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

2. 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

3. 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)

4. Discretized BIGBOSOR4 “oneskirt” model

5. 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

6. 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

7. 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

8. Sketch of propellant tank strut support ring and tapered doubler

9. Sketch of the configuration of the skirt support

10. Names of decision variables pertaining to the ends of the skirt

11. Diagram of the aft skirt support

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

13. Objective versus design iterations during 1st SUPEROPT

14. Objective versus design iterations during 2nd SUPEROPT

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

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

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

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

19. Buckling modes and load factors under axial acceleration

20. Buckling modes and load factors under lateral acceleration

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

22. PANDA-type model of buckling

23. BIGBOSOR4 shell segment numbering in the “twoskirt” case

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

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

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

27. GENOPT/BIGBOSOR4 vibration modes in which shell deformation predominates

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

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

30. 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.

31. Buckling modes and load factors under axial acceleration

32. STAGS finite element model of the "twoskirt" case

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

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

35. 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

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

37. 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

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

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

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

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

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

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

44. 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.