Elasticity Solution Approach for Functionally Graded Spherical Shell with Piezoelectric Properties

Document Type : Research Paper

Authors

1 Mechanical Engineering Department, Azarbaijan shahid madani University, Tabriz, Iran

2 Department of Mechanical Engineering, University of Kashan, Kashan, Iran

Abstract

Based on elasticity approach, 1D analytical method is adopted in radial direction to analyze spherical shell made of FGPM. The mechanical properties are regulated by volume fraction as a function of radial coordinate. Loading can be internal and external pressures, or electric field. All mechanical and piezoelectric properties except the Poisson’s ratio are assumed to be power functions of radius. The 3D governing equations are reduced to a 1D second order nonlinear differential equation in terms of radial displacement, which then is solved analytically. By satisfying four different sets of boundary conditions and incorporating them into governing equation, a system of algebraic equations is obtained that delivers the unknown constants. Static responses of FG shell to electro-mechanical loads with different powers of material in-homogeneity ‘n’ as well as the effects of size are investigated. The accuracy and computational efficiency of the proposed approach are verified by comparing the results with those obtained for homogenous material in the literature. The induced stresses are compared to the residual stresses locked in the homogeneous sphere.

Keywords

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References

[1] Crawley, E. F., "Intelligent Structures for Aerospace: a Technology Overview and Assessment", J. AIAA, Vol. 32, pp. 1689–1689, (1994).
 
[2] Niino, A., and Maeda, S., "Recent Development Status of Functionally Gradient Materials", Int. J. ISI Vol. 30, pp. 699– 703, (1990).
 
[3] Yamada, K., Yamazaki, D., and Nakamura, K., "A Functionally Graded Piezoelectric Material Created by an Internal Temperature Gradient", Jpn J. Appl. Phys. Vol. 2, No. 40, pp. 49–52, (2001).
 
[4] Chen, W. Q., Ding, H. J., and Liang, J., "The Exact Elastoelectric Field of a Rotating Piezoceramic Spherical Shell with a Functionally Graded Property", Int. J. Solids Struct., Vol. 38, pp. 7015–7027, (2001).
 
[5] Lim, C. W., and He, L. H., "Exact Solution of a Compositionally Graded Piezoelectric Layer under Uniform Stretch Bending and Twisting", Int. J. Mech. Sci., Vol. 43, pp. 2479–2492, (2001).
 
[6] Sinha, D.K., "Note on the Radial Deformation of a Piezoelectric, Polarized Spherical Shell with a Symmetrical Distribution", J. Acoust. Soc. Vol. 34, pp. 1073– 1075, (1962).
 
[7] Chen,W.Q., and Ding, H.J., "A State-space-based Stress Analysis of a Multilayered Spherical Shell with Spherical Isotropy", J. Applied Mech. Vol. 68, pp. 109–114, (2001).
 
[8] Ghorbanpour, A., Golabi, S., and Saadatfar, M., "Stress and Electric Potential Fields in Piezoelectric Smart Spheres", J. Mech. Sci. Technol. Vol. 20, pp. 1920–1933, (2006).
 
[9] Saadatfar, M., and Rastgoo, A., "Stress in Piezoelectric Hollow Sphere under Thermal Environment", J. Mech. Sci. Technol. Vol. 22, pp. 1460–1467, (2008).
 
[10] Shao, Z. S., Fan, L. F., and Wang, T. J., "Analytical Solutions of Stresses in Functionally Graded Circular Hollow Cylinder with Finite Length", J. Key Engng Mater., Vol. 261–263,  pp. 651–656, (2004).
 
[11] You, L.H., Zhang, J.J., and You, X.Y., "Elastic Analysis of Internally Pressurized Thick-walled Spherical Pressure Vessels of Functionally Graded Materials", Int. J. Pres. Ves. Pip. Vol. 82, pp. 347–354, (2005).
 
[11] Ding, H.J., Wang, H.M., and Chen, W.Q., "Analytical Solution for a Non-homogeneous Isotropic Piezoelectric Hollow Sphere", Arch. Appl. Mech. Vol. 73, pp. 49–62, (2003).
 
[12] Sladek, V., Sladek, J., and Zhang, Ch., "Transient Heat Conduction Analysis in Functionally Graded Materials by the Meshless Local Boundary Integral Equation Method", Comput. Mater. Sci. Vol. 28, pp. 494–504, (2003).
 
[13] Sladek, J., Sladek, V., Solek, P., and Saez, A., "Dynamic 3D Axisymmetric Problems in Continuously Non-homogeneous Piezoelectric Solids", Int. J. Solids Struct. Vol. 45, pp. 4523–4542, (2008).
 
[14] Wang, H.M., and Xu, Z.X., "Effect of Material Inhomogeneity on Electromechanical Behaviors of Functionally Graded Piezoelectric Spherical Structures", Comput. Mater. Sci. Vol. 48, pp. 440–445, (2010).
 
[15] Ghorbanpour, A., Salari, M., Khademizadeh, H., and Arefmanesh, A., "Magneto Thermoelastic Problems of FGM Spheres", Arch. Appl. Mech. Vol. 43, pp. 189–200, (2010).
 
[16] Setoodeh, A.R., Tahani, M., and Selahi, E., "Hybrid Layerwise-differential Quadrature Transient Dynamic Analysis of Functionally Graded Axisymmetric Cylindrical Shells Subjected to Dynamic Pressure", Composite Structures, Vol. 93, pp. 2663–2670, (2011).
 
[17] Ghorbanpour Arani, A., Kolahchi, R., Mosallaie Barzoki, A.A., and Loghman, A., "Electro-Thermo-mechanical Behaviors of FGPM Spheres using Analytical Method and ANSYS Software", Appl. Math. Modeling, Vol. 36, pp. 139–157, (2012).
 
[18] Zill, D.G., "A First Course in Differential Equations with Modeling Applications", Brooks/Cole Publishing Company, California, (2001).
 
[19] Sabzikar Boroujerdy, M., and Eslami, M. R., "Unsymmetrical Buckling of Piezo-FGM Shallow Clamped Spherical Shells under Thermal Loading", Journal of Thermal Stresses, Vol. 38, pp. 1290–1307, (2015).
 
[20] Shakeri, M., Saviz, M.R., and Yas, M.H., "Three-Dimensional Elasticity Solution for Thick Laminated Cylinder with Piezoelectric Layer", Iranian Journal of Mechanical Engineering, Transaction of ISME, Vol.16, No.2, pp. 4-10, (2005).
 
[21] Hafezalkotob, A., and Eslami, M. R., "Thermomechanical Buckling of Simply Supported Shallow FGM Spherical Shells with Temperature-dependent Material", Iranian Journal of Mechanical Engineering, Transaction of ISME, Vol. 11, pp. 39–65, (2010).
 
[22] Institute of Electrical and Electronics Engineers, Standard on Piezoelectricity, Std 176-1978 IEEE, New York, (1978).
 
[23] Reddy, J.N., "Mechanics of Laminated Composite Plates and Shells: Theory and Analysis", Boca Raton: CRC Press, (2004).
 
[24] Tiersten, H.F., "Linear Piezoelectric Plate Vibrations", Plenum Press, New York, (1969).
 
[25] Maleki, M., Farrahi, G.H., Haghpanah Jahromi, B., and Hosseinian, E., "Residual Stress Analysis of Auto frettaged Thick-walled Spherical Pressure Vessel", Int. J. Pressure Vessels and Piping, Vol. 87, pp. 396-401, (2010).
 

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