Global and local buckling load for an unstiffened isotropic shell (left) -stable dimple in a cylinder from [70] (right)

Global and local buckling load for an unstiffened isotropic shell (left) -stable dimple in a cylinder from [70] (right)

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Thin-walled shells like cylinders, cones and spheres are primary structures in launch-vehicle systems. When subjected to axial loading or external pressure, these thin-walled shells are prone to buckling. The corresponding critical load heavily depends on deviations from the ideal shell shape. In general these deviations are defined as geometric im...

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... As the dimple exacerbates, the first limit point decreases to a minimum and then increases to a certain load, which corresponds to the limit point of a fully localized single-dimple mode in the post-buckling regime. These observations are in line with the single perturbation load approach studies by Wagner [44], where it is shown that the shell structures collapse at this lower load. Friedrich & Schröder [45] also reported a similar observation that the local buckling in a displacement-controlled study corresponds to the global buckling in a load-controlled analysis. ...
... In §2, the snaking sequence of the shell is traced using the modified Riks solver, but it is impossible experimentally to trace the fingers of the load-displacement graph. Hence, to match the experimental buckling and post-buckling response, a nonlinear analysis is performed using a Newton-Raphson solver with artificial damping in ABAQUS [44,49]. Using the inverse distance weighted interpolation method, the measured geometrical imperfection is incorporated into the FE mesh [48,50]. ...
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... Data from the CMM were used to inform on the manufacturing quality and also used as inputs to the nonlinear finite element analyses with the as-manufactured imperfection signature. Following best practice in the experimental literature [23][24][25], to postprocess these data, a cylinder of best fit is first fitted to the 20,000-point data cloud by minimizing the root mean square of the imperfection data cloud against the best fit cylinder. The best fit QI cylinder has an outer radius of 302.20 mm, 1.15 mm larger than the designed outer radius. ...
... The imperfection measurements were carried out between x 40 mm and x 1060 mm, 93% of the unpotted length of the cylinder (0 to 24 mm and 1074 to 1098 mm of the total length of the cylinder are the regions of end-potting). Following best practice in the literature [23][24][25], the imperfection data cloud was deconstructed into Fourier coefficients and magnitudes based on a full four-term Fourier series decomposition. Once achieved, the Fourier series can be used to extrapolate the imperfections from x 50 mm to x 24 mm (the start of the bottom end-potting) and from x 1060 mm to x 1074 mm (the start of the top end-potting). ...
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... Data from the CMM were used to inform on the manufacturing quality and also used as inputs to the nonlinear finite element analyses with the as-manufactured imperfection signature. Following best practice in the experimental literature [18][19][20], to post-process these data, a cylinder of best fit is first fitted to the 20,000-point data cloud by minimizing the root mean square of the imperfection data cloud against the best fit cylinder. The best fit QI cylinder has an outer radius of 302.20 mm, 1.15 mm larger than the designed outer radius. ...
... The imperfection measurements were carried out between G = 40 mm and G = 1060 mm 93% of the unpotted length of the cylinder (0 to 24 mm and 1074 mm to 1098 mm is the end-potted region). Following best practice in the literature [18][19][20], the imperfection data cloud was deconstructed into Fourier coe cients and magnitudes based on a full four-term Fourier series decomposition. Once achieved, the Fourier series can be used to extrapolate the imperfections from G = 50 mm to G = 24 mm (the start of the bottom end-potting) and from G = 1060 mm to G = 1074 mm (the start of the top end-potting). ...
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... (27) and Eq. (28) of Ref. [37]. ...
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... Lower bound methods should deliver a theoretical plateau for the buckling load which is equal or less to every buckling load caused by multiple or large-amplitude imperfections. Note, that detailed description of the SBPA and its realization in finite element condes is given in Ref. [83]. A summary of alternative design approaches for buckling critical thin-walled shells is given in Appendix A. ...
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In this video buckling of an orthogrid stiffened cylinder under axial compression is shown. The model details and model creation via Python is shown. A download link for the input file for ABAUQS can be found here: https://www.researchgate.net/publication/342945965_TA03inp A more detailed description of the orthogrid stiffened shell can be found here: https://authors.elsevier.com/a/1bP7Ax-8RNfTw If there are any questions feel free to email me: ro.wagner@tu-braunschweig.de
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