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This is Fig. 60 from the 2012 GENOPT paper. This slide shows GENERAL bifurcation buckling of the optimized cylindrical balloon with 15 modules over 90 degrees of circumference and with truss-like webs.
This general buckling mode has one-half wave over 90 degrees of circumference of the cylindrical balloon, that is, two full waves over 360 degrees. Therefore, this GENERAL buckling mode represents "ovalization" of the 360-degree cylindrical balloon.
General buckling modes of this type were never found for the spherical balloons.
The true prismatic formulation is used for modeling the cylindrical balloons.
There are 31 nodal points in each segment of the model, which is the nodal point density specified in the “balloon” software, SUBROUTINE BOSDEC (NODSEG = 31) for optimization.
This figure is analogous to Fig. 11 of Ref. [1] (of the references listed in the Reference section of the 2012 GENOPT paper), which applies to cylindrical balloons made of the much softer and weaker material, polyethelene terephthalate.
In the optimized cylindrical balloon made of the much stronger and stiffer carbon fiber cloth the walls are much thinner than those of the optimized cylindrical balloon shown in Fig. 11 of [1].
For this reason BIGBOSOR4 produces an eigenvector that has a significant component of local spurious “zig-zag” buckling modal displacement.
The question arises: “Does the presence of the spurious ‘zig-zag’ component of buckling modal displacement significantly affect the critical buckling load factor (eigenvalue) predicted by BIGBOSOR4?” The answer from the predictions listed in Tables 21 and 22 of the 2012 GENOPT paper appears to be: “no”.
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