P Mohammadi Dashtaki, Nima Noormohammadi

Acta Mechanica

Abstract

We investigate on bending of composite nanoplates reinforced by defective graphene sheets through development of a simple boundary method by equilibrated basis functions. The kinematics is based on Kirchhoff's assumptions for thin plates coupled with second-order strain gradient theory to account for the size effects. The relationships of the theory, including the governing partial differential equation and the corresponding boundary conditions for orthotropic nanoplates, are developed in this paper. Various defect types are considered to affect the properties of the graphene-reinforced nanoplates based on well-known micro-mechanical models for composite materials. The proposed method satisfies the governing PDE in a weighted residual approach through a fictitious domain approach, allowing for various geometries to be modeled. The boundary conditions are strongly applied in collocation style, which grants the proposed method the application of the actual form of the edge forces or moments. Only one independent kinematic component, the out-of-plane displacement, is required to model the deformation field, unlike the finite element formulations which need multiple nodal degrees of freedom. No domain or boundary elements are required for modeling, while complete continuity is achieved throughout the domain. Verifications reveal proper accuracy of the method compared with available literature. The numerical results consider a wide range of various defect types such as single and double vacancies, Stone–Wales, single and double missed atoms, along with their effects for various boundary conditions usually seen in nanoplates including simple, clamped and free edges, and various values of the internal characteristic length. Results revealed that the relative effect by defective graphene slightly increases as the rigidity of the edge supports decrease, while variation of the internal characteristic length does not change this relativity significantly. Meanwhile, by increasing the characteristic length, the overall stiffness of the nanoplate increases, and those with stiffer edges got more affected in this case.