Loading History Effects for Deepwater S-Lay of Pipelines

2003 ◽  
Author(s):  
Heedo D. Yun ◽  
Ralf R. Peek ◽  
Paul P. Paslay ◽  
Frans F. Kopp
Keyword(s):  
Numerical Solutions ◽  
Loading History ◽  
Material Models ◽  
Plastic Deformations ◽  
Perfectly Plastic ◽  
History Effects ◽  
Departure Angle ◽  
Numerical Finite Element ◽  
Elastic Perfectly Plastic ◽  
The Moment

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.

Loading History Effects for Deep-Water S-Lay of Pipelines

2004 ◽  
Vol 126 (2) ◽  
pp. 156-163 ◽  
Author(s):  
Heedo D. Yun ◽  
Ralf R. Peek ◽  
Paul R. Paslay ◽  
Frans F. Kopp
Keyword(s):  
Deep Water ◽  
Numerical Solutions ◽  
Pipe Material ◽  
Loading History ◽  
Material Models ◽  
Plastic Deformations ◽  
History Effects ◽  
Departure Angle ◽  
Numerical Finite Element ◽  
The Moment

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 (or a large, low curvature stinger). Choosing the high curvature stinger 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 rollerbeds. To accommodate this (so that the pipe can still follow the stinger), higher curvatures occur at the roller beds. Analytical and numerical solutions are provided to quantify this effect. The analytical solution is fully developed for an arbitrary pipe 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. Proper loading history must be used in the numerical simulation, otherwise the level of strain concentration can be overpredicted.

The Elastic-Softening Failure of Floating Beams

1988 ◽  
Vol 32 (01) ◽  
pp. 37-43
Author(s):  
Paul C. Xirouchakis
Keyword(s):  
Carrying Capacity ◽  
Maximum Load ◽  
Point Load ◽  
Negative Stiffness ◽  
Load Carrying Capacity ◽  
Perfectly Plastic ◽  
Load Carrying ◽  
Elastic Perfectly Plastic ◽  
The Moment ◽  
Elastic Softening

The solution is presented for an infinite elastic-softening floating beam under a point load. The response depends on two nondimensional parameters: the negative stiffness coefficient that characterizes the descending part of the moment-curvature curve, and the nondimensional softening region half-length. The solution exhibits two important features that the elastic-perfectly plastic solution does not show. First, in certain ranges of parameters, the elastic-softening beam has a clearly defined maximum load carrying capacity. Second, in some other ranges of parameters, the elastic-softening beam has a minimum load or residual strength. The beam stiffens up upon further deformation due to the reactions of the water foundation. Critical softening parameters are calculated that separate stable from unstable behavior.

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

2009 ◽  
Vol 131 (3) ◽  
Author(s):  
Ralf Peek ◽  
Heedo Yun
Keyword(s):  
Finite Element ◽  
Analytical Solutions ◽  
Finite Element Solution ◽  
Reference Solution ◽  
Element Solution ◽  
Lateral Buckling ◽  
Elastic Plastic ◽  
Perfectly Plastic ◽  
Elastic Perfectly Plastic ◽  
The Moment

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 Π 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.

Analysis on the Moment-Curvature Relationship for Prestressed UHPFRC Beams without Stirrup

2011 ◽  
Vol 255-260 ◽  
pp. 236-240
Author(s):  
Sang Mook Han ◽  
Qing Yong Guo
Keyword(s):  
Experimental Data ◽  
Tensile Strength ◽  
Steel Fibre ◽  
Fibre Reinforcement ◽  
Cracking Behavior ◽  
Perfectly Plastic ◽  
History Of ◽  
Elastic Perfectly Plastic ◽  
The Moment ◽  
Good Agreement

To simplify the analysis, an elastic perfectly plastic stress-strain law was presented for UHPFRC. The post-cracking behavior was described by the average constant post-crack tensile strength. A strain parameter μ is proposed to evaluate the performance and efficiency of steel fibre reinforcement. 8 rectangular beams were tested in this investigation. Based on the proposed constitutive model, the full history of their flexural moment-curvature relationship for UHPFRC beams was calculated and compared with experimental data on prestressed UHPFRC beams. Good agreement between calculated strengths and experimental data was obtained.

