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This is Fig. 262 from the 2009 GENOPT paper. This slide shows a STAGS “soccerball” model of the optimized imperfect isogrid-stiffened equivalent ellipsoidal shell.
The optimum design, listed in columns 2 and 3 of Table 33 of the 2009 GENOPT paper, was obtained by GENOPT with plus and minus axisymmetric (n=0) mode 1 and mode 2 linear buckling modal imperfection shapes with amplitude, Wimp = 0.2 inch.
Shown here is the non-axisymmetric (2nd n=1 circumferential wave) linear buckling modal imperfection shape used as the n = 1 imperfection corresponding to the last trace in Fig. 254 (previous slide).
Compare with the 360-degree STAGS model displayed in Fig. 10 of the 2009 GENOPT paper. The difference in the eigenvalue, 3.5069 here vs 3.5518 in Fig. 10, is caused primarily by the difference in the finite element used in the STAGS model: STAGS Element 480 here vs STAGS Element 410 in Fig. 10 of the 2009 GENOPT paper.
Indicated in this figure is the location where normal inward-directed concentrated loads or displacements are imposed in a “cos(theta)” distribution in order to produce a dent that locally resembles the negative of this linear buckling mode shape.
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