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This is Fig. 10a from the 2012 GENOPT paper. This slide shows the critical LOCAL buckling mode shape of the optimized spherical balloon with 8 modules and truss-like (slanted) webs. This buckling mode, obtained from BIGBOSOR4, corresponds to N = 0 circumferential waves (axisymmetric buckling).
Buckling first occurs in Segment 15, that is, in Segment 3 of Module 3. (Segment 15 = (2 modules) x 6 segments per module) + (3rd segment in Module 3).
This location of the N = 0 (circumferential waves; N = 0 means axisymmetric) buckling mode obtained from the BIGBOSOR4 stability analysis agrees with the prediction of the location of the initial loss of meridional tension as listed in Item 10 of Table 9 of the 2012 GENOPT paper.
During optimization cycles (ITYPE = 1 in the *.OPT file) only the N = 0 buckling mode from BIGBOSOR4 is computed in order to save computer time and because often there exist, especially for balloons made of strong material such as carbon fiber cloth, spurious non-axisymmetric buckling modes with very low eigenvalues.
With ITYPE = 2 (analysis of a fixed design) a critical (minimum) buckling load factor is sought over a wide range of numbers of circumferential waves, N, as listed in Item 9 of Table 9 of the 2012 GENOPT paper.
For viewing figures and tables referred to here but not shown here, please download the 2012 GENOPT paper from this website.
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