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This is Fig. 7 from the 2007 Bushnell paper. This slide shows the nonlinear equilibrium state from a 60-degree STAGS model of the PANDA2-optimized stiffened cylindrical shell listed as Case 4 in Table 4. (Table 4 was shown three slides ago.)
A 60-degree model was chosen because the critical linear bifurcation buckling mode (shown six slides ago) has six full circumferential waves. Therefore, 60 degrees spans one full circumferential wavelength of this critical general buckling mode.
A 30-degree model could have been chosen, but is not as good as a 60-degree model because the most critical regions would then occur only along the two longitudinal edges and not in the interior of the model at the mid-width of the model. In the 30-degree model the symmetry conditions along the two longitudinal edges of that model would prevent the possible occurrence of incipient antisymmetric behavior there as the axial load applied to the imperfect shell is increased.
This slide shows the deformed state during a nonlinear dynamic STAGS run at the design load, PA=1.0 (axial load, Nx = -3000 lb/in), Time = 0.00255 seconds (See Fig.52 of the 2007 paper by Bushnell, shown two slides hence).
Notice local bending in the panel skin in the region where nodal points are concentrated in both the axial and circumferential coordinate directions.
The imperfect shell has only a general buckling modal imperfection shape (that shown in Fig. 49 of the 2007 paper by Bushnell) with amplitude, Wimp1 = -0.0625 inches.
This is a 60-degree STAGS model of the same optimized stiffened shell configuration (Case 4 in Table 4, listed 3 slides ago) as that shown in the previous slide. Symmetry conditions are applied in the STAGS model along the two straight edges of the 60-degree model.
The average agreement of predictions from the STAGS 360-degree compound model (previous slide) and the somewhat simpler STAGS 60-degree model shown here justifies use of the more efficient and locally much more detailed 60-degree STAGS model to verify results from PANDA2 for the optimized shell.
This slide shows the STAGS prediction of outer fiber effective stress (psi) at the design load, Nx= -3000 lb/in.
It is emphasized that the localized increased mesh density in this 60-degree STAGS model allows the prediction of local skin bending, obvious here but absent in the previous slide where the maximum mesh density in the panel skin is much lower and therefore not capable of picking up local skin bending.
The localized skin bending leads to the prediction of significantly higher maximum stresses in the panel skin and somewhat higher maximum stresses in the outstanding flanges of the T-shaped stringers than the model displayed in the previous slide.
This STAGS prediction confirms the conclusion that one should not skip the local post-buckling Koiter branch of PANDA2 when optimizing axially compressed, stiffened cylindrical shells. That is, one should choose the PANDA2 model listed as Case 5 in Table 4 rather than the PANDA2 model listed as Case 4 in Table 4.
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