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This and the next 8 slides are from:
Luc Wullschleger, “Numerical investigation of the buckling behavior of axially compressed circular cylinders having parametric initial dimple imperfections”, PhD dissertation, Swiss Federal Institute of Technology, Zurich, 2006
ABSTRACT: Accurate analysis concerning static instability and reliable appointment of the buckling loads is important for safe design of thin-walled shell structures. Real shells contain geometric imperfections and other deviations from nominal values which have to be considered, as for buckling analyses on the basis of ideal conditions extreme discrepancies between prediction and test data can result. This thesis deals with the buckling behaviour of thin-walled, unstiffened cylinders under pure axial compression because of their extraordinary sensitivity to imperfections in the shell geometry. The parameters required for an application of real imperfections in a buckling analysis are difficult to be specified. And measured values of real imperfections for the design of any new cylinder shell are hardly available. In the absence of such data in most cases buckling patterns are used that result for perfect geometry and whose buckling patterns can be described with harmonic displacement functions. For safe shell design that imperfection shape is significant which yields the minimum buckling load. But, in general neither the geometry nor the amplitudes of the buckling patterns which contribute to the most damaging imperfection shape are known a priori. In addition, the monotone wavelike dimples forming the buckling patterns of perfect cylinders enclose the entire shell surface, and hence localized irregularities like single dents or bulges of different amplitude are insufficiently included. Consequently, due to the lack of adequate imperfections parameters, cylindrical shells still have to be designed by use of reduction factors to be applied to the analytical buckling loads for perfect cylinders. These reduction factors consider smallest empirical values and therefore provide critical loads which appear to be rather conservative. Moreover, such instructions exist for steel and other isotropic shell materials but not for laminated composite cylinders, for instance.
For these reasons the thesis on hand focusses on cylinders having localized imperfections in form of local inward or outward dimples. To investigate the influences of a single initial dimple on the instability behaviour of such cylinders, and separate from any effect of other irregularities, discrete parametric dents or bulges were added to FE models of unstiffened circular cylinders of otherwise perfect geometry. The chosen shape of a parametric dimple allowed to investigate the influence of its initial amplitude, its initial axial height, its initial circumferential width, and its axial position systematically and independently of other parameters. With regard to the absence of practical design recommendations for laminated composite cylinders the thesis on hand covers analyses of isotropic as well as of laminated CFRP shells. (Abstract continued on next slide.)
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