## 1 Introduction  
Sandwich panels are widely used in construction due to the possibility of a deliberate selection of the properties of individual layers. In the initial period, the sandwich panel theory was mainly developed for applications in the aviation, space, and electronics and medicine industries [1, 2, 3]. Sandwich panels used in the construction industry must carry high utility loads, provide good thermal and acoustic insulation, and be resistant to biological and chemical corrosion. The standard sandwich construction has two homogeneous top layers and a soft homogeneous core in between. However, such a structure is characterized by a large heterogeneity of material and geometric properties between the outer layers and the core [4]. The top layers of the plate are composed of steel or concrete in order to ensure adequate strength of the element. On the other hand, the core is usually composed of a material with poor strength parameters, e.g., mineral wool, foam, and polyurethane. Its function is only to provide adequate thermal insulation. For this reason, often in the contact plane of the component layers, it is difficult to define stresses caused by thermal and mechanical loads [5, 6, 7]. The introduction of non-homogeneous materials, such as functionally graded materials (FGM), made layered structures even more attractive [8, 9],and they are used, for example, in the construction of submarines or space landers. The use of FGM materials reduces the inter-layer stresses and thermal stresses, improving the mechanical properties of sandwich structures [10; 11]. The literature contains a number of works on the statics of sandwich panels subjected to mechanical [12; 13; 14; 15; 16; 17; 18] and thermal [19; 20; 21; 22; 23; 24] loads, as well as on various types of constituent materials [1; 25]. The materials used for sandwich construction have a decisive influence on their statistical performance. By increasing the deformation modulus of the core material, its share of the work of the entire sandwich structure is significantly increased. The most advantageous solution was the experimental validation of the model used to carry out numerical tests [19; 26; 27; 28; 29]. Algorithmizing the calculation of sandwich panels assumes their actual geometric and material data would be a very sought-after solution in the design and creation of new types of structures in this category. Taking into account the possible construction materials for both the outer and middle layers, it was found that the most appropriate model reflecting the work of a sandwich panel would be the model of a three-dimensional panel given by [PERSON] [30]. For the model adopted in the work, equilibrium equations were given in the form of a system of three partial differential equations derived by [PERSON] [30] or the equivalent of one eight-order differential equation given in [31; 32]. This can be effectively computed by the finite difference method (FDM). As an alternative to the FDM approach, the well-established Finite Element Method (FEM) can be used, however, for sandwich panels with a large difference in stiffness between the outer layers and the core, the full 3D model should be used for the calculation. Another approach, which is extremely effective, especially when it is not necessary to fully model the layered structures, is numerical homogenization [33]. Performing deformation analysis of sandwich panels in an analytical manner results in a large number of complicated equations to be solved, which is associated with being a time-consuming calculation and a high possibility of making a mistake. Additionally, 3D modeling of such plate cross-sections is not very economical. Therefore, the possible solution may be to use the available homogenization methods. Thanks to which, the complex cross-section of a multi-layer panel can be reduced to a single-layer substitute model with equivalent parameters. This approach ensures that the behavior of the equivalent model is very similar to that of the three-dimensional reference model.