Linear elastic buckling of ring-stiffened cylindrical shell

5th Nov 2020

Buckling is one of the most important failure modes to consider in pressure vessel design as it can lead to a sudden and catastrophic collapse.  The animation below shows the first buckling mode obtained from a linear elastic buckling analysis of a ring-stiffened cylindrical shell subject to external pressure.   Overall collapse of the structure is predicted principally because of the short shell bay length and slender stiffeners used.


The bifurcation buckling load is determined by constructing a linear elastic stiffness matrix and geometric stiffness matrix.  Although this type of analysis almost always provides an overestimate of the real-world buckling load, a reasonable prediction of the actual buckling load can be obtained using a design factor depending on the requirements of the chosen design code.  The linear elastic buckling analysis method offers a fast, low cost solution, as the smallest eigenvalue returned can offer a quick indication as to whether the structure will be stable under the required service conditions.  It can also be used to highlight the regions of a structure in which stability issues could occur, as well as drawing attention to meshing irregularities that can themselves produce unexpected behaviour.  Linear elastic buckling analysis does have inherent limitations, however.  Due to being geometrically linear, the method can be a poor predictor of the importance of geometric imperfections.  It also cannot take material nonlinearity into account, although this isn’t necessarily an issue if the applied loading doesn’t result in any appreciable yielding.

In situations where linear elastic buckling analysis is deemed unsuitable, non-linear buckling analysis can be used. In this type of analysis the load is applied in a series of steps and, as the load is increased, the shape and, in turn, the stiffness of the structure changes, resulting in a solution that accounts for geometry and material nonlinearity.   Although such analyses are much more time consuming and expensive to run, with careful attention to material property definition and use of actual geometry, very accurate predictions of buckling load can be achieved.

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