Static bending analysis of pressurized cylindrical shell made of graphene origami auxetic metamaterials based on higher-order shear deformation theory

Static bending responses of a pressurized composite cylindrical shell made of a copper matrix reinforced with functionally graded graphene origami are studied in this paper. The kinematic relations are extended based on a new higher-order shear and normal deformation theory in the axisymmetric framework. The constitutive relations are extended for the composite cylindrical shell where the effective modulus of elasticity, Poisson's ratio, thermal expansion coefficient and density are estimated using the Halpin-Tsai micromechanical model and the rule of mixture. Some modified coefficients are employed for correction of the mentioned material properties in terms of the volume fraction and the folding degree of graphene origami, characteristics of copper and graphene nanoplatelets and thermal loads. The principle of virtual work is used to derive governing equations through computation of strain energy and external work. The static bending results including radial and axial displacements, circumferential strain and stress are presented along the longitudinal and radial directions in terms of volume fraction, folding degree and distribution of graphene origami. The results show an increase in radial displacement and circumferential strain with an increase in folding degree and a decrease in volume fraction of graphene origami. The main novelty of this work is investigating the effect of foldability parameter and various distribution of graphene origami on static results of short cylindrical shell.