Within the context of composite beam structure modeling, a refined model is combined with a simpler one solely within a region of interest, aiming to enhance result accuracy. The purpose is to gain computational cost without loss of precision. For that, the Partition Unity Method (PUM) is used to ensure the continuity condition on the displacement field. A 1D refined Sinus model and a 2D approach are involved to demonstrate the capability of the method. It is assessed on different numerical examples involving both laminated and sandwich beams. The accuracy of the results is shown using reference solutions and computations using a mono-model. The interest of the method is further demonstrating by estimating the computational cost with or without the coupling. The results are rather very promising. •A kinematics coupling is considered for the modeling of 2D laminated composite and sandwich beams.•The method is based on the Partition of Unity Method.•An enriched model is only localized in the region of interest.•The possibilities, the limitations and the accuracy of the method are highlighted.•The approach can be applied to different dimensionalities and FE approximations.