Imperfection sensitivity of axially compressed cylindrical shells under varying dimensions

This article conducts a theoretical study of the experimentally observed dependency of lower normalized buckling loads of axially compressed cylindrical shells on the radius-to-thickness ratio R/t. Medium length shells are studied, of equally elastic and isotropic material and of different dimensions. Given that geometric imperfections are viewed as a main source of imperfection sensitivity, their magnitudes are adjusted for individual shells by a previously introduced energy measure. The measure is defined as the square root of the total strain energy (linear analysis) of the shell deformed in the shape of an imperfection. Within the specified group, a relationship linking different energy measures of individual shells is suggested. The link is defined by the total strain energy per unit volume of a shell, which is a function of the shape and size of an imperfection and of the R/t ratio and the length-to-circumference/radius ratio. By equating a certain level of the function throughout the group of shells, a linked level of the energy measure of imperfections is provided for every single shell using a simple formula. Numerical examples showing the imperfection sensitivity of the shells for three-dimensional configurations are presented. FEM GNIA buckling strength calculations are based on a recently developed approach which employs the so-called influential eigenmode imperfections. The results are then compared to the lower bound knock-down factors recommended by NASA SP-8007 and to the normalized design buckling loads of Eurocode 1993-1-6. Furthermore, the authors propose an application of the linking ratio concerning shareable imperfection measurements and preliminary probabilistic estimates of the theoretical lower bound knock-down factors.

Automated summary

This article conducts a theoretical study on the dependency of lower normalized buckling loads of axially compressed cylindrical shells on the radius-to-thickness ratio. The study shows that the imperfection sensitivity of shells is affected by the R/t ratio and the length ratio. Various energy measures and numerical examples are presented to illustrate these relationships and imperfection sensitivities.