## 5 Conclusions  
The mechanical performance of an LPG cylinder for energy storage applications was successfully investigated under static loading within linear elastic, using isogeometric analysis (IGA) with the T-Splines function. The numerical results of the displacement and Von Mises stress were evaluated and verified with the FEM in Abaqus/standard. The processing time of the isogeometric analysis (IGA) with the T-Splines method is smaller in comparison to that of the FEM in Abaqus/Standard. This is confirmed by the numerical results in the studies by [PERSON] et al. and also by [PERSON] et al.  
The Von Mises stress numerical results obtained using the T-Splines method show a close correlation with the FEM results, with a minor but consistent difference. The stress results indicate that once the weight of 15 cylinders is reached, the elastic limit of the aluminum alloy 6061-T6 (298 MPa) is exceeded. This suggests that the storage capacity of a single cylinder is equivalent to that of 15 empty cylinders.  
The results demonstrate that the T-Splines approach provides superior numerical robustness, efficiently capturing stress variations in the loading application area while maintaining a stable and convergent solution. The method's ability to refine specific regions without increasing computational costs makes it a powerful alternative to the conventional FEM for structural applications involving complex geometries and high stress gradients.  
Future research could focus on further refining IGA and X-IGA techniques for crack growth simulations in multi-physics contexts, particularly in the analysis of fatigue, fracture mechanics, and failure prediction in real-world structures. Enhanced computational platforms and optimization algorithms will also be essential in making these methods more efficient and scalable, enabling their integration into real-time digital twin systems for predictive maintenance and structural health monitoring.  
Another important future research direction involves a complementary investigation into LPG cylinders under internal pressure, focusing on the integration and development of isogeometric analysis with the T-Splines function. The goal is to evaluate the mechanical structure performance of LPG cylinders under internal pressure, addressing challenges in both linear elastic and plastic scenarios.  
**Author Contributions:** Conceptualization, S.E.F., M.B.G., A.E. and M.L.S.; Methodology, M.B.G. and A.E.; Software, S.E.F., M.B.G. and A.E.; Validation, S.E.F., M.B.G., A.E. and S.V.; Formal analysis, S.E.F., M.B.G., A.E., S.V. and M.L.S.; Investigation, S.E.F., M.B.G. and A.E.; Resources, S.E.F., M.B.G. and A.E.; Data curation, S.E.F., M.B.G. and A.E.; Writing--original draft, S.E.F. and A.E.; Writing--review & editing, S.V. and M.L.S.; Visualization, S.V. and M.L.S.; Supervision, A.E., S.V. and M.L.S.; Project administration, A.E. and M.L.S.; Funding acquisition, S.V. and M.L.S. All authors have read and agreed to the published version of the manuscript.  
**Funding:** The APC was founded by the Transilvania University of Brasov (HBS 3412/2020).  
**Institutional Review Board Statement:** Not applicable.  
**Informed Consent Statement:** Not applicable.  
**Data Availability Statement:** The raw data supporting the conclusions of this article will be made available by the authors on request.  
**Conflicts of Interest:** The authors declare no conflicts of interest.