Effect of Exponentially-Varying Properties on Displacements and Stresses in Pressurized Functionally Graded Thick Spherical Shells with Using Iterative Technique

Subject Areas : Engineering

M Zamani Nejad ¹ , A Rastgoo ² , A Hadi ³

1 - Mechanical Engineering Department, Yasouj University
2 - Mechanical Engineering Department, University of Tehran
3 - Mechanical Engineering Department, University of Tehran

Received: 2014-07-08 Accepted : 2014-09-13 Published : 2014-12-30

Keywords: Iterative technique, Elastic analysis, Functionally graded material (FGM), Thick sphere, Exponential,

Abstract :

A semi-analytical iterative method as one of the newest analytical methods is used for the elastic analysis of thick-walled spherical pressure vessels made of functionally graded materials subjected to internal pressure. This method is accurate, fast and has a reasonable order of convergence. It is assumed that material properties except Poisson’s ratio are graded through the thickness direction of the sphere according to an exponential distribution. For different values of inhomogeneity constant, distributions of radial displacement, radial stress, circumferential stress, and von Mises equivalent stress, as a function of radial direction, are obtained. A numerical solution, using finite element method (FEM), is also presented. Good agreement was found between the semi-analytical results and those obtained through FEM.

References:

[1] Zenkour A. M., 2012, Dynamical bending analysis of functionally graded infinite cylinder with rigid core, Applied Mathematics and Computation 218: 8997-9006.
[2] Kalali A. T., Hadidi-Moud S., 2013, A semi-analytical approach to elastic-plastic stress analysis of FGM pressure vessels, Journal of Solid Mechanics 5(1): 63-73.
[3] Shariyat M., 2009, A rapidly convergent nonlinear transfinite element procedure for transient thermoelastic analysis of temperature-dependent functionally graded cylinders, Journal of Solid Mechanics 1(4): 313-327.
[4] Tutuncu N., Ozturk M., 2000, Exact solutions for stresses in functionally graded pressure vessels, Composites Part B-Engineering 32(8): 683-686.
[5] You L. H., Zhang J. J., You X. Y., 2005, Elastic analysis of internally pressurized thick-walled spherical pressure vessels of functionally graded materials, International Journal of Pressure Vessels and Piping 82(5): 347-354.
[6] Chen Y. Z., Lin X. Y., 2008, Elastic analysis for thick cylinders and spherical pressure vessels made of functionally graded materials, Computational Materials Science 44(2): 581-587.
[7] Li X. F., Peng X. L., 2009, Kang Y. A., Pressurized hollow spherical vessels with arbitrary radial nonhomogeneity, AIAA Journal 47(9): 2262-2265.
[8] Tutuncu N., Temel B., 2009, A novel approach to stress analysis of pressurized FGM cylinders, disks and spheres, Composite Structures 91(3): 385-390.
[9] Nejad M. Z., Rahimi G. H., Ghannad M., 2009, Set of field equations for thick shell of revolution made of functionally graded materials in curvilinear coordinate system, Mechanika 77(3): 18-26.
[10] Borisov A. V., 2010, Elastic analysis of multilayered thick-walled spheres under external load, Mechanika 84(4): 28-32.
[11] Nie G. J., Zhong Z., Batra R. C., 2011, Material tailoring for functionally graded hollow cylinders and spheres, Composites Science and Technology 71(5): 666-673.
[12] Ghannad M., Nejad M. Z., 2012, Complete closed-form solution for pressurized heterogeneous thick spherical shells, Mechanika 18(5): 508-516.
[13] Nejad M. Z., Abedi M., Lotfian M. H., Ghannad M., 2012, An exact solution for stresses and displacements of pressurized FGM thick-walled spherical shells with exponential-varying properties, Journal of Mechanical Science and Technology 26(12): 4081-4087.
[14] Hassani A., Hojjati M. H., Farrahi G., Alashti R. A., 2011, Semi-exact elastic solutions for thermo-mechanical analysis of functionally graded rotating disks, Composite Structures 93: 3239-3251.
[15] Adomian G., 1998, A review of the decomposition method in applied mathematics, Journal of Mathematical Analysis and Applications 135: 501-544.
[16] He J.H., 1999, Homotopy perturbation technique, Computer Methods in Applied Mechanics and Engineering 178: 257-262.
[17] He J.H., 2004, Comparison of homotopy perturbation method and homotopy analysis method, Applied Mathematics and Computation 156: 527-539.
[18] He J.H., 2004, Asymptotology by homotopy perturbation method, Applied Mathematics and Computation 156: 591-596.
[19] He J.H., 2005, Homotopy perturbation method for bifurcation of nonlinear problems, International Journal of Nonlinear Sciences and Numerical Simulation 6: 207-208.
[20] He J.H., 2005, Application of homotopy perturbation method to nonlinear wave equations, Chaos Solitons & Fractals 26: 695-700.
[21] He J.H., 2006, Some asymptotic methods for strongly nonlinear equations, International Journal of Modern Physics B 20: 1141-1199.
[22] Olver P. J., 1996, Applications of Lie Groups to Differential Equations, Berlin, Springer.
[23] Gardner C. S., Kruskal M. D., Miura R. M., 1967, Method for solving the Korteweg-de Vries equation, Physical Review Letters 19: 1095-1097.
[24] Hirota R., 1971, Exact solution of the Korteweg-de Vries equation for multiple collisions of solitons, Physical Review Letters 27: 1192-1194.
[25] Wang M. L., Exact solutions for a compound KdV-Burgers equation, Physical Review Letters 213: 279-287.
[26] He J.H., 2000, Variational iteration method for autonomous ordinary differential systems, Applied Mathematics and Computation 114: 115-123.
[27] He J.H., 1998, Approximate analytical solution for seepage flow with fractional derivatives in porous media, Computer Methods in Applied Mechanics and Engineering 167: 57-68.
[28] He J.H., 1998, Approximate solution of nonlinear differential equations with convolution product nonlinearities, Computer Methods in Applied Mechanics and Engineering 167: 69-73.
[29] He J.H., Wu X.H., 2006, Construction of solitary solution and compacton-like solution by variational iteration method, Chaos Solitons & Fractals 29: 108-113.
[30] Hojjati M. H., Jafari S., 2007, Variational iteration solution of elastic non uniform thickness and density rotating disks, Far East Journal of Applied Mathematics 29: 185-200.
[31] Hojjati M. H., Jafari S., 2008, Semi-exact solution of elastic non-uniform thickness and density rotating disks by homotopy perturbation and Adomian’s decomposition methods, International Journal of Pressure Vessels and Piping 85: 871-878.
[32] Hojjati M. H., Jafari S., 2009, Semi-exact solution of non-uniform thickness and density rotating disks, International Journal of Pressure Vessels and Piping 86: 307-318.
[33] Asghari M., Ghafoori E., 2010, A three-dimensional elasticity solution for functionally graded rotaing disks, Composite Structures 92: 1092-1099.
[34] Temimi H., Ansari A. R., 2011, A semi-analytical iterative technique for solving nonlinear problems, Computers & Mathematics with Applications 61: 203-210.
[35] Temimi H., Ansari A. R., 2011, A new iterative technique for solving nonlinear second order multi-point boundary value problems, Applied Mathematics and Computation 218: 1457-1466.