| Mechanics & Civil Engineering |
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| 3D analytical solution for a rotating transversely isotropic annular plate of functionally graded materials |
| CHEN Jiang-ying, CHEN Wei-qiu |
| Faculty of Engineering, Ningbo University, Ningbo 315211, China; Department of Civil Engineering, Zhejiang University, Hangzhou 310027, China |
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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.
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Received: 14 February 2007
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