3D analytical solution for a rotating transversely isotropic annular plate of functionally graded materials. (English) Zbl 1117.74034
Summary: An analytical solution for annular plate rotating at constant angular velocity is derived by means of direct displacement method from axisymmetric elasticity equations for functionally graded transversely isotropic media. The displacement components are assumed to be a linear combination of certain explicit functions of 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 an integrating scheme. The present solution can be degenerated into the solution for 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 material gradient index on the elastic field is illustrated numerically.
MSC:
| 74K20 | Plates |
| 74E05 | Inhomogeneity in solid mechanics |
| 74G05 | Explicit solutions of equilibrium problems in solid mechanics |
References:
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