On the nonlinear mechanics of hybrid skew aerospace structures

Abstract

This study proposes a functionally graded (FG) nanocomposite hybrid skew plate element which is fabricated from a polymeric matrix and is reinforced with two well-known nanoscale reinforcements, namely, carbon nanotubes (CNTs) and graphene platelets (GPLs). The Mori–Tanaka approach, the Halpin-Tsai scheme and standard rule of mixtures are employed to estimate the effective mechanical properties of the hybrid plates. To model this structural element, Reddy's third-order shear deformation theory (TSDT) is used. By considering the von-Kármán assumptions and using the Hamilton's principle, the nonlinear static bending and free vibration governing equations are determined. Then the isogeometric analysis (IGA) is employed to establish the structural stiffness and mass matrices of the skew hybrid plates. After validating the correctness of the presented solution procedure with the previously published results, the effects of various variables such as number of layers, distribution pattern of reinforcements (CNTs and GPLs) and their volume fractions, skew angle and width-to-thickness ratio are investigated. It is found that with considering nonlinear von-Kármán relationship in the strain field, the distributions of σxx and σyy about the mid-plane are no longer symmetric.