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PANDA2-optimized, axially compressed, ring and stringer stiffened, perfect and imperfect cylindrical shells

This is Table 4 from the 2007 Bushnell paper. This slide lists optimum designs obtained by Bushnell from PANDA2 suitable for analysis by STAGS (dimensions in inches).

Optimum designs were obtained by PANDA2 with the use of several different options and strategies (seven cases).

The terms used to identify these options and strategies, listed in the headings for each of the seven cases, include "perfect" or "imperfect" or "as if perfect", "no Koiter" or "yes Koiter", "yes change imperfection" or "no change in imperfection", and ICONSV.

These terms are defined as follows:

"Imperfect" means the shell has an imperfection shape in the form of the critical general buckling mode.

The term, "Koiter", refers to the branch in PANDA2 in which local post-buckling states are computed. "no Koiter" means this postbuckling analysis branch is skipped.

"yes change imperfection" means that during PANDA2 optimization cycles the amplitude of the general buckling modal imperfection is inversely proportional to the length and breadth of a combination of its axial and circumferential half-wave lengths.

"no change imperfection" means that the amplitude of the general buckling modal imperfection remains fixed at its user-provided value no matter what the shape of the critical buckling modal imperfection is.

"ICONSV" (-1 or 0 or 1) is an index for "conservativeness" used in PANDA2. ICONSV=1 (most conservative model) is the recommended value.

It is recommended that the PANDA2 user choose the model type identified as "Case 5". Cases 1 - 4 are unconservative, and Cases 6 and 7 are too conservative.

Case 1 is unconservative because the shell is assumed to be perfect. Cases 2 and 3 are unconservative because the Koiter local post-buckling branch of PANDA2 is skipped and because ICONSV = -1 and 0, whereas the recommended value of ICONSV is 1 . Case 4 is unconservative because the Koiter local post-buckling branch of PANDA2 is skipped.

Case 6 is too conservative because the complex effect of an initial buckling modal imperfection is replaced by simply assuming the shell is perfect and doubling the axial compression under which the optimum design is obtained.

Case 7 is too conservative because the same amplitude of buckling imperfection is used in the PANDA2 model no matter what the shape of the critical buckling modal imperfection is. In reality imperfections of a given amplitude are easier to detect if they have shorter wavelengths than if they have longer wavelengths. Case 5 accounts for this, whereas Case 7 does not.

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