Ralf Peek

Wrinkling of tubes in bending from finite strain three-dimensional continuum theory

Abstract The problem of a tube under pure bending is first solved as a generalised plane strain problem. This then provides the prebifurcation solution, which is uniform along the length of the tube. The onset of wrinkling is then predicted by introducing buckling modes involving a sinusoidal variation of the displacements along the length of the tube. Both the prebuckling analysis and the bifurcation check require only a two-dimensional finite element discretisation of the cross-section with special elements. The formulation does not rely on any of the approximations of a shell theory, or small strains. The same elements can be used for pure bending and local buckling a prismatic beam of arbitrary cross-section. Here the flow theory of plasticity with isotropic hardening is used for the prebuckling solution, but the bifurcation check is based on the incremental moduli of a finite strain deformation theory of plasticity. For tubes under pure bending, the results for limit point collapse (due to ovalisation) and bifurcation buckling (wrinkling) are compared to existing analysis and test results, to see whether removing the approximations of a shell theory and small strains (used in the existing analyses) leads to a better prediction of the experimental results. The small strain analysis results depend on whether the true or nominal stress–strain curve is used. By comparing small and finite strain analysis results it is found that the small strain approximation is good if one uses (a) the nominal stress–strain curve in compression to predict bifurcation buckling (wrinkling), and (b) the true stress–strain curve to calculate the limit point collapse curvature. In regard to the shell theory approximations, it is found that the three-dimensional continuum theory predicts slightly shorter critical wrinkling wavelengths, especially for lower diameter-to-wall-thickness ( D / t ) ratios. However this difference is not sufficient to account for the significantly lower wavelengths observed in the tests.

Postbuckling analysis and imperfection sensitivity of general shells by the finite element method

Abstract Buckling and imperfection sensitivity are the primary considerations in analysis and design of thin shell structures. The objective here is to develop accurate and efficient capabilities to predict the postbuckling behavior of shells, including imperfection sensitivity. The approach used is based on the Lyapunov–Schmidt–Koiter (LSK) decomposition and asymptotic expansion in conjunction with the finite element method. This LSK formulation for shells is derived and implemented in a finite element code. The method is applied to cylindrical and spherical shells. Cases of linear and nonlinear prebuckling behavior, coincident as well as non-coincident buckling modes, and modal interactions are studied. The results from the asymptotic analysis are compared to exact solutions obtained by numerically tracking the bifurcated equilibrium branches. The accuracy of the LSK asymptotic technique, its range of validity, and its limitations are illustrated.

An incrementally continuous deformation theory of plasticity with unloading

For predictions of plastic buckling, and especially postbuckling behaviour and imperfection sensitivity it is desirable to have a plasticity theory that combines some of the desired characteristics of both the flow and deformation theories of plasticity. For this purpose a way to include unloading within a deformation theory of plasticity is given that preserves the incremental continuity of the resulting constitutive equations. This can only be achieved by allowing plastic deformations to occur within the yield surface. Such plastic deformations are controlled by a parameter m, which describes how rapidly the possibility of such plastic deformations disappears as the stress state moves away from the yield surface. A finite strain version of the formulation is given. The approach can be implemented with minimal changes to an elastic predictor – radial return algorithm for the flow theory of plasticity, by changing the elastic predictor phase only. For tests involving thick-walled (D/t≈10) cylinders with known axisymmetric imperfections under axial compression, this new deformation theory overpredicted the concertina wrinkling type deformations for a given amount of applied axial shortening, whereas the flow theory underpredicted these wrinkling deformations in some cases.

