Coexisting equilibria and stability of a shallow arch: Unilateral displacement-control experiments and theory

Harvey, P. Scott; Virgin, Lawrence N.

doi:10.1016/j.ijsolstr.2014.11.016

Cited by 48 publications

(18 citation statements)

References 33 publications

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“…These additional probing points are feasible in a particularly straightforward way in experiments with simpler structures such as arches. Harvey & Virgin [2015] give an experimental demonstration of probing for shallow arches (though with only unilateral, one-sided clamping such that no unstable buckling states could be directly observed in the experiments).…”

Section: General Controllability Through Probingmentioning

confidence: 99%

Probing Shells Against Buckling: A Nondestructive Technique for Laboratory Testing

Thompson

Hutchinson

Sieber

2017

Int. J. Bifurcation Chaos

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Abstract. This paper addresses testing of compressed structures, such as shells, that exhibit catastrophic buckling and notorious imperfection sensitivity. The central concept is the probing of a loaded structural specimen by a controlled lateral displacement to gain quantitative insight into its buckling behaviour and to measure the energy barrier against buckling. This can provide design information about a structure's stiffness and robustness against buckling in terms of energy and force landscapes. Developments in this area are relatively new but have proceeded rapidly with encouraging progress.Recent experimental tests on uniformly compressed spherical shells, and axially loaded cylinders, show excellent agreement with theoretical solutions. The probing technique could be a valuable experimental procedure for testing prototype structures, but before it can be used a range of potential problems must be examined and solved. The probing response is highly nonlinear and a variety of complications can occur. Here, we make a careful assessment of unexpected limit points and bifurcations, that could accompany probing, causing complications and possibly even collapse of a test specimen. First, a limit point in the probe displacement (associated with a cusp instability and fold) can result in dynamic buckling as probing progresses, as demonstrated in the buckling of a spherical shell under volume control. Second, various types of bifurcations which can occur on the probing path which result in the probing response becoming unstable are also discussed. To overcome these problems, we outline the extra controls over the entire structure that may be needed to stabilize the response.

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Section: General Controllability Through Probingmentioning

confidence: 99%

Probing Shells Against Buckling: A Nondestructive Technique for Laboratory Testing

Thompson

Hutchinson

Sieber

2017

Int. J. Bifurcation Chaos

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“…When f reaches zero, snap-through occurs (Fargette et al, 2014;Harvey and Virgin, 2015) and the structure jumps to an inverted equilibrium configuration, assuming that the system is damped. The vertical position d at the onset of snap-through is denoted the critical displacement d cr .…”

Section: Formulationmentioning

confidence: 99%

“…Under force control related to the problem treated here, a concentrated downward force would be increased until snap-through occurs, which is associated with a critical point (bifurcation or limit point) on the equilibrium path (force versus displacement). The dependence of the critical force on its location has been examined in several papers, e.g., Plaut (1979) for shallow extensible arches with the three standard sets of end conditions, Camescasse et al (2013Camescasse et al ( , 2014 for shallow extensible buckled beams with pinned ends, Fargette et al (2014) for a shallow inextensible buckled beam with clamped ends, and Harvey and Virgin (2015) for shallow inextensible buckled beams with pinned ends. Some recent papers have examined snap-through under displacement control, but have not presented results revealing the dependency of the critical displacement on location.…”

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confidence: 99%

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Snap-through of arches and buckled beams under unilateral displacement control

Plaut

2015

International Journal of Solids and Structures

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Arches and beams buckled upward are analyzed. The structure is pushed downward from above at a specific location along the span until snap-through occurs and the structure jumps to an inverted equilibrium shape. Each beam or arch is modeled as an inextensible elastica. Critical displacements are computed for buckled beams with both ends pinned, both ends clamped, or one end clamped and the other end pinned. Circular arches with pinned ends are also investigated. The ends are immovable. The critical displacement is obtained directly from a theoretical equilibrium shape of the initial unloaded structure. Numerical results are presented for four height-to-span ratios of the initial structure, showing the critical displacement for any application point along the span. At the onset of snap-through, the imposed displacement is at or below the horizontal chord connecting the ends.

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“…Our approach differs in that the experimental setup stabilises otherwise unstable equilibria using additional control points. Additional control points have been used to constrain [7] or probe [5] nonlinear structures in one direction, but are here rigidly fixed to the structure to allow the push/pull control required to scan for additional equilibria. Figure 4 gives a detailed explanation of the experimental setup, including implementation of the loads and boundary conditions.…”

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confidence: 99%

Shape Control for Experimental Continuation

et al. 2018

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An experimental method has been developed to locate unstable equilibria of nonlinear structures quasistatically. The technique involves loading a structure by the application of either a force or a displacement at a main actuation point while simultaneously controlling the overall shape using additional bidirectional probe points. The method is applied to a shallow arch, and unstable segments of its equilibrium path are identified experimentally for the first time. Shape control is a fundamental building block for the experimental-as opposed to numerical-continuation of nonlinear structures, which will significantly expand our ability to measure their mechanical response.

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Coexisting equilibria and stability of a shallow arch: Unilateral displacement-control experiments and theory

Cited by 48 publications

References 33 publications

Probing Shells Against Buckling: A Nondestructive Technique for Laboratory Testing

Probing Shells Against Buckling: A Nondestructive Technique for Laboratory Testing

Snap-through of arches and buckled beams under unilateral displacement control

Shape Control for Experimental Continuation

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