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Presented herein is the buckling response of circular sandwich plates with a homogenous core of variable thickness and constant thickness functionally graded material (FGM) face sheets whose material properties are assumed to be graded in the thickness direction according to a simple power law. The plate is modeled using the first order shear deformation plate theory and subjected to a uniform radial compression. In order to determine the distribution of the prebuckling load along the radius, the membrane equation is solved using the shooting method. Subsequently, by employing the pseudospectral method that makes use of Chebyshev polynomials, the stability equations are solved numerically to evaluate the critical buckling load. Numerical solutions are presented for both clamped and simply supported plates and for linear and parabolic core thickness distributions. The results show that the buckling behavior is significantly influenced by the thickness variation profile, the aspect ratio, the volume fraction index, and the core-to-face sheet thickness ratio. Comparison studies demonstrate that the results obtained using the current method compare very well with those available in the literature.

Effects of volume fraction and random dispersion of carbon nanotubes on effective mechanical properties of carbon nanotube-reinforced nanocomposites are studied at continuum level using finite element methods. Utilizing a continuum model of tubes with specific pairing of elastic properties and wall thickness for describing carbon nanotubes, representative volume elements with non-uniform distribution of uniaxial nanotubes within a base matrix are generated. Furthermore, a dispersion quantification technique is employed to quantify nanotubes' dispersion degree. Finite element simulations are carried out in six independent loading conditions, while applying periodic boundary conditions to the models. Homogenizing the models and using the formulations of linear elasticity, equivalent mechanical properties of the models are computed and the effects of the aforementioned influential parameters as well as the modeling volume size are investigated. The results demonstrate that in volume fractions higher than 5%, the effects of carbon nanotubes' dispersion become more significant and if increasing the volume fraction leads to bigger agglomerations and subsequently worse dispersion, the effective properties of the composite as a whole will decrease. Moreover, the pre-and postprocessing procedures implemented are verified by analyzing previously studied models available in the literature and comparing the corresponding results.