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This and the next image are from:
Christian Huehne, Rolf Zimmermann, Raimund Rolfes, and Bodo Geier, DLR Braunschweig, Institute of Structural Mechanics, Germany, “Sensitivities to geometrical and loading imperfections on buckling of composite cylindrical shells”, (no publisher or date given, but the most recent reference listed at the end of the paper is 2002)
ABSTRACT: Thin-walled shell structures prone to buckling are sensitive to imperfections. The influence of loading and geometrical imperfecdtions on buckling loads of unstiffened composite cylindrical shells is investigated based on tests and computations. It is shown that their effect depends on laminate set-up. The results show that unification of imperfection sensitivity is allowed; systems sensitive to geometrical imperfections are also sensitive to loading imperfections. The results can be used to define lower limits for knock-down factors of composite shells.
In their paper the authors write [with some editing]:
"The inner surface of each test shell was measured with an optical sensor by EMPA. 30x90 uniformly distributed values were mapped. These values were transferred to a finite element model that consists of 180 uniformly distributed nodes over the circumference and 61 uniformly distributed nodes along the length of each cylindrical shell. Missing values are created by linear interpolation. A developed [imperfection] surface of one of the test shells is shown here. Single 'pre-buckles' are visible in this particular test specimen. For each geometrically imperfect shell the nonlinear buckling load is determined with use of ABAQUS/Standard. The buckling load is defined as the maximum load."
The next slide shows deformations of another of the imperfect axially compressed laminated composite test specimens (a) just before nonlinear buckling, (b) at buckling, (c) during a transient phase and (d) after a static stable post-buckled equilibrium state has been reached.
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