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This is Fig. 2 from the 2007 Bushnell paper. The result shown here corresponds to Case 4 in the table given two slides ago.
This slide shows the nonlinear static equilibrium state from a 360-degree STAGS model of a PANDA2-optimized stiffened cylindrical shell at a load factor, PA=1.005, that is, the axial load, Nx = 1.005 x Nx(applied) = 1.005 x 3000 lb/inch, in which 3000 lb/inch is the design load used for the PANDA2 optimization.
The imperfect shell has two initial buckling modal imperfection shapes: the general buckling mode shape shown 6 slides ago with amplitude, Wimp1=+0.0625 inch and the stringer bending-torsion buckling mode shown in the previous slide with amplitude, Wimp2= -0.0005 inch.
Prebuckling bending of the imperfect shell causes redistribution of stresses among the shell skin and the stiffener segments. Also, prebuckling bending gives rise to “flattened” regions with an “effective” circumferential radius of curvature that causes early general buckling. (See the right-most expanded insert).
This figure shows the outer fiber effective stress (psi) predicted by the STAGS model of the imperfect shell at axial load, Nx= -3000 x 1.005 lb/in.
In the PANDA2 optimization model the maximum allowable effective stress for loading Nx = -3000 lb/in was set at 60000 psi. According to this STAGS model the maximum effective stress at Nx = -3000 x 1.005 lb/in is close to 67000 psi. Hence, the Case 4 prediction by PANDA2 is somewhat unconservative. However, note that Case 4 corresponds to a strategy in which the local post-buckling "Koiter" branch of PANDA2 is skipped ("no Koiter" in the Case 4 heading in Table 4).
This choice,"no Koiter", probably is responsible for the somewhat unconservative optimum design with regard to maximum stress obtained by PANDA2 in Case 4. Case 5, the recommended strategy (See Table 4 shown two slides ago), probably leads to an optimum design in which the PANDA2 predictions are slightly conservative.
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