Probing shells against buckling: a non-destructive technique for laboratory testing

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.Comment: as accepted in International Journal of Bifurcation and Chaos (18 pages

Shock-Sensitivity in Shell-Like Structures: with Simulations of Spherical Shell Buckling

This is the author accepted manuscript. The final version is available from World Scientific Publishing via the DOI in this record.Under increasing compression, an unbuckled shell is in a metastable state which becomes increasingly precarious as the buckling load is approached. So to induce premature buckling a lateral disturbance will have to overcome a decreasing energy barrier which reaches zero at buckling. Two archetypal problems that exhibit a severe form of this behaviour are the axially-compressed cylindrical shell and the externally pressurized spherical shell. Focussing on the cylinder, a non-destructive technique was recently proposed to estimate the ‘shock sensitivity’ of a laboratory specimen using a lateral probe to measure the nonlinear load deflection characteristic. If a symmetry-breaking bifurcation is encountered on the path, computer simulations showed how this can be suppressed by a controlled secondary probe. Here, we extend our understanding by assessing in general terms how a single control can capture remote saddle solutions: in particular how a symmetric probe could locate an asymmetric solution. Then, more specifically, we analyse the spherical shell with point and ring probes, to test the procedure under challenging conditions to assess its range of applicability. Rather than a bifurcation, the spherical shell offers the challenge of a de-stabilizing fold (limit point) under the rigid control of the probe

Probing shells against buckling: a non-destructive technique for laboratory testing

This is the author accepted manuscript. The final version is available from the publisher via the DOI in this record.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

Shock sensitivity in the localised buckling of a beam on a nonlinear foundation: The case of a trenched subsea pipeline

We study jump instability phenomena due to external disturbances to an axially loaded beam resting on a nonlinear foundation that provides both lateral and axial resistance. The lateral resistance is of destiffening-restiffening type known to lead to complex localisation phenomena governed by a Maxwell critical load that marks a phase transition to a periodic buckling pattern. For the benefit of having a concrete and realistic example we consider the case of a partially embedded trenched subsea pipeline under thermal loading but our results hold qualitatively for a wide class of problems with non-monotonic lateral resistance. In the absence of axial resistance the pipeline is effectively under a dead compressive load and experiences shock-sensitivity for loads immediately past the Maxwell load, i.e., extreme sensitivity to perturbations as may for instance be caused by irregular fluid flow inside the pipe or landslides. Nonzero axial resistance leads to a coupling of axial and lateral deformation under thermal loading. We define a ‘Maxwell temperature’ beyond which the straight pipeline may snap into a localised buckling mode. Under increasing axial resistance this Maxwell temperature is pushed to higher (safer) values. Shock sensitivity gradually diminishes and becomes less chaotic: jumps become more predictable. We compute minimum energy barriers for escape from pre-buckled to post-buckled states, which, depending on the magnitude of the axial resistance, may be induced by either symmetric, or anti-symmetric or non-symmetric perturbations