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Composites Part B: Engineering, Volume 45, Issue 1, February 2013, Pages 1310-1324.
M. Fraldi, F. Carannante, L. Nunziante.
Department of Structural Engineering, University of Napoli “Federico II”, Italy
Abstract
Object of the paper is to show the exact analytical solutions for the elastic response of a solid circular cylinder composed by the assembly of a central core and n surrounding hollow phases, all made of different homogeneous elastic materials, under de Saint Venant load conditions, finally obtaining for the whole object an equivalent one-dimensional homogenized beam model. In particular, the exact solution for the case of combined shear and bending is new for this type of heterogeneous compound materials, and hence it can turn useful for the comparison with other classical simplified solutions widely adopted in practical engineering problems.
The analytical procedure, producing overall elastic relationships between generalized stresses and strains for Functionally Graded Material Cylinders (FGMCs) in cases of axial force, torque, bending and shear, leads to register possible large increases of selected homogenized stiffness coefficients as effect of mutual interactions among the constituents mediated by their different Poisson ratios. The special case of negative Poisson ratios is then considered, envisaging the possibility of exploiting their relevant effects on the overall stiffness of the heterogeneous media in the design of new materials, starting from the particular microstructures or work processes. At the end, some example applications and sensitivity analyses are shown for two-phase cylinders.
Additional Information:
In the present work an analytical procedure to obtain exact elastic solutions for Functionally Graded Material Cylinders constituted by a central core and an arbitrary number of n hollow isotropic phases has been presented, showing the way of constructing the solution in terms of displacement potentials for all the possible combinations of de Saint Venant load conditions, that is axial force, torsion, bending and shear. The proposed method leads to estimate stress profiles within the constituents, as well as possible stress peaks at the material interfaces, as functions of the geometrical and elastic parameters characterizing the compound object, thus being a candidate to be utilized as a complementary tool in the design of such kind of composites. Together with some new results of practical interest for several engineering applications, the work finally derives – for each DSV loading case – the analytical form of all the stiffness coefficients of the homogenized FGMC treated as an equivalent one-dimensional beam-like, highlighting the crucial role played by the differences in Poisson ratios of the constituent materials on the object overall stiffness. In particular, through examples and sensitivity analyses presented at the end, some unexpected significant effects of alternate signs of positive and mechanically consistent negative Poisson ratios of adjacent phases on the increase of the overall FGMC stiffness are analytically derived and discussed in detail, and it is felt that some results might be also helpfully utilized for both designing composites with enhanced mechanical performance and better understanding specific optimality criteria which Nature obeys.
