Fracture in Wrinkled Linepipe Under Monotonic Loading

2002 ◽  
Author(s):  
Sreekanta Das ◽  
J. J. Roger Cheng ◽  
David W. Murray
Keyword(s):  
Boundary Conditions ◽  
Axial Load ◽  
Test Procedure ◽  
Fluid Pressure ◽  
Monotonic Loading ◽  
Load History ◽  
University Of Alberta ◽  
Pipe Segment ◽  
The One ◽  
Full Scale Tests

Buried pipelines may undergo large deformations due to geotechnical movements, temperature effects, and fluid pressure which result in axial loads, shear loads, moments and various complex combinations of these loads and load histories. Consequently, localized buckles and wrinkles may form in the pipe wall and, subsequently, fractures may develop at wrinkle locations. Previous research showed that large deformation due to monotonically applied symmetric loading can produce accordion type wrinkle geometry but fracture is not normally produced unless strain reversals at the wrinkle location occur due to the application of variable loads. Recently, a field fracture that developed in an NPS10 pipe was brought to University of Alberta Structures Laboratory for investigation. From the description of the load history at the failure location, and the inspection of the deformed geometry and fracture surface, it was recognized that no significant strain reversals had occurred in this particular wrinkled pipe segment. Examination implied that the final failure was a “tearing” failure resulting from monotonic application of a longitudinal load not aligned with the axis of the pipe. However, the true load history that caused the pipe to fracture at the wrinkle location was unknown. To verify the nature of the failure mechanism, and determine the characteristics contributing to its formation, it was felt necessary to attempt to reproduce similar failures in a wrinkle by subjecting it simultaneously to monotonically applied axial load and shear. Two full-scale tests applying axial load, and a shear load with different boundary conditions were carried out on NPS12 pipe. The second test produced a deformed geometry and a fracture configuration very similar to the one that developed in the field. This paper describes the test procedure for these two tests and the mechanics of the fracture. It is concluded that, with the appropriate load history and boundary conditions, fractures can be triggered at wrinkle locations by monotonic loading histories.

scholarly journals Laboratory Study of Local Buckling, Wrinkle Development, and Strains for NPS12 Linepipe

2000 ◽  
Author(s):  
Sreekanta Das ◽  
J. J. Roger Cheng ◽  
David W. Murray ◽  
S. A. Wilkie ◽  
Z. Joe Zhou
Keyword(s):  
Fluid Pressure ◽  
Local Buckling ◽  
Pipe Material ◽  
Axial Loads ◽  
Buried Pipelines ◽  
Test Procedures ◽  
Complex Load ◽  
University Of Alberta ◽  
Full Scale Tests ◽  
Internal Pressures

Buried pipelines are subjected to fluid pressure (oil/gas/water), axial loads, moments, and complex load combination histories. As a result, they may develop large compressive strains and curvatures leading to formation of localized buckles or wrinkles in the pipe shell. Recently, full-scale tests on 12.75″ diameter (NPS12) energy pipes have been carried out at the University of Alberta to study the behavior of wrinkle development and the ultimate limiting strains at the wrinkle locations. Different internal pressures, and axial loads were applied to produce a wrinkle, followed by load variations intended to produce fracture that could develop in buried pipelines in the field. Three different axially loaded tests are reported. Two different internal pressures were applied, namely, (i) 0.8py and (ii) 0.4py, where py is the required internal pressure to cause the yield stress of the pipe material to be developed in the circumferential direction. Also, two different specimen lengths were adopted. They are: (i) 406 mm (16 inch) and (ii) 736 mm (29 inch). All specimens were loaded axially until the wrinkle formed. It was observed that the pipes are highly ductile and very large compressive strains can be developed without fracture or leakage in the pipe wall. Because the pipe specimens of the first two tests did not fail (i.e. fracture) under monotonically increasing displacements and strains, the third wrinkled specimen was subjected to load histories involving strain reversals. This load history resulted in a low cycle failure after a very few cycles. The paper addresses test procedures, buckling and post-buckling behavior of NPS12 energy pipelines and relates them to three different types of strain measures, namely, material strain, wrinkle strain and overall strain as observed from these tests.

scholarly journals Electrically turning periodic structures in cholesteric layer with conical–planar boundary conditions

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Oxana Prishchepa ◽  
Mikhail Krakhalev ◽  
Vladimir Rudyak ◽  
Vitaly Sutormin ◽  
Victor Zyryanov
Keyword(s):  
Boundary Conditions ◽  
Periodic Structures ◽  
Cholesteric Liquid Crystal ◽  
Growth Direction ◽  
Smooth Transition ◽  
Defect Structures ◽  
Optical Cell ◽  
Elastic Continuum ◽  
The One ◽  
Experimental Findings

