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Bifurcation of an elastic structure crucially depends on the curvature of theconstraints against which the ends of the structure are prescribed to move, aneffect which deserves more attention than it has received so far. In fact, weshow theoretically and we provide definitive experimental verification that anappropriate curvature of the constraint over which the end of a structure hasto slide strongly affects buckling loads and can induce: (i.) tensile buckling;(ii.) decreasing- (softening), increasing- (hardening), or constant-load (nullstiffness) postcritical behaviour; (iii.) multiple bifurcations, determiningfor instance two bifurcation loads (one tensile and one compressive) in asingle-degree-of-freedom elastic system. We show how to design a constraintprofile to obtain a desired postcritical behaviour and we provide the solutionfor the elastica constrained to slide along a circle on one end, representingthe first example of an inflexional elastica developed from a buckling intension. These results have important practical implications in the design ofcompliant mechanisms and may find applications in devices operating inquasi-static or dynamic conditions.

Effects of constraint curvature on structural instability: tensile buckling and multiple bifurcations