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This and the next three slides are from the paper, "Optimization of stiffened panels in which mode jumping is accounted for" by David Bushnell, Charles C. Rankin, and Eduard Riks, AIAA 38th Structures, Structural Dynamics, and Materials Conference, AIAA Paper No. AIAA-97-1141, 1997, called "1997 modejump paper" in the next three slides.
ABSTRACT: PANDA2 is a computer program for the minimum weight design of stiffened composite, flat or cylindrical, perfect or imperfect panels and shells subject to multiple sets of combined in-plane loads, normal pressure, edge moments and temperature. STAGS is a general nonlinear finite element code that is specifically designed to analyze especially difficult stability problems in shell structures. Weight optimization of stiffened panels can be particularly troublesome when local buckling is allowed to occur in the pre-collapse state. For these systems, designs may be affected by interaction between local modes, a mechanism that manifests itself as mode jumping and is difficult to characterize. In this paper we describe how in PANDA2 mode jumping is detected and suppressed in optimized panels. Two axially compressed blade stiffened panels optimized by PANDA2 for service in the far postbuckling regime were numerically tested by STAGS. Mode jumping was permitted to occur below the design load in the first panel and suppressed in the second. Results obtained by STAGS are in reasonably good agreement with predictions by PANDA2. The first panel exhibits mode jumping well below the design load. Application of STAGS to this panel reveals that even though the mode jump involves little change in potential energy it generates large-amplitude oscillating stresses with significant stress reversal that might well cause fatigue and delamination. The oscillating stresses are caused by postbuckling lobes moving to and fro along the panel axis immediately after initiation of the mode jump.
This is Fig. 21 of the 1997 modejump paper. Shown here is an axially compressed single skin-stringer module of a metallic panel with uniformly spaced stringers of rectangular cross section. Symmetry conditions are applied along the two longitudinal edges of this single module model.
The nonlinear static equilibrium states displayed in this slide are from the first phase of a three-phase STAGS analysis of a panel that was previously optimized by PANDA2 with a mode-jumping constraint turned off (called "PANEL I" in the 1997 modejump paper).
The three phases of the STAGS analysis are:
1. initial nonlinear static analysis with STAGS load factor PA in the range 0 < PA < 0.7013
2. nonlinear transient analysis with STAGS load factor PA held constant at 0.7013
3. post-transient nonlinear static analysis with STAGS load factor PA in the range 0.7013 < PA < 0.943
Results from these three phases of the STAGS analysis are displayed on the next slide.
As shown on the next slide, STAGS predicts that the panel collapses at load factor, PA - 0.943. The load factor for which the panel was previously optimized by PANDA2 is the design load factor, PA = 1.0.
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