AbstractElectro-optical cell based on the cholesteric liquid crystal is studied with unique combination of the boundary conditions: conical anchoring on the one substrate and planar anchoring on another one. Periodic structures in cholesteric layer and their transformation under applied electric field are considered by polarizing optical microscopy, the experimental findings are supported by the data of the calculations performed using the extended Frank elastic continuum approach. Such structures are the set of alternating over- and under-twisted defect lines whose azimuthal director angles differ by $$180^\circ$$ 180 ∘ . The $$U^+$$ U + and $$U^-$$ U - -defects of periodicity, which are the smooth transition between the defect lines, are observed at the edge of electrode area. The growth direction of defect lines forming a diffraction grating can be controlled by applying a voltage in the range of $$0\le \, V \le 1.3$$ 0 ≤ V ≤ 1.3  V during the process. Resulting orientation and distance between the lines don’t change under voltage. However, at $$V>1.3$$ V > 1.3  V $$U^+$$ U + -defects move along the defect lines away from the electrode edges, and, finally, the grating lines collapse at the cell’s center. These results open a way for the use of such cholesteric material in applications with periodic defect structures where a periodicity, orientation, and configuration of defects should be adjusted.

scholarly journals An Inverse Source Problem for the Generalized Subdiffusion Equation with Nonclassical Boundary Conditions

2021 ◽  
Vol 5 (3) ◽  
pp. 63
Author(s):  
Emilia Bazhlekova
Keyword(s):  
Boundary Conditions ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Stability Estimates ◽  
Inverse Source Problem ◽  
Time Data ◽  
Final Time ◽  
Generalized Eigenfunction ◽  
The One ◽  
Initial Boundary Value

An initial-boundary-value problem is considered for the one-dimensional diffusion equation with a general convolutional derivative in time and nonclassical boundary conditions. We are concerned with the inverse source problem of recovery of a space-dependent source term from given final time data. Generalized eigenfunction expansions are used with respect to a biorthogonal pair of bases. Existence, uniqueness and stability estimates in Sobolev spaces are established.

Initial-boundary value problems for the one-dimensional linear advection–dispersion equation with decay

2020 ◽  
Vol 75 (8) ◽  
pp. 713-725 ◽  
Author(s):  
Guenbo Hwang
Keyword(s):  
Boundary Conditions ◽  
Dirichlet Boundary ◽  
Boundary Value ◽  
Initial Boundary ◽  
Initial Boundary Value Problems ◽  
One Dimensional ◽  
Advection Dispersion ◽  
Asymptotically Periodic ◽  
The One ◽  
Initial Boundary Value

AbstractInitial-boundary value problems for the one-dimensional linear advection–dispersion equation with decay (LAD) are studied by utilizing a unified method, known as the Fokas method. The method takes advantage of the spectral analysis of both parts of Lax pair and the global algebraic relation coupling all initial and boundary values. We present the explicit analytical solution of the LAD equation posed on the half line and a finite interval with general initial and boundary conditions. In addition, for the case of periodic boundary conditions, we show that the solution of the LAD equation is asymptotically t-periodic for large t if the Dirichlet boundary datum is periodic in t. Furthermore, it can be shown that if the Dirichlet boundary value is asymptotically periodic for large t, then so is the unknown Neumann boundary value, which is uniquely characterized in terms of the given asymptotically periodic Dirichlet boundary datum. The analytical predictions for large t are compared with numerical results showing the excellent agreement.

scholarly journals On a stochastic Burgers equation with Dirichlet boundary conditions

2003 ◽  
Vol 2003 (43) ◽  
pp. 2735-2746 ◽  
Author(s):  
Ekaterina T. Kolkovska
Keyword(s):  
Weak Solution ◽  
Boundary Conditions ◽  
Dirichlet Boundary ◽  
Burgers Equation ◽  
Martingale Problem ◽  
Weak Limit ◽  
Dirichlet Boundary Conditions ◽  
One Dimensional ◽  
Stochastic Burgers Equation ◽  
The One

We consider the one-dimensional Burgers equation perturbed by a white noise term with Dirichlet boundary conditions and a non-Lipschitz coefficient. We obtain existence of a weak solution proving tightness for a sequence of polygonal approximations for the equation and solving a martingale problem for the weak limit.

scholarly journals Order parameter profiles in a system with Neumann – Neumann boundary conditions

2018 ◽  
Vol 145 ◽  
pp. 01009 ◽  
Author(s):  
Vassil M. Vassilev ◽  
Daniel M. Dantchev ◽  
Peter A. Djondjorov
Keyword(s):  
Boundary Conditions ◽  
Order Parameter ◽  
Neumann Boundary ◽  
Elliptic Functions ◽  
Thermodynamic System ◽  
Neumann Boundary Conditions ◽  
Ginzburg Landau ◽  
One Dimensional ◽  
The One ◽  
Field Plane

In this article we consider a critical thermodynamic system with the shape of a thin film confined between two parallel planes. It is assumed that the state of the system at a given temperature and external ordering field is described by order-parameter profiles, which minimize the one-dimensional counterpart of the standard ϕ4 Ginzburg–Landau Hamiltonian and meet the so-called Neumann – Neumann boundary conditions. We give analytic representation of the extremals of this variational problem in terms ofWeierstrass elliptic functions. Then, depending on the temperature and ordering field we determine the minimizers and obtain the phase diagram in the temperature-field plane.

