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This is Fig. 16 from the 2013 GENOPT paper2.
Fig. 16 Optimized “twoskirt” configuration, Load Case 1: STAGS prediction of nonlinear bifurcation buckling of the aft conical support. The nonlinear bifurcation buckling load factor is 5.7333.
This nonlinear load factor from STAGS and the bifurcation buckling mode shape are in reasonably good agreement with those from the BIGBOSOR4 model and from the approximate PANDA-type Model 2 listed near the end of Table 5: PANDA-type Model 2 buckling load factor = 5.6305 with MSKIN = 3 meridional half waves over the lowest 1/4 of the aft conical skirt, NSKIN = 32 circumferential half waves over 180 degrees of the circumference, and slope, SLOPE, of the buckling nodal lines of 0.10167. PANDA-type Model 2 includes only the lowest 1/4th of the aft conical skirt (nearest the large-diameter end). As listed in Table 6, in this PANDA-type Model 2 the hoop resultant, NYAVE, and in-plane shear resultant, NXYAVE, are set to zero, the meridional resultant from Load Set A (eigenvalue load), NXAVE = –247.87 lb/in, and the meridional resultant from Load Set B (fixed load), NXFIX = 1223.5 lb/in. In the PANDA-type Model 2 the lowest 1/4 of the aft conical skirt is modeled as an “equivalent” simply supported cylindrical shell with length, FLEFF = 34.821 inches and radius, RAVE = 160.71 inches. The stress resultants from Load Set A (NXAVE = N1VAR = –247.87 lb/in) and Load Set B (NXFIX = N1FIX = 1223.5 lb/in) are those corresponding to nodal point no. 10 in Segment 3 of the aft skirt, as listed in the section of the twoskirt.OPM file [2] pertaining to Load Case 1 and the prebuckling response of the aft conical skirt at circumferential coordinate, theta = 0 degrees. This list of the prebuckling response in the twoskirt.OPM file contains the following lines:
PREBUCKLING STRESS RESULTANTS IN THE SKIRT(1), THETA= 0.0000E+00
NODE MERIDIONAL RESULTANT CIRCUMFER.RESULTANT IN-PLANE SHEAR
J N1VAR N2VAR N12VAR N1FIX N2FIX
10 -2.4787E+02 -1.0030E-01 0.0000E+00 1.2235E+03 -1.8839E+01
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