Thermo-elastic damped nonlinear dynamic response of the initially stressed hybrid GPL/CNT/fiber/polymer composite toroidal shells surrounded by elastic foundation

Abstract

This paper aims to investigate the geometrical nonlinear response of the hybrid composite toroidal shells subjected to harmonic time-dependent external pressure and constant in-plane compressive loadings. The hybrid composite incorporates some layers made of the fibres and the matrix in which the polymeric matrix in some layers is reinforced by carbon nanotubes (CNTs) and in the other layers by graphene nanoplatelets (GPLs). The fundamental equations are extended based on the first-order shear deformation theory (FSDT) and are solved by introducing the harmonic functions to estimate the deformation field and employing Galerkin method. Finally, the obtained nonlinear dynamic differential equation of motion is numerically solved using fourth-order Runge–Kutta method. The extended formulation is verified by comparing the obtained results corresponding to some problems with those are achieved in the other studies using the various methods. Then, an extended parametric study is carried out by using the present method incorporating the effects of thermo-mechanical, geometrical, and loading factors on the forced vibration of the shell. The obtained results show that the novelty of the present study can be justified by some advantages. Firstly, it enables a robust tool for analysis of GPL/CNT/fiber/polymer hybrid composite shallow toroidal shell segments in the geometrical nonlinear state with no time consuming computational efforts. Secondly, the present formulation is so simple while it has not restriction for thin or moderately thick shells.