Nonlinear static behaviors of functionally graded polymer-based circular microarches reinforced by graphene oxide nanofillers

Abstract

This work investigates the nonlinear static behaviors of polymer-based nanocomposite circular microarches reinforced by a low content of graphene oxide (GO) and with inclusions of von Kármán nonlinearity. The weight fractions of the GO nanofillers are assumed to gradually vary along the thickness directions of the arches according to a given law. The GO nanofillers are considered to be circular reinforcements dispersed within a polymer matrix, and a modified Halpin–Tsai model is used to determine the effective modulus of the elasticity of the nanocomposite. In the present work, a modified couple stress-based model for analyzing the nonlinear behaviors of circular arches is developed based on the exponential shear deformation theory (ESDT). In this model, the trapezoidal shape factor is properly incorporated to receive more accurate stress-resultants along the thickness direction, making the present model capable of dealing with the mechanical behaviors of thick arches. The polynomial Ritz method is implemented to simulate the classical immovable end restraints of arches. Three kinds of external transverse loads are taken as external forces that act upon microarches. The governing equations of the considered problem are derived using the minimum energy procedures and are solved via the Newton-Raphson iteration technique. Comparisons are carried out to verify the results and accuracy of the proposed model. Some numerical illustrations are provided to show the effects of the load types, small scales, GO distribution patterns, and sizes of the GO nanofillers on the nonlinear response of nanocomposite arches reinforced by graphene oxide.

Keywords

• Polymer-based nanocomposite
• Graphene oxides
• Modified couple stress theory
• Exponential shear deformation theory
• Nonlinear analysis