scholarly journals KUHN-TUCKER CONDITIONS IN SHAKEDOWN PROBLEMS

1996 ◽  
Vol 2 (5) ◽  
pp. 14-28
Author(s):  
Juozas Atkočiūnas
Keyword(s):  
Cyclic Loading ◽  
Mathematical Programming ◽  
Safety Factor ◽  
Strain Field ◽  
Analysis Problem ◽  
Cyclic Plastic ◽  
Perfectly Plastic ◽  
History Of ◽  
Elastic Perfectly Plastic ◽  
The Moment

An elastic perfectly plastic structure at shakedown to given cyclić loading is under consideration. The stress-strain field of dissipative system in general is related to the history of loading. And only in a particular case, i.e. at the moment prior to the failure of an elastic perfectly plastic structure the distribution of the actual residual forces is unique for each prescribed history of loading (the safety factor of shakedown approaches unity). Nevertheless, there exist some domains where the plastic strains are equal to zero. The residual forces in the statically indeterminate parts of the structure may be non-unique: the stress field is only determined by the equilibrium equations. The extremum energy principle of minimum complementary energy allows to derive the actual residual forces out of all statically admissible residual forces at the moment prior to cyclic plastic failure. Then the stress-strain field analysis problem at the moment prior to the cyclic plastic failure is formulated as a problem of non-linear mathematical programming. Formulating the dual pair of non-linear programming problem (statical and kinematic formulation of analysis problem) the differential constraints are neglected or replaced by algebraic conditions. When the safety factor is approching a unity, the degeneracy of the statical formulation of the analysis problem often can occur. In this case a mathematical model is proposed for obtaining an upper bounds for the displacement at shakedown. It is pointed out that the known Kuhn-Tucker conditions of mathematical programming theory (i.e. compatibility equations of residual strains) in concert with restriction, limiting the maximum value of total energy dissipation, make up the adaptation conditions of the structure to given cyclic loading. Kuhn-Tucker conditions used in above—mentioned problem allow to correctly interprete the physical aspect of the degeneracy problem at shakedown. When the safety factor is larger than unity an artificial degeneracy situation for the statical formulation of analysis problem can be created. Then the mathematical models presented can be applied to the analysis of unloading elastoplastic structures. With this aim in view a fictitious equiplastic structure the behaviour of which is holonomic is derived. The displacements of the fictitious structure enclose the displacements of the actual structure subject to cyclic loading.

Evaluating Plastic Loads in Torispherical Heads Using a New Criterion of Collapse

2006 ◽  
Author(s):  
Duncan Camilleri ◽  
Donald Mackenzie ◽  
Robert Hamilton
Keyword(s):  
Pressure Vessels ◽  
Plastic Collapse ◽  
Total Work ◽  
Medium Thickness ◽  
Material Models ◽  
Hardening Material ◽  
Perfectly Plastic ◽  
Inelastic Analysis ◽  
Elastic Perfectly Plastic ◽  
New Criterion

In ASME Design by Analysis, the plastic load of pressure vessels is established using the Twice Elastic Slope criterion of plastic collapse. This is based on a characteristic load-deformation plot obtained by inelastic analysis. This study investigates an alternative plastic criteria based on plastic work dissipation where the ratio of plastic to total work is monitored. Two sample analyses of medium thickness torispherical pressure vessels are presented. Elastic-perfectly plastic and strain hardening material models are considered in both small and large deformation analyses. The calculated plastic loads are assessed in comparison with experimental results from the literature.

