A parametric study on the impact of graphene origami content on the deformation and strain results of a double curved shell is presented. The formulation is extended using the shear deformability property of the kinematic model and the constitutive relations are extended using the overall material properties for the nanofolded composite structures in the thermal environment. The analytical-based method is developed using the energy-based framework for derivation of the governing equations of a nanocomposite double curved shell. The analytical results are extracted using the trigonometric functions in order to satisfy the required boundary conditions.