The Effect of Uniform Magnetic Field on Pressurized FG Cylindirical and Spherical Vessels

Abstract

The stress analysis of functionally graded thick hollow cylindrical and spherical pressure vessels under the effect of uniform magnetic field are examined. These pressure vessels are designed in such a way that the material properties and magnetic permeability are exponentially graded in radial direction, provided that the inner surface is pure metal and the outer surface is pure ceramic. The differential equations with variable coefficients obtained under these conditions are handled by both Complementary Functions Method and Pseudospectral Chebyshev Method. Benchmark solutions available in the literature for some special cases are used to confirm the results. The effects of different mixture and uniform magnetic field on stresses and displacement distribution are shown in graphical form.

Keywords

• Functionally graded materials,Uniform magnetic field,Stress analysis,Pseudospectral Chebyshev method

References

1. Erdogan, F. (1995). Fracture mechanics of functionally graded materials. Comput Engng, 5(7):753--770.
2. Tutuncu, N. and Ozturk, M. (2001). Exact solutions for stresses in functionally graded pressure vessels. Composites: Part B, 32:683--686.
3. Tutuncu, N. (2007). Stresses in thick-walled FGM cylinders with exponentially-varying properties. Engineering Structures, 29:2032--2035.
4. Yarımpabuç, D., Eker, M. and Celebi, K. (2018). Mechanical Behavior of Functionally Graded Pressure Vessels Under the Effect of Poisson's Ratio. European Mechanical Science, 2(2):52--59.
5. Eker, M., Yarımpabuç, D., Celebi, K., Yıldırım, A. (2017). Stress Analysis of Functionally GradedCylindirical Pressure Vessels by Pseudospectral Chebyshev Method. IAREC 2017 Conference Proceedings, p. 481.
6. Eker M., Yarımpabuç, D., Çelebi K., Yıldırım, A. (2017). Stress Analysis of Functionally GradedSpherical Pressure Vessels by Pseudospectral Chebyshev Method. IMSEC 2017 Conference Proceedings, p. 417.
7. Chen, Y.Z. and Lin, X.Y. (2008). Elastic analysis for thick cylinderical and spherical pressure vessels made of functionally graded materials. Computational Material Science, 44(2):581--587.
8. Li, X.F., Peng, X.L. and Kang, Y.A. (2009). Pressurized hollow spherical vessels with arbitrary radial nonhomogeneity. AIAA Journal, 47(9):2263--2265.

9. Nejad, M.Z. and Gharibi, M. (2014). Effect of Material Gradient on Stresses of Thick FGM Spherical Pressure Vessels with Exponentially-Varying Properties. J. Adv. Materials and Processing, 2(3):39--46.
10. Dai, H.L., Xiao, X. and Fu, Y.M. (2010). Analytical solutions of stresses in functionally graded piezoelectric hollowstructures. Solid State Communications, 150:763--767.
11. Dai, H.L., Fu, Y.M. and Dong, Z.M. (2006). Exact solutions for functionally graded pressure vesselsin a uniform magnetic field. International Journal of Solids and Structures, 43:5570--5580.
12. Gottlieb, D. (1981). The Stability of Pseudospectral-Chebyshev Methods. Mathematics of Computation, 36(153):107--118.
13. Trefethen,L.N. (2000). Spectral Methods in Matlab, SIAM, Philadelphia, PA.
14. Tutuncu, N. and Temel, B. (2009). A novel approach to stress analysis of pressurized FGM cylinders, disks and spheres. Compos. Struct., 91(3):385--390.
15. Tutuncu, N. and Temel, B. (2013). An efficient unified method for thermoelastic analysis of functionally graded rotating disks of variable thickness. Mech. Adv. Mater. Struct., 30(1):38--46.