general boundary conditions, Applied Acoustics, 154, 2019, 236–250.‎
‎[5] Akbas, S., Thermal effects on the vibration of functionally graded deep beams with porosity, International Journal of Applied Mechanics, 9(5), 2017, 1750076.‎
‎[6] Daikh, A.A., Zenkour, A.M., Free vibration and buckling of porous power law and sigmoid functionally graded sandwich plates using a ‎simple higher order shear deformation theory, Materials Research Express, 6, 2019, 115707.‎
‎[7] Barati, M.R., Sadr, M.H., Zenkour, A.M., Buckling analysis of higher order graded smart piezoelectric plates with porosities resting on ‎elastic foundation, International Journal of Mechanical Sciences, 117, 2016, 309–320.‎
‎[8] Zenkour, A.M., A quasi-3D refined theory for functionally graded single layered and sandwich plates with porosities, Composite Structures, 201, 2018, 36–48.‎
‎[9] Sobhy, M., Zenkour, A.M., Porosity and inhomogeneity effects on the buckling and vibration of double FGM nanoplates via a quasi-3D ‎refined theory, Composite Structures, 220, 2019, 289–303.‎
‎[10] Zenkour, A.M., Radwan, A.F., Bending response of FG plates resting on elastic foundations in hygrothermal environment with ‎porosities, Composite Structures, 213, 2019, 133–143.‎
‎[11] Jabbari, M., Karampour, S., Eslami, M.R., Steady state thermal and mechanical stresses of a poro-piezo FGM hollow sphere, Meccanica, 48, 2013, 699–719.‎
‎[12] Barati, M.R., Zenkour, A.M., Electro-thermoelastic vibration of plates made of porous functionally graded piezoelectric materials ‎under various boundary conditions, Journal of Vibration and Control, 24(10), 2016, 1910–1926.‎
‎[13] Zenkour, A.M., Aljadani, M.H., Porosity effect on thermal buckling behavior of actuated functionally graded piezoelectric nanoplates, European Journal of Mechanics/A Solids, 78, 2019, 103835.‎
‎[14] Allam, M.N.M., Tantawy, R., Thermomagnetic viscoelastic responses in a functionally graded hollow structure, Acta Mechanica Sinica, 27(4), 2011, 567–577.‎
‎[15] Dai, H.L., Hong, L., Fu, Y.M., Xiao, X., Analytical solution for electro magneto thermoelastic behaviors of a functionally graded ‎piezoelectric hollow cylinder, Applied Mathematical Modelling, 34, 2010, 343–357.‎
‎[16] Allam, M.N.M., Tantawy, R., Zenkour, A.M., Magneto-thermo-elastic response of exponentially graded piezoelectric hollow spheres, ‎Advances in Computational Design, 3, 2018, 303–318.‎
‎[17] Dai, H.L., Xiao, X., Fu, Y.M., Analytical solutions of stresses in functionally graded piezoelectric hollow structures, Solid State Communications, 150, 2010, 763–767.‎
‎[18] Reddy, J.N., Chin, C.D., Thermomechanical analysis of functionally graded cylinders and plates, Journal of Thermal Stresses, 21, ‎‎1998, 593–626.‎
‎[19] Reddy, J.N., Analysis of functionally graded plates, International Journal for Numerical Methods in Engineering, 47, 2000, 663–684.‎
‎[20] Reddy, J.N., Cheng, Z.Q., Three-dimensional thermomechanical deformations of functionally graded rectangular plates, European Journal of Mechanics - A/Solids, 20, 2001, 841–855.‎
‎[21] Zenkour, A.M., A comprehensive analysis of functionally graded sandwich plates: Part 1 Deflection and stresses, International Journal of Solids and Structures, 42, 2005, 5224–5242.‎
‎[22] Zenkour, A.M., A comprehensive analysis of functionally graded sandwich plates: Part 2 Buckling and free vibration, International Journal of Solids and Structures, 42, 2005, 5243–5258.‎
‎[23] Zenkour, A.M., Generalized shear deformation theory for bending analysis of functionally graded plates, Applied Mathematical Modelling, 30, 2006, 67–84.‎
‎[24] Allam, M. N. M., Zenkour, A.M., Tantawy, R., Analysis of functionally graded piezoelectric cylinders in a hygrothermal environment, Advances in Applied Mathematics and Mechanics, 6, 2014, 233-246.‎
‎[25] Allam, M.N.M., Tantawy, R., Yousof, A., Zenkour, A.M., Elastic and viscoelastic stresses of nonlinear rotating functionally graded ‎solid and annular disks with gradually varying thickness, Archive of Mechanical Engineering, 4, 2017, 423–440.‎
‎[26] Sankar, B.V., An elasticity solution for functionally graded beams, Composites Science and Technology, 61, 2001, 689–696.‎
‎[27] Zenkour, A.M., Benchmark trigonometric and 3-D elasticity solutions for an exponentially graded thick rectangular plate, Archive of Applied Mechanics, 77, 2007, 197–214.‎
