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

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.

Upheaval Buckling Assessment Based on Pipeline Features

Upheaval buckling (UHB) is a common design issue for high temperature buried pipelines. This paper highlights some of thekey issues affecting out-of-straightness (OOS) assessment of pipelines. The following factors are discussed; uplift resistancesoil models, uplift resistance in cohesive soils, uplift mobilisation, ratcheting, uplift resistance at low H/D ratios and thecorrect methodology for load factor selection. A framework for determining ratcheting mobilisation is proposed. Furtherresearch is required to verify and validate this proposed framework. UHB assessment of three different diameter pipelineswere carried out using finite element SAGE PROFILE package incorporating pipeline mobilisation and the results arecompared with semi-analytical formulation proposed by Palmer et al. 1990. The paper also presents a summary of as-laidpipeline features based on projects over the past 10 years.

Dynamic buckling of an inclined strut

The dynamic compressive response of a sandwich plate with a metallic corrugated core is predicted. The back face of the sandwich plate is held fixed whereas the front face is subjected to a uniform velocity, thereby compressing the core. Finite element analysis is performed to investigate the role of material inertia, strain hardening and strain rate hardening upon the dynamic collapse of the corrugated core. Three classes of collapse mode are identified as a function of impact velocity: (i) a three-hinge plastic buckling mode of wavelength equal to the strut length, similar to the quasi-static mode, (ii) a 'buckle-wave' regime involving inertia-mediated plastic buckling of wavelength less than that of the strut length, and (iii) a 'stubbing' regime, with shortening of the struts by local fattening at the front face. The presence of strain hardening reduces the regime of dominance of the stubbing mode. The influence of material strain rate sensitivity is evaluated by introducing strain rate dependent material properties representative of type 304 stainless steel. For this choice of material, strain rate sensitivity has a more minor influence than strain hardening, and consequently the dynamic collapse strength of a corrugated core is almost independent of structural dimension. © 2012 Elsevier Ltd. All rights reserved.

Mobilization distance for upheaval buckling of shallowly buried pipelines

Buried pipelines may be subject to upheaval buckling because of thermally induced compressive stresses. As the buckling load of a strut decreases with increasing out of straightness, not only the maximum available resistance from the soil cover, but also the movement of the pipeline required to mobilize this are important factors in design. This paper will describe the results of 15 full-scale laboratory tests that have been carried out on pipeline uplift in both sandy and rocky backfills. The cover to diameter ratio ranged from 0.1 to 6. The results show that mobilization distance exhibits a linear relationship with H=D ratio and that the postpeak uplift force-displacement response can be accurately modeled using existing models. A tentative design approach is suggested; the maximum available uplift resistance may be reliably predicted from the postpeak response, and the mobilization distance may be predicted using the relationships described in this paper. © 2012 American Society of Civil Engineers.

Surface texturing through cylinder buckling

We consider the axial buckling of a thin-walled cylinder fitted onto a mandrel core with a prescribed annular gap. The buckling pattern develops fully and uniformly to yield a surface texture of regular diamond-shaped buckles, which we propose for novel morphing structures. We describe experiments that operate well into the postbuckling regime, where a classical analysis does not apply; we show that the size of buckles depends on the cylinder radius and the gap width, but not on its thickness, and we formulate simple relationships from kinematics alone for estimating the buckle proportions during loading. © 2014 by ASME.

The plastic collapse and energy absorption capacity of egg-box panels

The plastic collapse response of aluminium egg-box panels subjected to out-of-plane compression has been measured and modelled. It is observed that the collapse strength and energy absorption are sensitive to the level of in-plane constraint, with collapse dictated either by plastic buckling or by a travelling plastic knuckle mechanism. Drop weight tests have been performed at speeds of up to 6 m s-1, and an elevation in strength with impact velocity is noted. A 3D finite element shell model is needed in order to reproduce the observed behaviours. Additional calculations using an axisymmetric finite element model give the correct collapse modes but are less accurate than the more sophisticated 3D model. The finite element simulations suggest that the observed velocity dependence of strength is primarily due to strain-rate sensitivity of the aluminium sheet, with material inertia playing a negligible role. Finally, it is shown that the energy absorption capacity of the egg-box material is comparable to that of metallic foams. © 2003 Elsevier Ltd. All rights reserved.

