Optimisation of shell buckling using lower bound capacities

In the context of aerospace and marine applications there are considerable incentives for designers to adopt thin shells, whose performances are enhanced by appropriately chosen rib stiffeners or using high-performance composite materials. Imperfection-sensitive buckling in these circumstances is controlled by extremely high numbers of independent material and geometric parameters. As a basis for design, traditional reliance upon scatter of test results is suggested to be untenable and the increasing tendency to replace this approach by use of nonlinear finite elements is argued to bring with it all sorts of other quite considerable practical problems.This paper describes how the long established and very simple “reduced stiffness method” (RSM) is able to provide an alternative design strategy. It shows how a very straightforward extension of classical critical load analysis allows the definition of lower bounds to the potential imperfection sensitivity in each mode and consequently the delineation of the mode and load likely to provide the controlling influence on design. Reliability of its predictions is briefly demonstrated through comparisons with extensive test programmes and confirmation through carefully controlled nonlinear numerical studies. Use of the RSM is shown to offer scope for identifying material and geometric parameters that result in improved and even “optimum” buckling loads. Case studies from past and a current programme of research looking at the buckling of composite shells are used to illustrate this design potential.