Abstract
Even for relatively simple thin shell morphologies, many different buckled configurations can be stable simultaneously. Which state is observed in practice is highly sensitive to both environmental perturbations and shell imperfections. The complexity and unpredictability of postbuckling responses has therefore raised great challenges to emerging technologies exploiting buckling transitions. Here we show how the buckling landscapes can be explored through a comprehensive survey of the stable states and the transition mechanisms between them, which we demonstrate for cylindrical shells. This is achieved by combining a simple and versatile triangulated lattice model with efficient high-dimensional free-energy minimisation and transition path finding algorithms. We then introduce the method of landscape biasing to show how the landscapes can be exploited to exert control over the postbuckling response, and develop structures which are resistant to lateral perturbations. These methods now offer the potential for studying complex buckling phenomena on a range of elastic shells.
Highlights
Even for relatively simple thin shell morphologies, many different buckled configurations can be stable simultaneously
Buckled states have been elucidated by solving the von Kármán–Donnell equations relating the stress to the radial displacement in an elastic cylindrical shell, but only by assuming the solutions exhibit axial periodicity, reminiscent of the diamond pattern shown by Yoshimura to enable global, inextensible buckling[30]
Kbend, and R0 to maintain a constant dimensionless elastic control ratio kstretchR20=kbend = 2:5 ́ 105, and free energies E reported throughout are nondimensionalized such that the reduced free energy is Er 1⁄4 E=kbend
Summary
Even for relatively simple thin shell morphologies, many different buckled configurations can be stable simultaneously. We introduce the method of landscape biasing to show how the landscapes can be exploited to exert control over the postbuckling response, and develop structures which are resistant to lateral perturbations These methods offer the potential for studying complex buckling phenomena on a range of elastic shells. In transforming between the large number of different postbuckling states, only the first transition capable of buckling the unbuckled cylinder has been investigated previously[32,33] This particular transition has received significant interest, as capturing the minimum-energy pathway (MEP) enables the minimumenergy barrier to be obtained, which provides an absolute lower bound to the energy required for a compressed cylinder to buckle
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