‎[28] Zenkour, A.M., Elsibai, K.A., Mashat, D.S., Elastic and viscoelastic solutions to rotating functionally graded hollow and solid ‎cylinders, Applied Mathematics and Mechanics (English Edition), 29(12), 2008, 1601–1616. ‎
‎[29] Cuong, L. T., Nguyen, D. K., Nguyen, N., Khatir, S., Xuan, H. N., Abdel-Wahab, M., A three-dimensional solution for free vibration ‎and buckling of annular plate, conical, cylinder and cylindrical shell of FG porous-cellular materials using IGA, Composite Structures, ‎‎259, 2021, 113216.‎
‎[30] Nguyen, H. X., Nguyen, T. N., Abdel-Wahab, M., Bordas, S.P.A., Xuan, H.N., Vo, T. P., A refined quasi-3D isogeometric analysis for ‎functionally graded microplates based on the modified couple stress theory, Computer Methods in Applied Mechanics and Engineering, ‎‎313, 2017, 904-940.‎
‎[31] Praveen, G.N., Reddy, J.N., Nonlinear transient thermoelastic analysis of functionally graded ceramic–metal plates, International Journal of Solids and Structures, 35, 1998, 4457–4476.‎
‎[32] Zenkour, A.M., Alghamdi, N.A., Thermoelastic bending analysis of functionally graded sandwich plates, Journal of Materials Science, ‎‎43, 2008, 2574–2589. ‎
‎[33] Van, P.P., Thai, C. H., Xuan, H.N., Abdel Wahab, M., Porosity-dependent nonlinear transient responses of functionally graded ‎nanoplates using isogeometric analysis, Composites Part B: Engineering, 164, 2019, 215-225.‎
‎[34] Allam, M.N.M., Tantawy, R., Zenkour, A.M., Thermoelastic stresses in functionally graded rotating annular disks with variable ‎thickness, Journal of Theoretical and Applied Mechanics, 56(4), 2018, 1029–1041.‎
‎[35] Li, X.Y., Ding, H.J., Chen, W.Q., Axisymmetric elasticity solutions for a uniformly loaded annular plate of transversely isotropic ‎functionally graded materials, Acta Mechanica, 196, 2008, 139–159.‎
‎[36] Ueda, S., A cracked functionally graded piezoelectric material strip under transient thermal loading, Acta Mechanica, 199, 2008, 53–‎‎70.‎
‎[37] Thanh, C. L., Nguyen, T. N., Vu, T. H., Khatir, S., Abdel-Wahab, M., A geometrically nonlinear size-dependent hypothesis for porous ‎functionally graded micro-plate, Engineering with Computers, 2020, DOI: 10.1007/s00366-020-01154-0. ‎
‎[38] Heyliger, P., A note on the static behavior of simply-supported laminated piezoelectric cylinders, International Journal of Solids and Structures, 34, 1997, 3781–3794.‎
‎[39] Bayat, M., Saleem, M., Sahari, B.B., Hamouda, A.M.S., Mahdi, E., Analysis of functionally graded rotating disks of variable thickness, Mechanics Research Communications, 35, 2008, 283–309.‎
‎[40] Dunn, M.L., Taya, M., Electrostatic field concentrations in and around inhomogenities in piezo-electric solids, Journal of Applied Mechanics, 61, 1994, 474–475.‎
‎[41] Ghorbanpour Arani, A., Kolahchi, R., Mosallaie Barzoki, A. A., Effect of material in-homogeneity on electro-thermo-mechanical ‎behaviors of functionally graded piezoelectric rotating shaft, Applied Mathematical Modelling, 35, 2011, 2771–2789.‎
‎[42] Sinha, D.K., Note on the radial deformation of a piezoelectric polarized spherical shell with symmetrical temperature distribution, Journal of the Acoustical Society of America, 34, 1962, 1073–1075.‎
‎[43] Dai, H.L., Wang, X., Thermo-electro-elastic transient responses in piezoelectric hollow structures, International Journal of Solids and Structures, 42, 2005, 1151–1171.‎
‎[44] Raja, S., Sinha, P.K., Prathap, G., Dwarakanathan, D., Influence of active stiffening on dynamic behavior of piezo-hygro-thermo elastic ‎composite plates and shell, Journal of Sound and Vibration, 278, 2004, 257–283.‎
‎[45] Sih, G.C., Michopoulos, J.G., Chou, S.C., Hygrothermoelasticity, Dordrecht, Martinus Nijhoff Publisheres, 1986.‎
‎[46] Paria, G., Magneto-elasticity and magneto-thermo-elasticity, Advances in Applied Mechanics, 10(1), 1967, 73–112.‎
‎[47] Ootao, Y., Tanigawa, Y., Transient piezothermoelastic analysis for a functionally graded thermopiezoelectric hollow sphere, Composite Structures, 81, 2007, 540–549.‎
‎[48] Ghorbanpour Arani, A., Kolahchi, R., Mosallaie Barzoki, A. A., Loghman, A., Electro-thermo-mechanical behaviors of FGPM spheres ‎using analytical method and ANSYS software, Applied Mathematical Modelling, 36, 2012, 139–157.‎