Modified couple stress-based nonlinear static bending and transient responses of size-dependent sandwich microplates with graphene nanocomposite and porous layers

This paper investigates the nonlinear static bending and dynamic transient responses of the rectangular and circular sandwich microplates composed of functionally graded graphene nanocomposite (GNC) face sheets and a porous polymeric core layer based on the modified couple stress theory (MCST) within the isogeometric analysis (IGA) framework. The four-variable higher-order shear deformation refined plate theory (RPT) and the von Kármán large deflection assumption are synthetically employed to describe the kinematics of the microplate. The nonlinear governing equations of motion are derived from the Hamilton’s principle. The nonlinear bending problem is solved by the Newton–Raphson technique under a displacement criterion strategy, while the dynamic responses under transient loads are obtained by the Newmark integration scheme in conjunction with Newton–Raphson iterative procedure. Comparisons are carried out to test the accuracy of iteration procedure in present formulation and the reliability in capturing small scale effect of present model. Obtained outcomes reveal that raising the material length scale (MLS) parameter and volume fraction index of graphene nanofillers both leads to reductions in nonlinear static deflections, dynamic amplitudes of deflection and periods of motion. The examples for porosity coefficient show that embedding pores in core layer leads to slight changes in terms of static and dynamic responses and an improvement in weight reduction of the sandwich microplate.