Post-buckling analysis of imperfect multi-scale hybrid nanocomposite beams rested on a nonlinear stiff substrate

Abstract

Present paper undergoes with the analysis of the post-buckling behaviors of multi-scale hybrid nanocomposite beam-type structures manufactured from both macro- and nanoscale reinforcing elements, namely carbon fibers and carbon nanotubes (CNTs), respectively, in addition to the host polymeric matrix. The equivalent material properties of the hybrid nanocomposite will be gathered utilizing a two-step micromechanical scheme while the influences of the CNTs’ agglomeration phenomenon are covered. Continued by using the concept of the virtual work’s principle, the nonlinear governing equation of the motion will be derived on the basis of the combination of the von Karman hypothesis with the well-known Euler–Bernoulli beam theory while the beam is rested on a three-parameter nonlinear foundation. It is noteworthy that the impact of the existence of an initial deflection in the continuous system is included in the present study, too. At the end of the manuscript, the obtained governing equation will be solved analytically within the framework of the Galerkin’s method once both simply supported–simply supported (S–S) and clamped–clamped (C–C) boundary conditions are considered. It is shown that the stability response of the NC structure can be deeply influenced tailoring the agglomeration parameters.