A Hybrid Legendre Basis Functions/Taylor Series Expansion-Based Variational Pseudo-Spectral Method for Bending Analysis of Three-Phase PM/rGO/CF Cylindrical Shells

A computational approach was developed to investigate the static bending behavior of nanocomposite cylindrical shell panels (NCSPs) subjected to distinct boundary conditions. These nanocomposite panels are constituted of a matrix of polymeric materials strengthened by reduced-graphene oxide (rGO) nanofillers and carbon fibers (CF). The effective mechanical properties are estimated using a homogenization procedure that employs the modified Halpin–Tsai model with the rule of mixture and a micromechanical scheme. The structural model is formulated within the framework of first-order shear deformation theory (FSDT), with the associated governing equations derived through a consistent weak form. A hybrid variational pseudo-spectral method is introduced, combining shifted spectral Legendre collocation method for derivative evaluation with a generalized Taylor series expansion for integral approximation. The numerical approach is employed to examine the impact of geometric parameters, boundary conditions, and material composition on the bending response of NCSPs. The numerical outcomes illustrate the approach’s precision in capturing the mechanical behavior of these advanced composite structures, making it suitable for large-scale simulations and the design of lightweight structural components in aerospace and civil engineering applications.