Dynamic Expansion of a Spherical Cavity in an Elastic, Perfectly Plastic Material

1968 ◽  
Vol 35 (2) ◽  
pp. 372-378 ◽  
Author(s):  
Chi-Hung Mok
Keyword(s):  
Spherical Cavity ◽  
High Speed ◽  
Numerical Solutions ◽  
Plastic Material ◽  
Numerical Technique ◽  
Nonlinear Dependence ◽  
Static Approximation ◽  
Elastic Plastic ◽  
Perfectly Plastic ◽  
Elastic Perfectly Plastic

It is shown that initial and boundary-value problems involving high-speed elastic-plastic deformation with spherical symmetry can be solved using a finite-difference numerical technique. Numerical solutions for the dynamic expansion of a spherical cavity under a constant pressure are presented to demonstrate the nature and capability of the numerical scheme. While the solution for an elastic material agrees closely with the exact one, the solution for an elastic, perfectly plastic material also receives support from Green’s analytic predictions concerning the motion of the elastic-plastic boundary. At large times, the asymptotic solution of the dynamic elastic-plastic problem is different from the quasi-static solution. This result indicates that the concept of quasi-static approximation may not hold in dynamic plasticity. A nonlinear dependence of the plastic solution on the boundary condition is also observed.

Plastic Strain Concentrations in Ligaments

1977 ◽  
Vol 99 (2) ◽  
pp. 328-336 ◽  
Author(s):  
J. S. Porowski ◽  
W. J. O’Donnell
Keyword(s):  
Plastic Strain ◽  
Numerical Solutions ◽  
Pure Shear ◽  
Solid Material ◽  
Shear Loading ◽  
Plastic Strains ◽  
Perfectly Plastic ◽  
Circular Holes ◽  
Elastic Perfectly Plastic ◽  
Conservative Values

The sheet perforated with a uniform array of circular holes arranged in a square pattern is investigated. The plastic strains are derived for progressive in-plane loading which eventually results in gross yielding. The finite element method is used to obtain numerical solutions. Plane stress conditions and elastic perfectly plastic solid material properties are assumed. Thus the results provide conservative values of plastic strain concentrations for a considerable range of perforated materials. The plastic strain multipliers for equibiaxial and pure shear loading are given for three ligament efficiencies of the penetration pattern. The tendency of forming highly localized plastic strains with progressive yielding is observed, and the implications of the results in plastic design are discussed.

scholarly journals Descriptions of reversed yielding in bending

2007 ◽  
Vol 221 (9) ◽  
pp. 981-991 ◽  
Author(s):  
D W A Rees
Keyword(s):  
Bauschinger Effect ◽  
Neutral Axis ◽  
Strain Response ◽  
Stress Distributions ◽  
Material Models ◽  
Hardening Material ◽  
Perfectly Plastic ◽  
Beam Curvature ◽  
Beam Section ◽  
The Moment

Existence of Bauschinger effect in bending-unbending of copper beams has been shown from experiment. In modelling of the Bauschinger effect, it is shown that a significant second plastic penetration can occur with the release of the moment required for an elasticplastic bending of a beam. The theory is given for both linear and parabolic hardening material models. The elastic and plastic strains are developed from each hardening model to express the beam curvature of the unstressed neutral axis. Conditions are expressed, using the normalized stress—strain response of a rectangular beam section, for which the release is purely elastic and elastic—plastic. Under the latter the depth to which a second zone of plasticity penetrates is given. Two stress distributions: one for applying the moment and the other for its release, are sufficient to derive the residual stress. Residuals found for parabolic hardening are believed to be more realistic than those from simpler linear or perfectly plastic models, particularly, where a second penetration is evident.

Experiment and FEM Simulation on Residual Stress of Cold Expansion Hole

2007 ◽  
Vol 561-565 ◽  
pp. 1783-1786 ◽  
Author(s):  
Xiao Jun Shao ◽  
Jun Liu ◽  
Yong Shou Liu ◽  
Zhu Feng Yue
Keyword(s):  
Residual Stress ◽  
Plastic Material ◽  
Fem Simulation ◽  
Stress Fields ◽  
Material Models ◽  
Hardening Material ◽  
Cold Expansion ◽  
Perfectly Plastic ◽  
Elastic Perfectly Plastic ◽  
Cold Expansion Hole

A 2D cylindrical plate model has been established to study the distribution of residual stress of cold expansion hole under different interference values. In addition, the effects of material models on residual stress fields are considered also. Experiments are carried out to measure the residual stress of cold expansion hole and verify simulation results. FEM results show, with interference values increasing, the higher residual radial and circumferential stresses are obtained. At same interference value, the residual stress of Hardening Material( HM ) model is much larger than that of Elastic Perfectly Plastic Material( EPPM ) model.

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