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This slide is from the 1999 paper: "Additional buckling solutions in PANDA2", by David Bushnell, Hao Jiang, and Norm F. Knight, Jr., AIAA 40th Structures, Structural Dynamics and Materials Conference, AIAA Paper 99-1233, 1999, referred to as called "1999 addsoln paper" in the next two slides.
Shown here are the double trigonometric series expansions for the buckling modal displacements, u, v, w.
Local, inter-ring, and general buckling load factors and margins obtained with this "alternative" buckling model contain the string, "altsoln" in the definitions of the design margins.
The PANDA2 user can optimize panels with or without use of this "alternative" buckling model, which requires significantly more computer time than the simple PANDA-type closed form model and the semi-analytical (strip) model in which a single skin-stringer module is discretized as shown 10 slides hence.
The double-trigonometric-series "alternative" model is applied to a "patch" of the stiffened panel or shell. The size of this "patch" depends on whether the "alternative" model is being applied for local buckling, inter-ring buckling, or general buckling.
For more information about this "alternative" buckling model download the 1999 addsoln paper from this website.
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