Functionally graded materials are materials with tailored properties in one or more directions. This paper analyzes functionally graded cylinders with variation of properties according to various gradation laws available in literature of functionally graded materials. These gradation laws determine response of material under different loading and boundary conditions. The whole analysis is carried out in ABAQUS. USDFLD subroutine has been used for varying the material properties at elemental level. FGM cylinder under analysis has been loaded with coupled thermo-mechanical load where one surface of the plate is loaded with mechanical force and a temperature gradient is provided over the thickness of the cylinder. Another surface is free from any kind of mechanical forces. On application of force and thermal gradient maximum stresses generated and the maximum nodal temperature observed in the cylinder is compared with the failure limits considering factor of safety for the working conditions.On the basis of maximum stress observed and the corresponding nodal temperature using different gradation laws the application of these laws are justified.
A closed-form analytical solution is developed for a planar inhomogeneous beam subjected to transverse loading, using Variational Asymptotic Method (VAM). The VAM decouples the problem into a cross-sectional and an along-the-length analysis, leading to a set of ordinary differential equations. These equations along with associated boundary conditions have been solved to obtain the closed-form analytical solutions. Three distinct gradation models have been used to validate the present formulation against 3D FEA and few prominent results from the literature. Excellent agreement has been obtained for all the test cases. Key contributions of the present work are (a) the solutions have been obtained without any ad-hoc and a-prior assumptions (b) the ordered warping solutions results in Euler-Bernoulli type deformation in the zeroth-order, whereas the higher-order solutions provide novel closed-form expressions for transverse shear strain and stress. Finally, the effect of inhomogeneity on various field variables has been analyzed and discussed.
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