## 4 Discussion  
The paper presents several methods for calculating the deformation of a three-layer [PERSON]'s plate. In the first case, the finite difference method in the variational approach was \begin{table}
\begin{tabular}{c c} \hline
**Name of Model** & **Value of Displacements (mm)** \\ \hline Analytical model & 9.82 \\ Model 1 & 10.18 \\ Model 2 & 9.93 \\ Model 3 & 9.94 \\ Model 4 & 17.43 \\ Homogenization model & 9.71 \\ CLPT model & 9.89 \\ \hline \end{tabular}
\end{table} 
Table 4: Maximum displacement of plate. \begin{table}
\begin{tabular}{c c c c c} \hline
**Grid Point No** & \multicolumn{3}{c}{**Finite Difference Method in the**} & \multicolumn{3}{c}{**Numerical Homogenization**} \\ \cline{2-5}  & **m\({}_{\text{x}}\) (Nm/m)** & **M\({}_{\text{x}}\) (Nm/m)** & **m\({}_{\text{x}}\) (Nm/m)** & **M\({}_{\text{x}}\) (Nm/m)** \\ \hline
12 & 3381 & 19,550 & 3214 & 18,753 \\
18 & 3036 & 14,016 & 2963 & 13,507 \\
24 & 2856 & 12,134 & 2731 & 11,834 \\
30 & 2777 & 11,244 & 2663 & 10,868 \\
36 & 2746 & 10,619 & 2615 & 10,054 \\
42 & 2735 & 9865 & 2597 & 9352 \\ \hline \end{tabular}
\end{table} 
Table 5: Value of selected cross-sectional forces for the slab. Figure 7: A diagram of the displacements in the middle of the plate span. used. In the second case, the numerical FE model was used, and in the third case, the homogenization method enhanced with an analytically computed shear correction factor was used. The correctness of the calculations using the finite difference method has been confirmed in numerous computational scientific works, as well as being confirmed by model tests. Work [19] presents the results of the differential calculations of a slab of variable thickness. The obtained results were verified with model tests composed of resin and subjected to thermal loads. The compliance of the results of the calculations and model tests confirms the correctness of the determined matrix and systems of equations in accordance with the finite difference method. The effect of temperature is often neglected when calculating plate structures, and yet it gives moment values greater than in the case of other loads. The bending moments due to the applied thermal load increase in direct proportion to the square of the wall thickness. Work in [57] concerns the calculation of a floor slab with a static scheme of a slab with free edges loaded in bands along the perimeter of the slab, resting on a Winkler elastic foundation. The calculations were performed for two variants, taking into account two values of the subsoil stiffness modulus. It was indicated in the paper that taking into account the influence of the thermal insulation layer composed of spray-applied polyurethane foam in the calculations of the slab causes an increase in the substrate compliance modulus and deflection, and the bending moments decrease. The obtained results show the necessity to calculate the floor as a layered element. Paper [59] presents the results of verification of the static calculations of a monolithic rectangular tank with walls with a trapezoidal cross-section. Static calculations were performed with the use of a computer program based on the finite element method (FEM) as well as the finite difference method (FDM) in terms of energy (taking into account the spatial static operation of the tank). The verification of the obtained results was carried out on a concrete tank model with the use of a modern measuring tool: a coordinate measuring arm with a contact head. The compliance of the obtained results proves the correctness of the adopted calculation methods, i.e., the finite element method, on the basis of which the calculations with Autodesk Robot Structural Analysis Professional were performed, and the finite difference method in terms of energy, with the use of which the calculations were carried out traditionally. Work [62] concerns the cooperation between the tank walls and the polystyrene filling treated as a Winkler-type elastic substrate, assuming the Poisson's ratio of \(v=0\).