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

TL;DR

This paper investigates how the curvature of constraints influences structural buckling, revealing new phenomena like tensile buckling and multiple bifurcations, with experimental verification and design guidelines for desired postcritical behaviors.

Contribution

It provides a theoretical and experimental analysis of the impact of constraint curvature on buckling, introducing new bifurcation phenomena and design methods for elastic structures.

Findings

Constraint curvature significantly affects buckling loads.

Multiple bifurcations can occur, including tensile and compressive bifurcations.

Design of constraint profiles can control postcritical behavior.

Abstract

Bifurcation of an elastic structure crucially depends on the curvature of the constraints against which the ends of the structure are prescribed to move, an effect which deserves more attention than it has received so far. In fact, we show theoretically and we provide definitive experimental verification that an appropriate curvature of the constraint over which the end of a structure has 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, representing the first example of an inflexional elastica developed from a buckling in tension. 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.