Penguins Flowline Lateral Buckle Formation Analysis and Verification

The Penguins pipeline is a 60 km PIP system designed to buckle laterally on the seabed. The pipeline has been laid in a snaked shape in order to initiate regular lateral buckles. However there is significant uncertainty over the buckle formation process and concern over the robustness of the snake lay approach. A detailed as-laid ROV survey was undertaken to define the geometry of the pipeline system. This has been supplemented by two high precision ROV surveys of the pipeline in the operating configuration. This paper outlines how the buckling uncertainty was addressed at the design stage, the as-laid stage, and finally compares the predictions with the actual observations of lateral buckles in the operating flowline.Copyright

Zero-Radius Bend Method to Trigger Lateral Buckles

By deliberately triggering lateral buckles in a subsea pipeline at a sufficiently low axial load, one can ensure that the distance between lateral buckles is sufficiently small, so that the thermal expansion to be absorbed by each buckle is not excessive. A method of triggering such buckles by a zero-radius bend (ZRB) on a trigger that elevates the pipeline above the seabed is described. This method is more effective than other methods that have been proposed and/or used. The use of triggers designed to work only in the vertical direction by laying the line over a linear support aligned at 90° to the pipeline route, is already known. For the ZRB method, a post is added at one side of the trigger to prevent the pipe of being pulled off the trigger on that side. Once the pipe is firmly seated on the trigger, but not yet touching down onto the seabed on the downlay side of the trigger, the laybarge moves laterally without paying out more pipe, thereby pulling the pipe against the post on the trigger, i.e., the movement of the laybarge is as if it was laying a bend of zero radius, but because of the stiffness of the pipe the radius of curvature remains finite and can be kept well within the elastic range. This paper describes the method, a simple approximate analysis method used to assess the performance of the approach and the pipe stresses due to pulling the pipe around the post, and experiences from application of this method.

Scaling of Solutions for the Lateral Buckling of Elastic-Plastic Pipelines

Analytical solutions for the lateral buckling of pipelines exist for the case when the pipe material remains in the linearly elastic range. However for truly high temperatures and/or heavier flowlines, plastic deformation cannot be excluded. One then has to resort to finite element analyses, as no analytical solutions are available. This paper does not provide such an analytical solution, but it does show that if the finite element solution has been calculated once, then that solution can be scaled so that it applies for any other values of the design parameters. Thus the finite element solution need only be calculated once and for all. Thereafter, other solutions can be calculated by scaling the finite element solution using simple analytical formulas. However, the shape of the moment-curvature relation must not change. That is, the moment-curvature relation must be a scaled version of the moment-curvature relation for the reference problem, where different scale factors may be applied to the moment and curvature. This paper goes beyond standard dimensional analysis (as justified by the Bucklingham II theorem), to establish a stronger scalability result, and uses it to develop simple formulas for the lateral buckling of any pipeline made of elastic-plastic material. The paper includes the derivation of the scaling result, the application procedure, the reference solution for an elastic-perfectly plastic pipe, and an example to illustrate how this reference solution can be used to calculate the lateral buckling response for any elastic-perfectly plastic pipe.

HotPipe JI Project: Experimental Test and FE Analyses

In the last twenty years, experimental tests and FEM-based theoretical studies have been carried out to investigate the buckling mechanisms of thin-walled pipes subject to internal pressure, axial force and bending moment. Unfortunately, these studies do not completely cover the scope relevant for offshore pipelines i.e. outer diameter to thickness ratio lower than 50. In the HotPipe Phase 2 JI Project, full-scale bending tests were performed on pressurized pipes to verify the Finite Element Model predictions from HotPipe Phase 1 of the beneficial effect of internal pressure on the capacity of pipes to undergo large plastic bending deformations without developing local buckling. A total of 4 pipes were tested, the key test parameters being the outer-diameter-to-wall-thickness ratio (seameless pipes with D/t = 25.6, and welded UOE pipes with D/t = 34.2), and the presence of a girth weld in the test section. For comparison a Finite Element Model was developed with shell elements in ABAQUS. The test conditions were matched as closely as possible: this includes the test configuration, the stress-strain curves (i.e. using measured curves as input), and the loading history. The FE results very realistically reproduce the observed failure mechanisms by formation and localization of wrinkles on the compression side of the pipe. Good agreement is also achieved in the moment capacities (with predictions only 2.5 to 8% above measured values), but larger differences arose for the deformation capacity, suggesting that the DNV OS-F101 formulation for the characteristic bending strain (which is based on FE predictions from HotPipe Phase I) may be non-conservative in certain cases.Copyright

