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OPTIMIZATION OF PROPELLANT TANKS SUPPORTED BY ONE OR TWO OPTIMIZED LAMINATED COMPOSITE SKIRTS

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David Bushnell, AIAA Fellow, 775 Northampton Drive, Palo Alto, California 94303 Michael S. Jacoby, AIAA Member, Lockheed Martin Missiles and Space, Palo Alto, California 94304 Charles C. Rankin, AIAA Associate Fellow, Rhombus Consultants Group, Inc., 1121 San Antonio Rd., Palo Alto, CA 94303

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Summary Formulation of optimization problem (Slides 5 and 6 and 7) Geometry (Slides 4 and 8 - 12) “oneskirt” case (Slides 4 and 13 - 22) “twoskirt” case (Slides 23 - 43) Conclusions (Slide 44)

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Discretized BIGBOSOR4 “oneskirt” model

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The propellant tank2/skirt system is optimized subject to: the minimum modal vibration frequency must be greater than a given value five stress components in each ply of the laminated composite wall(s) of the skirt(s) shall not exceed five specified allowables The skirt(s) shall not buckle as a thin conical shell(s) the maximum effective (vonMises) stress in the tank wall shall not exceed a specified value the tank wall shall not buckle

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The objective is: Objective= W x (normalized empty tank mass) + (1-W) x (normalized skirt(s) conductance), in which W is a user-selected weight between 0.0 and 1.0

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Optimization in the presence of two load cases: Load Case 1: 10g axial acceleration plus 25 psi internal ullage pressure plus 200-degree cool-down of the propellant tank Load Case 2: 10g lateral acceleration plus 25 psi internal ullage pressure plus 200- degree cool-down of the propellant tank

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Sketch of propellant tank strut support ring and tapered doubler

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Sketch of the configuration of the skirt support

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Names of decision variables pertaining to the ends of the skirt

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Diagram of the aft skirt support

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Skirt segment 4 with tapered “prongs” that enclose the composite laminate

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Objective versus design iterations during 1st SUPEROPT

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Objective versus design iterations during 2nd SUPEROPT

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Two axisymmetric vibration modes from BIGBOSOR4 for the optimized “oneskirt” case

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Two lateral/pitching vibration modes from BIGBOSOR4 for the optimized “oneskirt” case

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Two shell deformation vibration modes from BIGBOSOR4 for the optimized “oneskirt” case

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Deformed pre-buckled state of the shell meridian at theta=0, (A) axial acceleration, (B) lateral acceleration

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Buckling modes and load factors under axial acceleration

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Buckling modes and load factors under lateral acceleration

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PANDA-type model of critical buckling at theta = 90 degrees corresponding to Load Case 2 (lateral acceleration)

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PANDA-type model of buckling

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BIGBOSOR4 shell segment numbering in the “twoskirt” case

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"twoskirt" case, Evolution of the objective during the first execution of the GENOPT processor called "SUPEROPT”

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“twoskirt” case: GENOPT/BIGBOSOR4 axisymmetric vibration modes: (A) Tank rolling and (B) tank axial motion

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“twoskirt” case: GENOPT/BIGBOSOR4 lateral-pitching vibration modes: (C) Primarily lateral tank motion and (D) primarily tilting tank motion

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GENOPT/BIGBOSOR4 vibration modes in which shell deformation predominates

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Deformed pre-buckled state of the shell meridian and skirts at theta=0, (A) axial acceleration, (B) lateral acceleration

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From Table 6: Buckling prediction from PANDA model 1, Load Case 2: Lateral acceleration, theta = 90 degrees

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Prebuckling deformation under Load Case 2 of the forward part of the propellant tank with (A) tapered and (B) constant-thickness external doubler. Model (B) simulates the STAGS model.

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Buckling modes and load factors under axial acceleration

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STAGS finite element model of the "twoskirt" case

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“twoskirt” case: STAGS vibration modes analogous to the GENOPT/BIGBOSOR4 modes displayed 3 and 4 slides ago

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Prebuckling stress in the skin of the propellant tank predicted by STAGS for Load Case 1: axial acceleration + internal pressure + thermal loading

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Prebuckling stress at the tips of the stringers in the internal orthogrid of the propellant tank predicted by STAGS for Load Case 1: axial acceleration + internal pressure + thermal loading

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Prebuckling stress in the skin of the propellant tank predicted by STAGS for Load Case 2: lateral acceleration + internal pressure + thermal loading

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Prebuckling stress at the tips of the stringers in the internal orthogrid of the propellant tank predicted by STAGS for Load Case 2: lateral acceleration + internal pressure + thermal loading

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Spurious buckling mode from the STAGS model of the aft conical support analyzed by itself

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Nonlinear equilibrium states of the aft skirt predicted by STAGS: axial compression

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Maximum in-plane shear resultant in the aft skirt from the STAGS nonlinear equilibrium analysis: axial compression

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Nonlinear bifurcation buckling mode from the STAGS model of the aft conical support under uniform axial compression

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Buckling mode and load factors under axial acceleration corresponding to the prebuckling state at theta = 0

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Buckling of the tank/skirt system under lateral acceleration as predicted by STAGS

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Conclusions The GENOPT/BIGBOSOR4 "tank2" model seems to work. Comparisons of predictions from STAGS and GENOPT/BIGBOSOR4 demonstrate that this application of GENOPT/BIGBOSOR4 can be used for PRELIMINARY design. The GENOPT software in the directory../genopt/sources was significantly modified to permit more than 50 decision variable candidates. The maximum number of decision variable candidates has been raised from 50 to 98. BIGBOSOR4 does not handle the effect of buckling under in-plane shear loading, which is present especially at the circumferential coordinate, theta = 90 degrees in the supporting skirt in Load Case 2 (10g lateral acceleration). In order to compensate for this an approximate PANDA-type model [4] has been introduced into the “tank2” software in order to predict with reasonable accuracy buckling of the laminated composite skirt(s) under both Load Case 1 and Load Case 2. STAGS models with tapered doubler thicknesses should be constructed in order to obtain accurate predictions of maximum compressive stress at the tips of the stringers in the internal orthogrid. The reader should read [1] in order to obtain much background information required for a fuller understanding of how GENOPT/BIGBOSOR4 works.

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