  The complexity and unpredictability of postbuckling responses in even simple
thin shells have raised great challenges to emerging technologies exploiting
buckling transitions. Here we comprehensively survey the buckling landscapes to
show the full complexity of the stable buckling states and the transition
mechanisms between each of them. This is achieved by combining a simple and
versatile triangulated lattice model for modelling the shell morphologies with
efficient high-dimensional free-energy minimisation and transition path finding
algorithms. We show how the simple free energy landscapes of short, lightly
compressed cylinders become vastly more complex at high compressive strains or
aspect ratios. We then exploit these landscapes to introduce an effective
method for targeted design - landscape biasing. This is used to inform
thickness modifications enabling landscape redesign, and the development of
structures which are highly resistant to lateral perturbations. Our methods are
general, and can be extended to studying postbuckling responses of other
geometries.