Loading History Effects for Deepwater S-Lay of Pipelines

For economic reasons S-Lay is often preferred to J-Lay. However in very deep water S-Lay requires a high curvature of the stinger to achieve the required close-to-vertical departure angle. This can lead to plastic deformations of the pipe. The high top tension increases the plastic deformations in two ways: firstly it adds an overall tensile component to the strains, thereby increasing the strains at the 12 o’clock position. Secondly it increases the strain concentrations which arise due to discontinuous support of the pipe on the stinger. Typically the pipe is guided over a series of roller beds. The high top tension tends to straighten the spans between the roller beds. To accommodate this (so that the pipe can still follow the stinger), higher curvatures are required at the roller beds. Analytical and numerical solutions are provided to quantify this effect. The analytical solution is fully developed for an elastic-perfectly-plastic pipe, but can also be applied for other material models provided that: (i) the moment-curvature relation for the pipe under tension is known, and (ii) no cyclic plastic ratchetting occurs due to repeated bending of the pipe over the roller beds and straightening in the spans between roller beds. Agreement between the analytical and numerical (finite element) results is excellent, if the proper loading history is used in the numerical simulation. Otherwise the level of strain concentration can be overpredicted.Copyright

Pipe-Clamping Mattress to Stop Flowline Walking

Thermal gradients from a heating front travelling down a flowline at start-up can cause a flowline to walk much like a worm creeps by repeated contractions and expansions of its body. To stop this for the Malampaya flowline, pipe-clamping mattresses (PCMs) were invented, developed, and deployed within a period of 12 months. The objective of this paper is to share the knowledge and experience from this novel but effective solution to mitigate pipeline walking. PCMs provide a cost-effective alternative to rockdump or conventional mattresses to axially restrain a pipeline at a location chosen so that the required restraint capacity is minimized. They are inspired by conventional mattresses and bear some similarity to them, but they are designed so that the weight of the mattress acts to clamp the pipeline with a high leverage. Thus 100% of the weight of the mattress is effective in generating axial friction with the seabed. This solution can be applied at any point along the line (chosen to minimize the required resistance) without requiring flanges or collars on the pipeline. From the most recent survey results 15 PCMs with a dry weight of around 9 tons per PCM, plus 7 tons for the logmat installed over every PCM appear to be effective to stop the walking of the Malampaya flowline. This performance is as expected from extensive analysis (FE and otherwise) to reproduce the observed walking behavior prior to restraining, to estimate the required restraint capacity, and to estimate the resistance provided by the PCMs. This paper describes the PCM, the clamping forces they generate by leveraging the weight of the PCM and logmats installed over them, and how the friction generated with the soil is estimated from interface shear tests on samples collected from the site, considering cyclic pore pressure generation and dissipation effects. It also briefly covers FE analyses to reproduce the observed walking behavior, and determine the required restraint capacity, the PCM fabrication, installation, and monitoring of the post-installation performance.

Thermal Expansion by Lateral Buckling: Structural Reliability Analysis for the Penguins Flowline

The Penguins pipeline is a 60 km PIP system designed to buckle laterally on the seabed. This is an effective way to accommodate thermal expansion. However excessive bending could lead to local buckling or wrinkling of the pipe wall. Existing design criteria based on load-controlled or displacement-controlled conditions are not directly applicable here, because the actual conditions fall somewhere in between. For this reason a structural reliability analysis has been performed for the Penguins flowline, to demonstrate that it is safe to allow the flowline to buckle laterally. Thereby the uncertainties that can affect the peak bending moments and curvatures at the buckles are addressed explicitly i.e. one does not rely on an assumption of load- or displacement control. This paper describes how describes how the various uncertainties are combined to assess the structural reliability. Details of the various inputs, including full-scale tests and finite element analyses addressing both global response and local buckling or wrinkling to develop the capacity and response functions are reported in a companion paper.Copyright