Analysis of caffeine action in single trabeculae of the frog heart

1981 ◽  
Vol 213 (1192) ◽  
pp. 303-324 ◽  
Keyword(s):  
Calcium Influx ◽  
Test Procedure ◽  
Frog Heart ◽  
Heart Cells ◽  
Store Depletion ◽  
Perfusion Chamber ◽  
Rapid Perfusion ◽  
The One ◽  
Intracellular Action ◽  
External Calcium

Effects of caffeine on contractile tension and on intracellular action and resting potentials were examined in single frog heart trabeculae suspended in a rapid perfusion chamber. Trabeculae from atria responded more readily than those from ventricles and were therefore studied in greater detail. Both the contracture and twitch responses, the one obtained at high (>10 mM), the other at low (<10mM) caffeine concentrations, consisted of a transient tension rise followed by a maintained phase of lower, but still enhanced, tension. The hypothesis was tested that the transient response is due to the release of calcium from the sarcoplasmic reticulum (s.r.), whereas the maintained tension results from enhanced calcium influx through the cell surface. Support for these ideas was obtained by examining the response to step changes of external calcium and caffeine concentrations, applied in various combinations, simultaneously and in sequence. It also emerged that the effects on twitch tension of calcium derived from (a) s.r. discharge and ( b) influx are additive, to a first approximation. A test procedure for monitoring the s.r. store content was evolved to follow the accumulation of s.r. calcium after a preceding depletion. The results obtained, and others, suggest that the s.r. calcium pump can be operative in atrial heart cells and capable, after store depletion, of reabsorbing up to some 40 % of calcium activating a twitch, the remainder being, presumably, extruded from the cells.

scholarly journals Flexural-Torsional Vibration of Thin-Walled Beams Subjected to Combined Initial Axial Load and End Bending Moment: Application to the Design of Saw Tooth Blades

2019 ◽  
Vol 2019 ◽  
pp. 1-11
Author(s):  
Van Binh Phung ◽  
Anh Tuan Nguyen ◽  
Hoang Minh Dang ◽  
Thanh-Phong Dao ◽  
V. N. Duc
Keyword(s):  
Boundary Conditions ◽  
Axial Load ◽  
Stability Boundary ◽  
Bending Moment ◽  
Element Analysis ◽  
The Finite Element Analysis ◽  
Rayleigh Method ◽  
Thin Walled ◽  
The Stability ◽  
Fixed End

The present paper analyzes the vibration issue of thin-walled beams under combined initial axial load and end moment in two cases with different boundary conditions, specifically the simply supported-end and the laterally fixed-end boundary conditions. The analytical expressions for the first natural frequencies of thin-walled beams were derived by two methods that are a method based on the existence of the roots theorem of differential equation systems and the Rayleigh method. In particular, the stability boundary of a beam can be determined directly from its first natural frequency expression. The analytical results are in good agreement with those from the finite element analysis software ANSYS Mechanical APDL. The research results obtained here are useful for those creating tooth blade designs of innovative frame saw machines.

scholarly journals Seismic deformation at the Alban Hills volcano during the 1989-1990 seismic sequence

1998 ◽  
Vol 41 (2) ◽  
Author(s):  
G. Selvaggi ◽  
F. D'Ajello Caracciolo
Keyword(s):  
Strain Rate ◽  
Fluid Pressure ◽  
Strain Rate Tensor ◽  
Seismic Structure ◽  
Fault Plane Solutions ◽  
Alban Hills ◽  
Shear Failures ◽  
One Year ◽  
The One ◽  
Seismic Moment Release

We analysed the one-year-long seismic swarm at the Alban Hills volcano which occurred during 1989-1990. We portray spatial distribution of seismic moment release, better delineating the activated volume during the swarm. The seismic structure is imaged as a 7-km long, 3-km wide, and 3-km thick volume, located between 2 and 5 km depth, and NW-SE striking. Fault plane solutions and scalar seismic moments for the largest earthquakes provide the description of the average strain rate tensor. The principal strain rate axes show a dominant extension in NE-SW direction, a SE-NW direction of compression and a negligible thickening rate. P and T axes direction of the smaller earthquakes suggests that the same mode of deformation is distributed all over the activated volume. These results are discussed in terms of seismic deforming processes active at the Alban Hills volcano, in the frame of magmatic inflation recently invoked to explain the rapid vertical uplift affecting part of the volcano. The observed average deformation is consistent with shear failures occurring on faults connecting stress-oriented dykes in response to an increasing fluid pressure.

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