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MODE JUMPING

This study examines the optimization of a stiffened panel design in the far post-buckling regime using a nonlinear equilibrium analysis with mode jumping phenomenon. The panel has 10 modules and was optimized with different settings to observe mode jumping behavior. Dynamic responses and stress analysis are also presented during load steps.

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MODE JUMPING

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  1. MODE JUMPING AIAA Paper-97-1141 AIAA 38th SDM Meeting, 1997

  2. STAGS model of one module of the axially compressed stiffened panel designed for service in the far post-buckling regime. Panel has 10 modules. Linear buckling mode shape Buckling load factor

  3. Mode jumping phenomenon

  4. Nonlinear equilibrium: load factor v. load step number from the STAGS one-module model. This panel was optimized by PANDA2 with the “stop modejump” switch turned OFF (PANEL I) Nonlinear equilibrium: load v step See next slide for the state of the panel at load steps 22, 42, 52, and 62.

  5. Post-buckled panel Post-buckled state of the panel optimized by PANDA2 with the “stop modejump” switch turned off. Prediction is from the STAGS one-module model at 4 load factors, PA Step 22. PA=0.318 Step 42. PA=0.220 Step 52. PA=0.428 Step 62. PA=0.649

  6. Dynamic response starting at 62 Dynamic response of the one-module STAGS model of the axially compressed, stiffened plate starting at Load Step 63

  7. Stress: top surface of the panel skin next to the stiffener v. time Stress in top surface of panel skin next to the stiffener v. time States of the panel at a, b, c, d, e, f are shown on the next slide.

  8. Dynamic state of the panel at the 6 time steps shown on the previous slide Dynamic state of the panel at 6 time steps

  9. Nonlinear load-endshortening curve showing transient phase, 2nd static phase and collapse NOTE: This panel was optimized by PANDA2 with the “stop modejump” switch turned OFF. Note that mode jumping occurs well below the design load. Nonlinear load-end-shortening curve showing initial static phase of the STAGS analysis, transient phase, post-transient static phase, and final collapse of the stiffened panel.

  10. Optimization cycles with modejump switch off, then on PANDA2 optimization cycles with the “stop modejump” switch first turned OFF (PANEL I), then turned ON (PANEL II)

  11. Model used in PANDA2 for secondary buckling Model used in PANDA2 for secondary buckling, that is, mode jumping: (a) = primary buckling and post-buckling mode; (b) = secondary buckling mode.

  12. Nonlinear load-end-shortening curve with the modejump switch turned on Nonlinear load-end-shortening curve for the stiffened panel optimized by PANDA2 with the modejump switch turned ON. The optimized panel is heavier than that optimized with modejump OFF, but note that, unlike the “modejump OFF” panel, the first mode jump in this panel occurs well above the design load, which corresponds to load factor PA = 1.0

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