# The Ultimate Strength of Fully Transparent Pressure-Resistant Spherical Cabins
## 4 Summary and Conclusions  
The ultimate strength of a fully transparent spherical cabin made of PMMA is studied by taking the initial geometrical imperfection and metal cover stiffness into account. The boundary point of \(t/R\) between strength failure and buckling failure of PMMA spherical cabin through classical theoretical formulas is determined first as the present study aims at investigation within the range of buckling mode. When \(t/R\) of the PMMA spherical hull is less than 0.0424, buckling failure occurs first ahead of strength failure. Based on that, a series of numerical models including the intact spherical cabin, spherical cabin with a single access opening, spherical cabin with double access openings are established and the eigenvalue buckling results were introduced into the initial imperfection shape for nonlinear buckling analysis. The changing tendency of critical buckling pressure was observed with varieties of the initial geometrical imperfections and \(t/R\).  
Results show that the critical pressure has a decreasing trend as the initial geometrical imperfection increases, and that the intact spherical cabin shows the greatest decrease, indicating a higher sensitivity to initial imperfection. The critical buckling pressure linearly increases with the increase of \(t/R\) for PMMA spherical cabin with access openings. The reduction extent of the spherical cabin with a single access opening is smaller than that with double access openings, indicating the strength sensitivity of PMMA spherical cabins to initial imperfections and openings. Moreover, for PMMA pressure-resistant cabin, the thickness of the metal hatch cover also significantly affects its critical pressure. Within a certain range, the strength of the spherical cabin will increase with the increase of hatch cover thickness. However, a metal cover that is too thick will reduce its structural strength due to the constraints at the contact between the cover hatch cover and the PMMA shell. It is absolutely necessary to determine a reasonable range of hatch cover thicknesses in the future. Coordinated design is compulsory and subsequent improvements can be made by aiming at improving the simulation accuracy and locally refined structure design to reduce the stress concentration effect which will be fully considered for safety evaluation.  
Methodology, F.W.; Software, Y.L., Z.H. and B.Z.; Validation, J.Z.; Formal analysis, Y.L. and Z.H.; Investigation, F.W. and Y.L.; Data curation, Z.H., B.Z. and J.Z.; Writing--original draft, F.W.; Writing--review & editing, Y.W.; Supervision, F.W.; Project administration, F.W.; Funding acquisition, F.W. All authors have read and agreed to the published version of the manuscript.  
The National Key Research and Development Program of China provides funding for this work. (Grand No. 2021 YFC2800600), National Natural Science Foundation of China (Grant No. 52071203), The authors would like to thank Shanghai High-level Local University's Fishery Engineering and Equipment Innovation Team for their support, as well as the Open Fund of the Fujian Province Key Laboratory of Ship and Ocean Engineering.  
Figure 14: Comparison of strength reduction tendency with initial geometrical imperfections.  
Data Availability Statement: The data can be provided by the corresponding authors when needed. The data are not publicly available due to privacy.  
Conflicts of Interest: The authors declare that they have no known competing financial interest or personal relationships that could have appeared to influence the work reported in this paper. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript; or in the decision to publish the results.