Three-dimensional analytical solution for a rotating disc of functionally graded materials with transverse isotropy |
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Authors: | Jiangying Chen Haojiang Ding Weiqiu Chen |
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Institution: | (1) Faculty of Engineering, Ningbo University, Ningbo, 315211, China;(2) Department of Civil Engineering, Zhejiang University, Hangzhou, 310027, China |
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Abstract: | Based on the basic equations for axisymmetric problems of transversely isotropic elastic materials, the displacement components
are expressed in terms of polynomials of the radial coordinate with the five involved coefficients, named as displacement
functions in this paper, being undetermined functions of the axial (thickness) coordinate. Five equations governing the displacement
functions are then derived. It is shown that the displacement functions can be found through progressive integration by incorporating
the boundary conditions. Thus a three-dimensional analytical solution is obtained for a transversely isotropic functionally
graded disc rotating at a constant angular velocity.The solution can be degenerated into that for an isotropic functionally
graded rotating disc. A prominent feature of this solution is that the material properties can be arbitrary functions of the
axial coordinate. Thus, the solution for a homogeneous transversely isotropic rotating disc is just a special case that can
be easily derived. An example is finally considered for a special functionally graded material, and numerical results shows
that the material inhomogeneity has a remarkable effect on the elastic field. |
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Keywords: | Rotating disc Functionally graded material Transverse isotropy 3D analytical solution |
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