*2.3. Case Study*

Within the case study, the influence of the curvature of the component panes of an IGU on the internal pressure and static values (stress in glass and panes' deflection) under the same loading conditions was investigated. For this purpose, the validated numerical model and methodology described in the previous section were used.

Two geometries of an IGU were considered. The first case is a flat reference IGU with the dimensions of 500 × 1000 mm2 (width × length) composed of two 4 mm flat panes and a 16 mm wide flexible silicone foam spacer. The build-up and spatial geometry of the second model are the same as for the reference IGU; however, the component panes are bent to a radius of curvature of 1500 mm.

The analysis was limited to two load cases, according to [6]. The standard provides two climatic design situations for IGUs that generate extreme internal pressure values in the cavity in summer and winter (Table 1). It can be seen that the climatic load in winter is almost a reverse version of summer. The load cases involve temperature differences in the gas in the cavity and changes in atmospheric pressure.

**Table 1.** Load actions by [6].


### **3. Results**

*3.1. Validation of the Curved IGU Model by Physical Experiments*

Table 2 presents the quantitative results of the experiments and numerical simulations. In general, the numerical model underestimates the measured values by approximately 8%, which proves its correctness and the sound reproduction of the experimental results. Considering all the measured and simulated values pairs, the relationship shows excellent agreement (R2-value 0.99). The most significant difference was 10.8% for the withdrawal of 75 mL from the cavity. The difference between the measured and simulated values of the internal pressure is probably due to how the interface between the spacer and the panes is modelled. It exhibits a hinged connection, which does not transfer any bending moments between the components. In physical samples, the interface provides a certain degree of restraint that limits the deformation of the panes and results in increased pressure inside the space between the panes.

**Table 2.** Comparison of measured and simulated values of internal pressure in the IGU cavity.


*3.2. Validation of the Reference (Flat) IGU Model with Alternative Software*

The modelling methodology and material parameters for the flat IGU were the same as those for the validated bent glass IGU model. Since laboratory tests did not include a flat IGU, additional model validation was carried out using the engineering programme SJ-Mepla, widely used for the structural design of IGUs in the glass industry [14]. Only the temperature difference load case included in Table 1 was selected for validation purposes.

Figures 3 and 4 present the validation results for the 'summer' case. The results agree regarding the deformation and maximum principal (tensile) stress. Differences are less than 11%. In terms of internal pressure, the numerical model overestimates the reference values (obtained from SJ-Mepla) by approximately 4.5% (701 Pa vs. 733 Pa). The same overestimation was achieved in the 'winter' load case. The difference between the models and consequent results is related to the fact that, contrary to the modelling approach developed within this study, the SJ-Mepla software never regards the bending rigidity, i.e., no bending stiffness of the spacer nor the sealing material is used [14]. The results obtained prove the correctness of the flat IGU model.

**Figure 3.** Validation of the flat IGU model ('summer' load case): (**a**) deflections obtained from the SJ-Mepla software (values in mm); (**b**) deflections obtained from the ABAQUS software (values in m).

**Figure 4.** Validation of the flat IGU model ('summer' load case): (**a**) maximum principal (tensile) stress obtained from the SJ-Mepla software (values in MPa); (**b**) maximum principal (tensile) stress obtained from the ABAQUS software (values in Pa).
