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Displacements, Strains, and Stresses Investigations in an Inhomogeneous Rotating Hollow Cylinder Made of Functionally Graded Materials under an Axisymmetric Radial Loading

DOI: 10.4236/wjm.2018.83005, PP. 59-72

Keywords: Functionally Graded Materials, Radial Stresses, Tangential Stresses, Cylinder Wall

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Abstract:

In this paper, an analytical and numerical study of strain fields, stress fields and displacements in a rotating hollow cylinder, whose walls were completely made in Functionally Graded Materials (FGM), was conducted. We have considered the rotating hollow cylinder submitted to an asymmetric radial loading. It is assumed that, because of the functional graduation of the material, the mechanical properties such as Young elastic modulus and the density varies in the radial direction, in accordance with a the power law function. The inhomogeneity parameter was selected between -1 and 1. On the basis of the second law of Newton, Hooke’s law and the strain-stress relationship, we established the differential equation which governs the equilibrium for a rotating hollow cylinder. We found the analytical solution and compared to the numerical solution obtained by using the shooting method and the fourth order Runge-Kutta algorithm. The analytical and numerical results lead to the conclusion that the magnitude of the tangential stresses is greater than that of the radial stresses. The changes due to the graduation of FGM does not produce consistent variations in the distribution of radial stresses, but strongly affects the distribution of tangential stresses. The tangential stresses, tangential strains and displacements are much higher at the inner surface of the cylinder wall. The internal radial pressure intensely affects the radial stresses and the radial strain.

References

[1]  Ndop, J. (2000) Mechanische Charakterisierung gradierter Materialien mit der Raster Ultraschallmikroskopie mit Vektorkontrast, Dissertation Fakultaet fuer Physik und Geowissenschaften, Universitaet Leipzig, Germany.
[2]  Suresh, S. and Mortensen, A. (1998) Fundamentals of Functionally Graded Materials, Book 698, IOM Communications Ltd.
[3]  Amada, S., Munekata, T., Nagase, Y. and Shimizu, N. (1995) Hierarchical Gradient Structure of Bamboo. In: Ilschner, B. and Cheraldi, N., Eds., Pro. 3rd International Symposium on Functionally Graded Materials, Presses Polytechniques Etuniversitaires Romandes, Lausanes.
[4]  Nogata, F., Matsui, K., Kagechika, K., Sueyoshi, Y. and Tomita, K. (1999) Estimation of In Vivo Bone Mineral Density (BMD) and Shape Characterization for Diagnosing Osteoporosis by Ultrasonic Inspection. Journal of Biomechanical Engineering, 121, 298-303.
[5]  Parviz, N. (1995) Wood Multilevel Gradient Structure. In: Ilschner, B. and Cheraldi, N., Eds., Pro. 3rd International Symposium on Functionally Graded Materials, Presses Polytechniques et Universitaires Romandes, Lausanes.
[6]  Ndop, J., Kim, T.J. and Grill, W. (1999) Mechanical Characterization of Graded Materials by Ultrasonic Microscopy with Phase Contrast. Materials Science Forum, 308-311, 873878.
https://doi.org/10.4028/www.scientific.net/MSF.308-311.873
[7]  Mahamood, R.M., Akinlabi, E.T., Shukla, M. and Pityana, S. (2012) Functionally Graded Material: An Overview. Proceedings of the World Congress on Engineering 2012, Vol. III, London, 4-6 July 2012.
[8]  Makwana, A.B. and Panchal, K.C. (2014) A Review of Stress Analysis of Functionally Graded Material Plate with Cut-out. International Journal of Engineering Research and Technology (IJERT), 3.
[9]  Sburlati, R. (2012) Analytical Elastic Solutions for Pressurized Hollow Cylinders with Internal Functionally Graded Coatings. Composite Structures, 94, 3592-3600.
https://doi.org/10.1016/j.compstruct.2012.05.018
[10]  Tutanku, N. (2007) Stresses in Thick-Walled FGM Cylinders with Exponentially-Varying Properties. Engineering Structures, 29, 2032-2035.
https://doi.org/10.1016/j.engstruct.2006.12.003
[11]  Peng, X.L. and Li, X.F. (2010) Thermal Stress in Rotating Functionally Graded Hollow Circular Disks. Composite Structures, 92, 1896-1904.
https://doi.org/10.1016/j.compstruct.2010.01.008
[12]  Jahromi, B.H., Nayeb-Hashemi, H. and Vaziri, A. (2012) Elasto-Plastic Stresses in a Functionally Graded Rotating Disk. Journal of Engineering Materials and Technology.
[13]  Eraslan, A.N. (2003) Elastic-Plastic Deformations of Rotating Variable Thickness Annular Disks Withfree, Pressurized and Radially Constrained Boundary Conditions. International Journal of Mechanical Sciences, 45, 643667.
https://doi.org/10.1016/S0020-7403(03)00112-7
[14]  Çallioglu, H., Bektas, N.B. and Sayer, M. (2011) Stress Analysis of Functionally Graded Rotating Discs: Analytical and Numerical Solutions. Acta Mechanica Sinica, 27, 950-955.
https://doi.org/10.1007/s10409-011-0499-8
[15]  Reddy, J.N. (2000) Analysis of Functionally Graded Materials. International Journal for Numerical Methods in Engineering, 47, 663-684.
https://doi.org/10.1002/(SICI)1097-0207(20000110/30)47:1/3<663::AID-NME787>3.0.CO;2-8
[16]  Sladeka, J., Sladeka, V. and Zhangb, Ch. (2005) Stress Analysis in Anisotropic Functionally Graded Materials by the MLPG Method. Engineering Analysis with Boundary Elements, 29, 597-609.
https://doi.org/10.1016/j.enganabound.2005.01.011
[17]  Horgan, C.O. and Chan, A.M. (1999) The Pressurized Hollow Cylinder or Disk Problem for Functionally Graded Isotropic Linearly Elastic Materials. Journal of Elasticity, 55, 43-59.
https://doi.org/10.1023/A:1007625401963
[18]  Timoshenko, S.P. and Goodier, J.N. (1970) Theory of Elasticity. 3rd Edition, McGraw Hill Book Company, California.

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