Effects of the constraint’s curvature on structural instability

Summary

An elastic structure subjected to a purely compressive force buckles when a deflection appears, an occurrence strongly influenced by the end constraints. We show theoretically and we provide definitive experimental verification that an appropriate curvature of the constraint over which the end of a structure is prescribed to slide strongly affects buckling loads and can induce: (i.) tensile buckling; (ii.) decreasing- (softening), increasing- (hardening), or constant-load (null stiffness) postcritical behaviour; (iii.) multiple bifurcations, determining for instance two bifurcation loads (one tensile and one compressive) in a single-degree-of-freedom elastic system. We show how to design a constraint profile to obtain a desired postcritical behaviour and we provide the solution for the elastica constrained to slide along a circle on one end. These results have important practical implications in the design of compliant mechanisms and may find applications in devices operating in quasi-static or dynamic conditions, even at the nanoscale.

Related papers:

  • Bigoni, D., Misseroni, D., Noselli, G. and Zaccaria, D. (2012).
    Effects of the constraint’s curvature on structural instability: tensile buckling and multiple bifurcations.
    Proceedings of the Royal Society A, 468 (2144), 2191-2209.
  • Misseroni, D., Noselli, G., Zaccaria, D. and Bigoni, D. (2015).
    The deformation of an elastic rod with a clamp sliding along a smooth and curved profile.
    International Journal of Solids and Structures, 69-70, 491-497.