Uplift resistance of buried pipelines at low cover-diameter ratios

Reliable estimates for the maximum available uplift resistance from the backfill soil are essential to prevent upheaval buckling of buried pipelines. The current design code DNV RP F110 does not offer guidance on how to predict the uplift resistance when the cover:pipe diameter (H/D) ratio is less than 2. Hence the current industry practice is to discount the shear contribution from uplift resitance for design scenarios with H/D ratios less than 1. The necessity of this extra conservatism is assessed through a series of full-scale and centrifuge tests, 21 in total, at the Schofield Centre, University of Cambridge. Backfill types include saturated loose sand, saturated dense sand and dry gravel. Data revealed that the Vertical Slip Surface Model remains applicable for design scenarios in loose sand, dense sand and gravel with H/D ratios less than 1, and that there is no evidence that the contribution from shear should be ignored at these low H/D ratios. For uplift events in gravel, the shear component seems reliable if the cover is more than 1-2 times the average particle size (D50), and more research effort is currenty being carried out to verify this conclusion. Strain analysis from the Particle Image Velocimetry (PIV) technique proves that the Vertical Slip Surface Model is a good representation of the true uplift deformation mechanism in loose sand at H/D ratios between 0.5 and 3.5. At very low H/D ratios (H/D < 0.5), the deformation mechanism is more wedge-like, but the increased contribution from soil weight is likely to be compensated by the reduced shear contributions. Hence the design equation based on the Vertical Slip Surface Model still produces good estimates for the maximum available uplift resistance. The evolution of shear strain field from PIV analysis provides useful insight into how uplift resistance is mobilized as the uplift event progresses. Copyright 2010, Offshore Technology Conference.

Observation of large-scale features on graphite by scanning tunnelling microscopy

Superlattice structures and rippling fringes were imaged on two separate pieces of graphite (HOPG) by scanning tunnelling microscopy (STM). We observed the corrugation conservation phenomenon on one of the superlattice structures where an overlayer does not attenuate the corrugation amplitude of the superlattice. Such a phenomenon may illustrate an implication that nanoscale defects a few layers underneath the surface may propagate through many layers without decay and form the superlattice structure on the topmost surface. Some rippling fringes with periodicities of 20 nm and 30 nm and corrugations of 0.1 nm and 0.15nm were observed in the superlattice area and in nearby regions. Such fringes are believed to be due to physical buckling of the surface. The stress required to generate such structures is estimated, and a possible cause is discussed. An equation relating the attenuation factor to the number of overlayers is proposed. © 2005 The Japan Society of Applied Physics.

The use of object oriented modelling and simulation tools in constraint satisfaction for embodiment design

The software package Dymola, which implements the new, vendor-independent standard modelling language Modelica, exemplifies the emerging generation of object-oriented modelling and simulation tools. This paper shows how, in addition to its simulation capabilities, it may be used as an embodiment design tool, to size automatically a design assembled from a library of generic parametric components. The example used is a miniature model aircraft diesel engine. To this end, the component classes contain extra algebraic equations calculating the overload factor (or its reciprocal, the safety factor) for all the different modes of failure, such as buckling or tensile yield. Thus the simulation results contain the maximum overload or minimum safety factor for each failure mode along with the critical instant and the device state at which it occurs. The Dymola "Initial Conditions Calculation" function, controlled by a simple software script, may then be used to perform automatic component sizing. Each component is minimised in mass, subject to a chosen safety factor against failure, over a given operating cycle. Whilst the example is in the realm of mechanical design, it must be emphasised that the approach is equally applicable to the electrical or mechatronic domains, indeed to any design problem requiring numerical constraint satisfaction.

