Probing Shells Against Buckling: A Nondestructive Technique for Laboratory Testing

Abstract

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.

Harnessing energy landscape exploration to control the buckling of cylindrical shells

“…Computationally, the only transition which has been followed previously is the simplest unbuckled-singly dimpled pathway, where the dimple is centrally located on the cylinder 32,33 . Meanwhile, local probing of cylindrical shells has been suggested as an experimental technique which may allow the true dimpling transition state to be accessed 26,[34][35][36] . In Fig.…”

“…An explicit link has therefore been made between the ease of single dimple formation and the sensitivity of loaded cylinders to lateral loading 32 . As important for structural applications, it has been suggested that these theoretical minimum-energy barriers can be accessed experimentally via a local probing technique for cylindrical 26,[34][35][36] and spherical shells 37,38 .…”

Nonlinear dynamics of spherical shells buckling under step pressure

“…In the limit for very thin shells, /0 hR → , the energy barriers for prescribed pressure and prescribed volume change are the same. The barrier in the case of prescribed volume change does depend somewhat on / hR , as discussed in [11]. , is given for the two states in a) and the radial displacements of two of the most important modes are presented in b).…”

Buckling of thermally fluctuating spherical shells: Parameter renormalization and thermally activated barrier crossing

“…Recently, a number of publications addressed the energy barrier for axisymmetric dimples on spherical shells by applying an additional point force in order to induce formation of a single dimple, where the point force F is applied, and in order to control the indentation depth ζ by the point force [34,35,40,41]. The barrier state corresponds to an indented state with F = 0 at ζ = ζ B , which is unstable with respect to growth and shrinkage.…”