*3.4. Velocity*

Analysing the maximum velocities, the impact of two different methods of creating strut dome structures can be observed. Based on the obtained results, it can be seen that using method 1 for the construction of a dome, the vibration of velocities as a result of the seismic excitation was much higher than for the structures formed according to method 2 (Figure 7). This tendency was noted in both the records with high ground acceleration (Ancona, Denizli) and records with low ground acceleration (Friuli, Kilini).

In the analysed numerical models (models I–VIII), the highest values for velocity were obtained in model I, i.e., in the dome created according to method 1, with the Ancona record. This value was 1.34 m/s (Figure 7a). In the other models, lower values, ranging from 41% to 95%, (compared to model I) were obtained.

**Figure 6.** Maximum axial forces in numerical model records of: (**a**) Ancona—models I and II, (**b**) Denizli—models III and IV, (**c**) Friuli—models V and VI, (**d**) Kilini—models VII and VIII.

**Figure 7.** Maximum velocities in numerical model record of: (**a**) Ancona—models I and II, (**b**) Denizli—models III and IV, (**c**) Friuli—models V and VI, (**d**) Kilini—models VII and VIII.

It should also be mentioned that there was a slight difference between the velocities from models II and IV (method 2), which was only 2%. This was not much, considering the fact that for the same excitations in the case of method 1, the difference between models I and III was 41%.

On the basis of Figure 7, it can be seen that the places of the occurrence of the maximum velocities in time for individual records and methods of shaping the dome structure were different. Therefore, it was not possible to clearly define the influence of the acceleration value of the analysed recording as well as the method of shaping the dome (methods 1 or 2). On the other hand, it can be seen (especially in the case of domes designed according to method 1) that as the record intensity decreases, the velocity values decrease. For method 2, it was less noticeable because the obtained results were lower in the range of 42% to 66% (compared to method 1).

However, it can be seen that the strut domes were excited as a result of the seismic excitation application. Figure 7 shows that after the maximum ground acceleration occurs in the record (Figure 4), the vibration velocities remain at relatively the same level for a particular record for the rest of its duration. The method of shaping (method 1 or 2) of the strut domes does not matter.

#### *3.5. Acceleration*

In the case of maximum accelerations, a similar tendency can be observed for displacements, axial forces, and velocities. The method of generating the strut dome structure clearly matters. For method 1, higher values were obtained than for method 2. This trend was repeated for all analysed records, i.e., Ancona, Denizli, Friuli, and Kilini (Figure 8).

**Figure 8.** Maximum accelerations in numerical model record of: (**a**) Ancona—models I and II, (**b**) Denizli—models III and IV, (**c**) Friuli—models V and VI, (**d**) Kilini—models VII and VIII.

It was noticed that with a decrease in the intensity of the excitation, the maximum accelerations of the dome structure were reduced. Thus, it can be concluded that for the accelerations of the domes, the ground acceleration value has greater significance than the duration of the earthquake.

The highest accelerations were observed in model I (method 1, Ancona), where the obtained value was 81.71 m/s<sup>2</sup> (Figure 8a). In the other analysed models, the acceleration values in the dome were lower compared to model I and amounted to (i) 55.78 m/s<sup>2</sup> (method 1, model III, Denizil—Figure 8b), (ii) −34.35 m/s2 (method 2, model IV, Denizil—Figure 8b), (iii) 32.42 m/s2 (method 2, model II, Ancona—Figure 8a), (iv) 13.50 m/s<sup>2</sup> (method 1, model V, Friuli—Figure 8c), (v) 8.90 m/s<sup>2</sup> (method 1, model VII, Kilini—Figure 8d), (vi) 6.66 m/s<sup>2</sup> (method 2, model VI, Friuli—Figure 8c) and (vii) 4.78 m/s2 (method 2, model VIII, Kilini— Figure 8d). Analysing the results of the obtained values, it should be also noted that in the case of domes created according to method 2, higher values were obtained in model IV (Denizil) than in model II (Ancona), although the value of ground acceleration for the given excitation in model II was higher by 10%.

Taking into account the time of the appearance of the maximum accelerations in the dome, it can be seen that it was not identical for the analysed methods of creating the dome (methods 1 and 2). In models I and II, as well as VII and VIII, the time when the maximum values appeared was similar. On the other hand, in models III, IV, V, and VI, big differences were noted between the time when the maximum acceleration values appeared in the dome. The difference was 10 s (V and VI models), which was a very significant value with the recording duration of about 17 s.

As in the case of the previously analysed quantities (displacements, axial forces, and velocities), it was noticed that after the occurrence of the maximum input in the record, the structure was excited. From that moment, the acceleration values were relatively close to the maximum values.

### **4. Conclusions**

After the numerical analysis, it can be concluded that the method of shaping the steel structure of domes (methods 1 and 2) has a significant impact on the obtained values of displacements, axial forces, velocities, and accelerations. In addition, the following were noted:


Undoubtedly, the numerical analysis that was performed allowed the determination of how seismic excitation affects the dome shaping method. However, the obtained results were carried out only on relatively small domes. They were new structures, without damage, which was also important. In future, additional analyses are planned for domes of different sizes, as well as damaged domes. In addition, it is planned to optimise the dome structure under seismic excitation.

The obtained results may be helpful in designing this type of structure in seismic areas and may also be a source of information for architects when designing geodesic domes. Additionally, this paper can be helpful in assessing the effects of earthquakes on lightweight structures.

**Author Contributions:** Conceptualisation, D.P. and T.M.; methodology, T.M.; software, T.M.; validation, D.P. and T.M.; formal analysis, D.P. and T.M.; investigation, D.P. and T.M..; resources, D.P.; data curation, D.P. and T.M.; writing—original draft preparation, D.P. and T.M.; writing—review and editing, D.P. and T.M.; visualisation, T.M.; supervision, T.M.; project administration, T.M.; funding acquisition, T.M. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research received no external funding. The APC was funded by Opole University of Technology.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** The data presented in this study are available within the article.

**Conflicts of Interest:** The authors declare no conflict of interest.
