Although structural instabilities have traditionally been avoided in design as undesirable causes of failure, the rapid and potentially significant energy changes that result from the large displacements induced by buckling have gained recent interest as a favorable design feature for systems whose intent is energy dissipation or energy storage. Computational methods to quantify the energy changes associated with buckling of a transversely loaded curved beam are developed in this work. The methods are then used to predict the occurrence of buckling based on initial geometry and input load. The influence of the parameters of the numerical approximation, such as mesh and time step, is also explored. Correlations are made between the simpler behavior of a truss structure and the more complex behavior of a curved beam so that analytical solutions may be used to guide the understanding of structures whose response can only be predicted computationally. The techniques which are presented can aid in the more efficient design of energy dissipation, transfer, and storage systems that take advantage of buckling instability phenomena.

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