首页|Analytical solution and semi-analytical solution for anisotropic functionally graded beam subject to arbitrary loading
Analytical solution and semi-analytical solution for anisotropic functionally graded beam subject to arbitrary loading
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NETL
NSTL
万方数据
维普
Analytical and semi-analytical solutions are presented for anisotropic functionally graded beams sub-ject to an arbitrary load, which can be expanded in terms of sinusoidal series. For plane stress prob-lems, the stress function is assumed to consist of two parts, one being a product of a trigonometric function of the longitudinal coordinate (x) and an undetermined function of the thickness coordinate (y), and the other a linear polynomial of x with unknown coefficients depending on y. The governing equa-tions satisfied by these y-dependent functions are derived. The expressions for stresses, resultant forces and displacements are then deduced, with integral constants determinable from the boundary conditions. While the analytical solution is derived for the beam with material coefficients varying exponentially or in a power law along the thickness, the semi-analytical solution is sought by making use of the sub-layer approximation for the beam with an arbitrary variation of material parameters along the thickness. The present analysis is applicable to beams with various boundary conditions at the two ends. Three numerical examples are presented for validation of the theory and illustration of the effects of certain parameters.
NETL
NSTL
万方数据
维普