Computational fluid-structure interaction methods for simulation of inflatable aerodynamic decelerators

Inflatable aerodynamic decelerators have potential advantages for planetary re-entry in robotic and human exploration missions. It is theorized that volume-mass characteristics of these decelerators are superior to those of common supersonic/subsonic parachutes and after deployment they may suffer no instabilities at high Mach numbers. A high fidelity computational fluid-structure interaction model is employed to investigate the behavior of tension cone inflatable aeroshells at supersonic speeds up to Mach 2.0. The computational framework targets the large displacements regime encountered during the inflation of the decelerator using fast level set techniques to incorporate boundary conditions of the moving structure. The preliminary results indicate large but steady aeroshell displacement with rich dynamics, including buckling of the inflatable torus that maintains the decelerator open under normal operational conditions, owing to interactions with the turbulent wake. Copyright © 2009 by the American Institute of Aeronautics and Astronautics, Inc.

Pipeline uplift response in thawed sandy backfills: Preliminary findings

Offshore and onshore buried pipelines under high operating temperature and pressures may lead to upheaval buckling (UHB) if sufficient soil cover is not present to prevent the upward movement of the pipeline. In regions where seasonal changes involve ground soil undergoing freezing-thawing cycles, the uplift resistance from soil cover may be minimum when the soil is undergoing thawing. This paper presents the results from 2 directly-comparable minidrum centrifuge tests conducted at the Schofield Centre, University of Cambridge, to investigate the difference in uplift resistance responses between fully-saturated and thawed sandy backfill conditions. Both tests were conducted drained at 30g using an 8.6 mm diameter aluminium model pipe, corresponding to a prototype pipe diameter of 258 mm. The soil cover/pipe diameter ratio, H/D, was kept at 1. Fraction E fine silica sand was used as the backfill. Preliminary experimental results indicated that the ultimate uplift resistance of a thawing sand backfill to be lower than that of a fully saturated sand backfill. This suggests that in regions where backfill soil undergoes freeze-thaw cycles, the thawing backfill may be more critical than fully saturated backfill for uplift resistance. The 2-dimensional displacement field during the experiment was accurately measured and analysed using the Particle Image Velocimetry technique. Copyright © 2011 by the International Society of Offshore and Polar Engineers (ISOPE).

Collapse mechanism maps for the hollow pyramidal core of a sandwich panel under transverse shear

The finite element method has been used to develop collapse mechanism maps for the shear response of sandwich panels with a stainless steel core comprising hollow struts. The core topology comprises either vertical tubes or inclined tubes in a pyramidal arrangement. The dependence of the elastic and plastic buckling modes upon core geometry is determined, and optimal geometric designs are obtained as a function of core density. For the hollow pyramidal core, strength depends primarily upon the relative density ρ̄ of the core with a weak dependence upon tube slenderness. At ρ̄ below about 3%, the tubes of the pyramidal core buckle plastically and the peak shear strength scales linearly with ρ̄. In contrast, at ρ̄ above 3%, the tubes do not buckle and a stable shear response is observed. The predictions of the current study are in excellent agreement with previous measurements on the shear strength of the hollow pyramidal core, and suggest that this core topology is attractive from the perspectives of both core strength and energy absorption. © 2011 Elsevier Ltd. All rights reserved.

Modelling of liquefaction-induced instability in pile

Centrifuge testing has been undertaken to investigate instability failure of pile groups during seismic liquefaction, with specific reference to the 'top-down' propagation of liquefaction during the earthquake and to account for initial imperfections in pile geometry. The results of these tests were used to validate numerical models within the finite element program ABAQUS, based on the popular p-y analysis method. Pseudostatic classical and post-buckling analyses were conducted to examine the collapse behaviour of the pile groups and were found to give reasonable predictions of collapse load and conservative predictions of the associated deflection conditions. This numerical model was compared to currently published methods which were found to over-predict collapse loads. The resulting insights into the collapse of axially loaded pile groups revealed that the failure load is strongly dependent on both the depth of liquefaction propagation and initial imperfections, which reduce the collapse load.