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Abstract: The analytical solution for an annular plate rotating at a constant angular velocity is derived by means of direct displacement method from the elasticity equations for axisymmetric problems of functionally graded transversely isotropic media. The displacement components are assumed as a linear combination of certain explicit functions of the radial coordinate, with seven undetermined coefficients being functions of the axial coordinate z. Seven equations governing these z-dependent functions are derived and solved by a progressive integrating scheme. The present solution can be degenerated into the solution of a rotating isotropic functionally graded annular plate. The solution also can be degenerated into that for transversely isotropic or isotropic homogeneous materials. Finally, a special case is considered and the effect of the material gradient index on the elastic field is illustrated numerically.

[1] Chen, W.Q., Lee, K.Y., 2004. Stresses in rotating cross-ply laminated hollow cylinders with arbitrary thickness. The Journal of Strain Analysis for Engineering Design, 39(5):437-445.

[2] Chen, J.Y., Ding, H.J., Hou, P.F., 2003. Three-dimensional analysis of magnetoelectroelastic rotating annular plate. J. Zhejiang Univ. (Engineering Science), 37(4):440 (in Chinese).

[3] Chen, J.Y., Ding, H.J., Chen, W.Q., 2007. Three-dimensional analytical solution for a rotating disc of functionally graded materials with transverse isotropy. Arch. Appl. Mech., 77(4):241-251.

[4] Ding, H.J., Chen, W.Q., Zhang, L., 2006. Elasticity of Transversely Isotropic Materials. Springer, Dordrecht.

[5] Jain, R., Ramachandra, K., Simha, K.R.Y., 1999. Rotating anisotropic disc of uniform strength. Int. J. Mech. Sci., 41(6):639-648.

[6] Kordkheili, H.S.A., Naghdabadi, R., 2007. Thermoelastic analysis of a functionally graded rotating disk. Compos. Struct., 79(4):508-516.

[7] Leissa, A.W., Vagins, M., 1978. The design of orthotropic materials for stress optimization. Int. J. Solids Struct., 14(6):517-526.

[8] Lekhnitskii, S.G., 1968. Anisotropic Plates. Gordon and Breach, London.

[9] Mian, M.A., Spencer, A.J.M., 1998. Exact solutions for functionally graded and laminated elastic materials. J. Mech. Phys. Solids, 46(12):2283-2295.

[10] Murthy, D.N.S., Sherbourne, A.N., 1970. Elastic stresses in anisotropic disks of variable thickness. Int. J. Mech. Sci., 12(7):627-640.

[11] Ramu, S.A., Iyengar, K.J., 1974. Quasi-three dimensional elastic stresses in rotating disks. Int. J. Mech. Sci., 16(7):473-477.

[12] Seireg, A., Surana, K.S., 1970. Optimum design of rotating disks. J. Eng. Ind., 92:1-10.

[13] Timoshenko, S.P., Goodier, J.N., 1970. Theory of Elasticity (3rd Ed.). McGraw-Hill, New York.

[14] Yeh, K.Y., Han, R.P.S., 1994. Analysis of high-speed rotating disks with variable thickness and inhomogeneity. J. Appl. Mech., 61:186-191.

[15] Zhou, F., Ogawa, A., 2002. Elastic solutions for a solid rotating disk with cubic anisotropy. J. Appl. Mech., 69(1):81-83.