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EXAMPLE 4, Slide 10: Design margins that affect the evolution of the optimum design of the externally pressurized isogrid-stiffened ellipsoidal shell

Design margins corresponding to Load Set No. 1 (+mode 1 and +mode 2 imperfection shapes) that may be active during GENOPT optimization of an axisymmetrically imperfect, externally pressurized, isogrid-stiffened ellipsoidal shell.

The "behavioral" variables are defined as follows:
CLAPS = collapse load factor
GENBK = general bifurcation buckling load factor
SKNBK = local skin buckling load factor (buckling of the triangular piece of skin between adjacent isogrid stiffeners)
STFBK = isogrid stiffener buckling load factor
SKNST = maximum effective (von Mises) stress in the skin of the ellipsoidal shell
STFST = maximum stress in any of the isogrid stiffeners
WAPEX = deflection at the apex of the ellipsoidal shell.

The numerals in the names and in the array indices have the following meanings:

CLAPS1(1), GENBK1(1), WAPEX1(1) mean respectively collapse, general buckling, apex deflection of the ellipsoidal shell with a "Mode 1" initial imperfection shape [e.g. CLAPS1] or a "Mode 2" initial imperfection shape [e.g. CLAPS2], under the Load Set 1 environment [e.g. CLAPS1(1)] or a Load Set 2 environment [e.g. CLAPS1(2)].

Load Set 1 = positive buckling modal imperfection shapes, +mode 1 and +mode 2;
Load Set 2 = negative buckling modal imperfection shapes, -mode 1 and -mode 2.

SKNBKi(j,k), STFBKi(j,k), SKNSTi(j,k), STFSTi(j,k) mean local skin buckling, stiffener buckling, skin stress, stiffener stress for the ellipsoidal shell with axisymmetric imperfection shape i (i = 1 = Mode 1 imperfection shape or i = 2 = Mode 2 imperfection shape), load set j (j = 1 = positive imperfection shape or j = 2 = negative imperfection shape), region k (k = 1 = shell segments 1 through 6 or k = 2 = shell segments 7 through 12). (Regions 1 and 2 and Shell segments 1 - 12 are indicated in the figure shown 8 slides ago.)

There is an additional analogous set of 22 design margins corresponding to Load Set No. 2 (not shown here).

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