|
|
||
|
|
|
|
(Abstract continued from the previous slide) The asymmetrically laminated CFRP cylinders analysed stem from a preceding European project which focused on the correlation of measured buckling loads of test cylinders with analytical and numerical buckling load predictions. The FE analyses of these shells have shown that for such cylinders calculated buckling loads close to test values may be attained if measured imperfections are included in the analysis. It was further found that the consideration of imperfections requires the use of FE analysis methods which take geometric nonlinearity into account. The nonlinear buckling and transient dynamic FE analyses of these CFRP cylinders with perfect geometry and with measured imperfections applied finally provided the basis for the FE analyses of such cylinders having a single localized dimple.
The FE analyses of cylinders with an initial local dent or bulge yielded particular deformation processes including different local buckling phenomena which were hardly known from unstiffened circular cylinders with neither perfect geometry nor with imperfections distributed over the entire shell surface. Nevertheless, by means of systematic parameter variation some interrelationships between the results and the nominal dimensions of the cylinder and the dimple could be derived.
The initial circumferential curvature of a shell in the dimple plays a decisive role in the deformation process of the cylinders and in the run of their FE analyses. The differences in the behaviour pattern and the initial curvature led to a distinction between "shallow" and "deep" dents. Shallow dents with an initial amplitude smaller than a certain marginal depth provoke a distinct local buckling with a sudden snapping inwards of the dent to form a local flattened shell strip of reduced geometric axial stiffness. Deep dents, in turn, result in a continuous local flattening of the shell without any dynamic local-buckling incident prior to the total cylinder collapse.
Localized, shallow dents of particular initial circumferential width and axial height reduce the buckling load as much as axisymmetric inward dimples of identical initial amplitude. And a non-axisymmetric, shallow dent of adequate initial width and height may be as damaging as an imperfection-pattern that is given by a classical buckling mode of initial amplitude that is half the initial amplitude of the dent. Further, localized non-axisymmetric bulges impair the load carrying capacity less than localized dents of the same absolute initial amplitude, width, and height. Finally, the buckling load of a cylinder with single localized dent is only little different from that of a cylinder having two dents of identical size.
For isotropic cylinders the initial axial heights of dimples that reduces the buckling load the most for a preselected initial depth is close to the wavelength for classical axisymmetric buckling of a perfect cylinder. The initial circumferential widths of the worst dent is between two to three times the initial height, whereas the worst bulge is always axisymmetric.
The studies yielded that the cylinder length is also decisive for the local deformation processes of the shell in and in the adjacency of the initial dimples (local buckling) observed. The design recommendations in standards and literature considered for thin-walled, unstiffened isotropic cylinders under axial compression are conservative if the nominal radius and wall-thickness as well as the nominal cylinder length are taken into account.
For the laminated cylinders investigated accurate and general predictions of minimal buckling loads and of critical dimple dimensions could not be derived on basis of the cylinder geometry alone as the buckling behavior patterns of such shells depend strongly on the laminate stacking. However, there was no indication that any laminated cylinder with any non-axisymmetric dimple results in a lower buckling load than anisotropic cylinder of identical radius, length and wall thickness also having a non-axistymmetric dimple.
Page 223 / 444