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This is Fig. 18 from the 2013 GENOPT paper1. Shown here are results from the specific case called “test”: Optimized long propellant tank with two sets of struts (aft and forward), 4 pairs of struts in each set. Shown here are “design sensitivity” plots from an analysis in which all decision variables are held constant except for THKMID = thickness of the skin of the cylindrical part of the propellant tank. Typical behavior at the optimum design is exhibited: several margins are critical or near-critical at the optimum value of THKMID.
In the “behavior” and margin lists the following conventions apply:
Behavioral variable names:
FREQ means modal vibration frequency
STRES means stress component in a ply of a composite strut tube
COLBUK means buckling of a strut as a column
SHLBUK means buckling of a strut as a thin shell
FORCE means force in a strut tube during launch-hold
TNKSTR means stress in the propellant tank wall
TNKBUK means buckling of the propellant tank
"A", "F", and "F.S.":
An "A" added to a behavioral variable name means "allowable"
An "F" added to a behavioral variable name means "factor of safety"
"F.S." means "factor of safety"
Indices, i,j,k:
FREQ(i,j) = modal vibration frequency: i = load case; j = vibration mode
j = 1 means first eigenvalue for n = 0 waves (usually the mode with significant axial motion of the tank)
j = 2 means first eigenvalue for n = 1 waves (a mode with significant lateral-pitch motion of the tank)
j = 3 means first eigenvalue for n = 2 waves (a mode in which the tank wall deforms with 2 circ. waves)
j = 4 means first eigenvalue for n = 3 or 4 waves (a mode in which the tank wall deforms)
STRESSi(j,k) = stress component in strut: i = material no., j=load case, k = stress component
i = 1 means "material no. 1" which also means "strut type no. 1" (aft ring of struts)
i = 2 means "material no. 2" which also means "strut type no. 2" (forward ring of struts)
j = 1 means “Load Case 1” (See the section above entitled TWO LOAD CASES)
j = 2 means “Load Case 2” (See the section above entitled TWO LOAD CASES)
k = 1 means tension along the fibers of a ply
k = 2 means compression along the fibers of a ply
k = 3 means tension transverse to the fibers of a ply
k = 4 means compression transverse to the fibers of a ply
k = 5 means in-plane shear in a ply
COLBUK(i,j) = buckling of the strut as a column: i = load case; j = strut type
j = 1 means the type of strut attached to the aft propellant tank support ring. All these struts are the same.
j = 2 means the type of strut attached to the forward propellant tank support ring. All these struts are the same.
SHLBUK(i,j) = buckling of the strut as a thin shell: i = load case; j = strut type
j = 1 means the type of strut attached to the aft propellant tank support ring.
j = 2 means the type of strut attached to the forward propellant tank support ring.
FORCE(i,j) = maximum force in a strut: i = load case; j = strut type
j = 1 means the type of strut attached to the aft propellant tank support ring.
j = 2 means the type of strut attached to the forward propellant tank support ring.
TNKSTR(i,j) = maximum effective stress: i = load case; j = meridian number
j = 1 = effective stress in the tank is the maximum from the distribution along meridian no. 1
j = 2 = effective stress in the tank is the maximum from the distribution along meridian no. 2
TNKBUK(i,j) = buckling load factor: i = load case; j = meridian number
j = 1 means buckling load factor of the tank from the stress distribution along meridian no. 1
j = 2 means buckling load factor of the tank from the stress distribution along meridian no. 2
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