###### Abstract
However, Lagrange multipliers require the introduction of additional constraint equations, leading to a larger system of equations and consequently, to an increase in the computational cost [22]. As a consequence, the lack of the delta Kronecker property tempered the enthusiasm for meshless methods. This difficulty drives the computational mechanics research community to employ their efforts in the development and enhancement of interpolating shape functions. The Natural Element Method (NEM), introduced by [PERSON] et al. [26], stands as a pioneering example of a successful interpolating meshless methods. The NEM's shape functions are interpolating, allowing for the direct imposition of boundary conditions, as in the FEM. Following the success of the NEM, a multitude of interpolating meshless methods emerged, including the Point Interpolation Method (PIM) [27], the Radial Point Interpolation Method (RPIM) [28], the Meshless Finite Element Method (MFEM) [29], and the Natural Radial Element Method (NREM) [30]. Further advancements in interpolating meshless methods were achieved by [PERSON] et al. with the development of the Natural Neighbour Radial Point Interpolation Method (NNRPIM) [31]. This method combines the connectivity strategy of the NEM with the radial point interpolating technique of the RPIM. Using only the nodal discretisation information (the Cartesian coordinates of the nodes) of the problem's domain, the NNRPIM is capable to autonomously calculate the position and weight of the background integration points and enforce the nodal connectivity using the natural neighbour concept. Lke the NEM, the NNRPIM is a truly meshless method. Meshless methods have demonstrated their potential for analyzing sandwich structures, particularly when combined with equivalent single-layer (ESL) deformation theories [32], which offers a computationally efficient alternative to full 3D analyses. For this reason, 3D meshless formulations for sandwich structures remain less prevalent in the literature [4; 33; 34]. Concerning meshless methods combined with multiscale homogenisation techniques, the most common applications are for composite structures. [PERSON] et al. successfully extended the capabilities of the RPIM [35] and NNRPIM [36] to perform multiscale analyses of laminated composites. Similarly, [PERSON] et al. developed a multiscale approach using a different meshless technique to model the mechanical behaviour of carbon nanotube-reinforced cement composites [37]. The research on advanced computational methods for the design of sandwich structures allows us to develop and deliver light-weight structures with high stiffness/mass ratios. [PERSON] et al. present an extensive review on sandwich structures for the construction industry [38]. Their work focus on five types of sandwich panels: lightweight timber-framed panels, light-gauge-steel-framed panels, structural insulated panels, cross-laminated timber panels, and precast concrete sandwich panels [38], showing the large variety of applications that prefabricated sandwich structures possess in the construction industry. Nevertheless, sandwich structures are the focus of attention in other demanding engineering areas, such as the aeronautics and aerospace industry. For instance, in the work [PERSON] et al., the bending response of laminated composite sandwich structures with corrugated and spiderweb-inspired cores for aircraft flaps is analysed [39]. Simulations included the effects of hail impact, leading to a final design incorporating the spiderweb core with optimal fibre orientation and ply thickness and allowing for higher load resistance and bending stiffness. In the research study of [PERSON] et al., the dynamic behaviour of a new flexible sandwich structure for morphing aircraft capable of shape adaptation during flight [40] was examined. The structure was experimentally tested and numerically validated with finite element simulations. The literature also possesses impact studies on sandwich structures, such as the work of [PERSON] et al.