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This is Fig. 16 from the 1993 posbuckling paper. This slide shows the PANDA2 prediction of deformation of a cross section of the locally post-buckled skin-stringer panel module for Load Set 1 with Nxy = 0 and axial load Nx = 0, -1000, -2000, -3000, -4000, -5000, -6000 lb/inch. The axial compression Nx acts normal to the screen.
The local postbuckling analysis is based on the local linear bifurcation buckling mode. The postbuckling deflection pattern in the panel skin can change with increasing load above the bifurcation load because of the existence of a "flattening" unknown, "a", in the postbuckling theory and because the axial wavelength of the buckles is permitted to change as the panel is loaded further and further into its local post-buckling regime.
There are 4 unknowns in the Koiter-type nonlinear local postbuckling analysis:
"f" (the amplitude of the local buckles),
"a", (the "flattening" parameter),
"m", (the slope of the nodal lines of the buckles in the panel skin), and
"N", (a parameter inversely proportional to the square of the axial length of the buckles).
These four quantities change as the load is increased above the local bifurcation buckling load. The Newton method is used to solve the four simultaneous nonlinear postbuckling equations.
A sophisticated strategy of successively removing and re-introducing unknowns is used to ensure convergence of the nonlinear solution.
In this slide one can clearly see the change in the postbuckling deformation pattern as the blade stiffened panel is loaded further and further into the postbuckling region.
In the local postbuckling model it is assumed that the skin is flat. Therefore, the postbuckling model used in PANDA2 is valid only if the stringer spacing is very small compared to the radius of the cylindrical panel. (This is usually the case in optimized panels.)
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