Geometrically nonlinear analysis of doubly curved imperfect shallow shells made of functionally graded carbon nanotube reinforced composite (FG_CNTRC)

Abstract

This article presents an analytical approach to investigate the geometrically nonlinear response of doubly curved imperfect shallow shells made of functionally graded carbon nanotube reinforced composite (FG_CNTRC) under in-plane and lateral loads. For all of the case studies, the edges of shells are assumed to be diaphragm supports, which are subjected to in-plane edge-loads. The governing equations are developed for thin shells based on the classical theory considering the geometric nonlinear terms using the Von Karman–Donnell sense. The Galerkin method is used to solve the extended nonlinear system of differential equilibrium and compatibility equations. The solution results in a closed-form formula representing the equilibrium path (load-deflection relationship) of the shell which is validated by numerical methods, such as finite element and mesh-free methods. The parametric studies are performed for doubly curved and cylindrical shells subjected to uniform external pressure and in-plane edge loads, respectively. The effects of various parameters such as volume fraction of FG_CNTRCs and geometrical properties on the equilibrium paths are examined in detail.