Static and free vibration analysis of functionally graded carbon nanotube reinforced skew plates

The remarkable mechanical and sensing properties of carbon nanotubes (CNTs) suggest that they are ideal candidates for high performance and self-sensing composites. However, the study of CNT-based composites is still under development. This paper provides results of static and dynamic numerical simulations of thin and moderately thick functionally graded (FG-CNTRC) skew plates with uniaxially aligned reinforcements. The shell element is formulated in oblique coordinates and based on the first-order shear deformation plate theory. The theoretical development rests upon the Hu-Washizu principle. Independent approximations of displacements (bilinear), strains and stresses (piecewise constant subregions) provide a consistent mechanism to formulate an efficient four-noded skew element with a total of twenty degrees of freedom. An invariant definition of the elastic transversely isotropic tensor is employed based on the representation theorem. The FG-CNTRC skew plates are studied for a uniform and three different distributions (two symmetric and one asymmetric) of CNTs. Detailed parametric studies have been carried out to investigate the influences of skew angle, CNT volume fraction, thickness-to-width ratio, aspect ratio and boundary conditions. In addition, the effects of fiber orientation are also examined. The obtained results are compared to the FE commercial package ANSYS and the limited existing bibliography with good agreement.