###### Abstract
[41], in which the impact resistance of metallic sandwich structures is analysed and explored by encasing the foam core with ultra-high strength composite fabric. Experimental and numerical tests show that the encasement significantly improves energy absorption and reduces damage, enhancing overall impact resistance while maintaining lightweight properties and offering new perspectives on improving structural protection against complex impact loading [41]. Another very recent trend is the production of sandwich structures using 3D printing or additive manufacturing technologies. As shown in the works of [PERSON] et al. [42] and [PERSON] et al. [43], 3D printing is a suitable manufacturing technique to produce efficient lightweight sandwich structures. Aiming to reduce the weight of sandwich panels for shock absorption, [PERSON] et al. [42] were able to produced panels with 3D printing showing 28% weight reduction while improving energy absorption. The sandwich panels demonstrated enhanced structural effectiveness through comparative analysis of absorption indices, force-time and force-displacement graphs, and CT scans. On the other hand, [PERSON] et al. [43] mechanically characterised honeycomb sandwich structures fabricated with 3D printing, demonstrating very high energy absorption and, at the same time, preventing delamination and debonding. The research study here presented proposes a novel approach for analysing the macroscale behaviour of sandwich structures by integrating in the NNRPIM a multiscale homogenisation technique. The proposed framework takes advantage of both techniques: the NNRPIM flexible and organic discretisation procedure allows us to analyse unstructured nodal distributions, while multiscale homogenisation simplifies the analysis of complex microstructures by capturing their homogenised mechanical properties. The proposed methodology starts with the estimation of the homogenised mechanical properties of the cellular unit, which are then correlated with the foam density. Subsequently, at the macroscale level, various sandwich structures with varying density distributions throughout the thickness are modelled using the NNRPIM. The resulting solutions are then compared with those obtained with FEM analyses. This research aims to achieve a two-fold objective: first, to assess the performance and efficiency of the NNRPIM compared to the FEM in terms of computational cost, accuracy, and stress field distribution, and second, to explore the potential of meshless multiscale analysis for sandwich structures with both homogeneous and functionally graded foam cores. This manuscript comprises four distinct sections. The initial section delineates the state of the art of sandwich structures, alongside corresponding mathematical formulations, multiscale homogenisation methodologies, and typical discretisation approaches. The subsequent section shows the mathematical formulation of the meshless method for elasticity, coupled with the employed homogenisation technique. Next, the third section presents the numerical findings. Initially, the homogenised mechanical properties of cellular foams are correlated with its apparent density. Subsequently, the results of macroscale numerical examples of sandwich structures are presented, accompanied by the respective discussion. Ultimately, the most relevant conclusions and observations of this study are documented within the Section 4.