Professor of Solid and Structural Mechanics

# The deformation of an elastic rod with a clamp sliding along a smooth and curved profile

The design of compliant mechanisms is crucial in several technologies and relies on the availability of solutions for nonlinear structural problems. One of these solutions is given and experimentally validated in the present article for a compliant mechanism moving along a smooth curved profile. In particular, a deformable elastic rod is held by two clamps, one at each end. The first clamp is constrained to slide without friction along a curved profile, while the second clamp moves in a straight line transmitting its motion through the elastic rod to the first clamp. For this system it is shown that the clamp sliding on the profile imposes nontrivial boundary conditions (derived via a variational and an asymptotic approach), which strongly influence buckling and nonlinear structural behavior. Investigation of this behavior shows that a compliant mechanism can be designed, which gives an almost neutral response in compression. This behavior could easily be exploited to make a force limiting device. Finally a proof-of-concept device was constructed and tested showing that the analyzed mechanical system can be realized in practice and it behaves tightly to the model, so that it can now be used in the design of machines that use compliant mechanisms.*If you're having trouble playing videos on YouTube,*

*click here to watch it.*# Effects of the constraint’s curvature on structural instability: tensile buckling and multiple bifurcations

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.*If you're having trouble playing videos on YouTube,*

*click here to watch it.***Related papers:**

- D. Misseroni, G. Noselli, D. Zaccaria, and D. Bigoni,
The deformation of an elastic rod with a clamp
sliding along a smooth and curved profile.
*International Journal of Solids and Structures*, 2015, in press; doi:10.1016/j.ijsolstr.2015.05.004. - D. Bigoni, D. Misseroni, G. Noselli and D. Zaccaria,
Effects of the constraint’s curvature on structural instability: tensile buckling and multiple bifurcations.
*Proceedings of the Royal Society A*, 2012, 468, 2191-2209; doi:10.1098/rspa.2011.0732. - D. Bigoni, Nonlinear Solid Mechanics Bifurcation Theory and Material Instability. Cambridge University Press, 2012, ISBN:9781107025417.
- D. Bigoni, D. Misseroni, G. Noselli, D. Zaccaria Surprising instabilities of simple elastic structures. In
*Nonlinear Physical Systems - Spectral Analysis, Stability and Bifurcations*, Kirillov, N. and Pelinovsky, D.E. Eds., Wiley, pp. 1-14, 2014; ISBN: 978-1-84821-420-0.

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