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The shell shape parameter is given by:
Lambda = 2[3(1-nu^2)]^1/4 x (H/h)^1/2
in which H is the rise of a spherical cap above the plane of its edge and h is the shell wall thickness.
FROM:
H.N.R. Wagner, E.M. Sosa, T. Ludwig, J.G.A. Croll and C. Huehne (First author is from: Institute of Adaptronic and Functional Integration, Langer Kamp 6, 38106 Braunschweig, Germany),
“Robust design of imperfection sensitive thin-walled shells under axial compression, bending or external pressure”, International Journal of Mechanical Science, Vol. 156, pp 205-220, June 2019, https://doi.org/10.1016/j.ijmecsci.2019.02.047
ABSTRACT: Thin-walled shells like cylinders, cones and spheres are primary structures in launch-vehicle systems. When subjected to axial loading, bending 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 imperfections, and although imperfections exhibit comparatively low amplitudes, they can significantly reduce the critical load. Considering the influence of geometric imperfections adequately into the design process of thin-walled shells poses major challenges for structural design. The most common procedure to take into account the influence of imperfections is based on classical buckling loads obtained by a linear analysis which are then corrected by a knockdown factor. The knockdown factor represents a statistical lower-bound with respect to data obtained experimentally for different types of thin-walled shells. This article presents a versatile and simple numerical design approach for buckling of critical shell structures. The new design procedure is based on the reduced stiffness method and leads to significantly improved critical load estimations in comparison to lower-bounds obtained empirically. An analysis example is given which is based on the launch-vehicle stage adapter (LVSA) of NASAs Space Launch-system (SLS).
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