On the modeling of bending responses of graphene-reinforced higher order annular plate via two-dimensional continuum mechanics approach

Abstract

This research presents bending responses of FG-GPLRC plates based upon higher order shear deformation theory (HSDT) for various sets of boundary conditions. The rule of the mixture and modified Halpin–Tsai model are engaged to provide the effective material constant of the composite layers. By employing Hamilton’s principle, the governing equations of the structure are derived and solved with the aid of the differential quadrature method (DQM). Afterward, a parametric study is done to present the effects of three kinds of FG patterns, weight fraction of the GPLs, radius ratio, and thickness to inner radius ratio on the bending characteristics of the FG-GPLRC disk. Numerical results reveal that in the initial value of the $$Zt/h$$ , using more GPLs for reinforcing the structure provides an increase in the normal stresses but this matter is inverse for the higher value of the $$Zt/h$$ . The results show that considering the smaller radius ratio is a reason for boosting the shear stresses of the structure for each $$Zt/h$$ . Another consequence is that for the negative value of $$Zt/h$$ , it is true that by increasing $$h/{R}_{i}$$ , the normal stresses increases but if there is positive value for $$Zt/h$$ , the radial and circumferential stresses fall down by having an increase in the $$h/{R}_{i}$$ .