Onset and Post Buckling of Pipe-in-Pipe’s Helical Buckling Using Improved Energy Method

2018 ◽  
Author(s):  
Lixin Gong
Keyword(s):  
Potential Energy ◽  
Energy Method ◽  
Normal Force ◽  
Horizontal Wells ◽  
Energy Methods ◽  
Buckling Mode ◽  
Buckling Behavior ◽  
Post Buckling ◽  
Helical Buckling ◽  
Remarkable Agreement

The purpose of this paper is to present theoretical solutions based on an improved energy method for predicting the helical buckling (HB) behavior of pipes in vertical, inclined, and horizontal wells. The energy method has been applied to solve the pipe-in-pipe’s (PIP) helical buckling behavior since Lubinski, et al [2] in the 1950’s. However, in the preceding studies, the energy methods are not yet completely correct because the pipe’s potential energy of the distributed contact normal force induced by the helical buckling was considered to be negligible. This deficiency caused improper deductive procedures. In this paper, the energy method is improved by adding the term of the potential energy of the distributed contact normal force. With this improvement, not only can the PIP’s critical helical buckling forces be successfully derived, but it also provides a deeper insight on the PIP’s helical buckling onset, as well as the post helical buckling behavior. For inclined and horizontal wells, equations are provided to determine the critical forces required to initiate the helical buckling mode for both “long” and “short” pipes. In addition, the post buckling behavior is also described, and a new concept of helical buckling zone (HBZ) for “short” pipes is introduced based on the force-pitch plots as an area in-between the helical buckling’s onset curve and the classical Lubinski curve. Finite element ABAQUS models have also been utilized to confirm the analysis using the improved energy method. And the ABAQUS results show remarkable agreement with the theoretical solutions.

Stability of the neutral equilibrium of columns with a rotational end restraint by the generalized Fourier series

2019 ◽  
Vol 25 (4) ◽  
pp. 961-967
Author(s):  
Yan-Ping Zhao ◽  
Lin Li ◽  
Ming Jin
Keyword(s):  
Fourier Series ◽  
Potential Energy ◽  
Energy Functional ◽  
Buckling Mode ◽  
Generalized Fourier Series ◽  
Order Variation ◽  
Neutral Equilibrium ◽  
Post Buckling ◽  
The Stability ◽  
End Restraint

In this paper, stability of the neutral equilibrium and initial post-buckling of a column with a rotational end restraint is analyzed based on Koiter initial post-buckling theory. The potential energy functional is written in terms of the angle. By the generalized Fourier series of the disturbance angle, it is proved that the second-order variation of the potential energy is semi-positive definite at the neutral equilibrium. The stability of the neutral equilibrium is determined by the sign of the fourth-order variation for the buckling mode. For all values of the stiffness of the rotational end restraint, the neutral equilibrium is stable and the bifurcation equilibrium is upward in the initial post-buckling.

Effects of Friction on Post-Buckling Behavior and Axial Load Transfer in a Horizontal Well

SPE Journal ◽  
2010 ◽  
Vol 15 (04) ◽  
pp. 1104-1118 ◽  
Author(s):  
Guohua Gao ◽  
Stefan Miska
Keyword(s):  
Boundary Conditions ◽  
Critical Load ◽  
Axial Load ◽  
Load Transfer ◽  
Experimental Studies ◽  
Proper Solution ◽  
Buckling Behavior ◽  
Post Buckling ◽  
Helical Buckling ◽  
Lateral Friction

Summary In this paper, the buckling equation and natural boundary conditions are derived with the aid of calculus of variations. The natural and geometric boundary conditions are used to determine the proper solution that represents the post-buckling configuration. Effects of friction and boundary conditions on the critical load of helical buckling are investigated. Theoretical results show that the effect of boundary conditions on helical buckling becomes negligible for a long pipe with dimensionless length greater than 5π Velocity analysis shows that lateral friction becomes dominant at the instant of buckling initiation. Thus, friction can increase the critical load of helical buckling significantly. However, once buckling is initiated, axial velocity becomes dominant again and lateral friction becomes negligible for post-buckling behavior and axial-load-transfer analysis. Consequently, it is possible to seek an analytical solution for the buckling equation. Analytical solutions for both sinusoidal and helical post-buckling configurations are derived, and a practical procedure for modeling of axial load transfer is proposed. To verify the proposed model and analytical results, the authors also conducted experimental studies. Experimental results support the proposed solutions.

LOCAL/DISTORTIONAL/GLOBAL MODE INTERACTION IN SIMPLY SUPPORTED COLD-FORMED STEEL LIPPED CHANNEL COLUMNS

2011 ◽  
Vol 11 (05) ◽  
pp. 877-902 ◽  
Author(s):  
P. B. DINIS ◽  
D. CAMOTIM
Keyword(s):  
Shell Element ◽  
Mode Interaction ◽  
Buckling Mode ◽  
Global Mode ◽  
Simply Supported ◽  
Elastic Plastic ◽  
Buckling Behavior ◽  
Geometrical Imperfections ◽  
Post Buckling ◽  
Cold Formed Steel

This paper reports the results of a numerical investigation concerning the elastic and elastic-plastic post-buckling behavior of cold-formed steel-lipped channel columns affected by local/distortional/global (flexural-torsional) buckling mode interaction. The results presented and discussed are obtained by means of analyses performed in the code ABAQUS and adopting column discretizations into fine four-node isoparametric shell element meshes. The columns analysed (i) are simply supported (locally/globally pinned end sections with free warping), (ii) have cross-section dimensions and lengths ensuring equal local, distortional, and global (flexural-torsional) critical buckling loads, thus maximizing the mode interaction phenomenon under scrutiny, and (iii) contain critical-mode initial geometrical imperfections exhibiting different configurations, all corresponding to linear combination of the three "competing" critical buckling modes. After briefly addressing the lipped channel column "pure" global post-buckling behavior, one presents and discusses in detail numerical results concerning the post-buckling behavior of similar columns experiencing strong local/distortional/global mode interaction effects. These results consist of (i) elastic (mostly) and elastic-plastic equilibrium paths, (ii) curves and figures providing the evolution of the deformed configurations of several columns (expressed as linear combinations of their local, distortional, and global components) and, for the elastic-plastic columns, (iii) figures enabling a clear visualization of (iii1) the location and growth of the plastic strains, and (iii2) the characteristics of the failure mechanisms more often detected in this work.

scholarly journals Numerical Simulation of Buckling and Post-Buckling Behavior of a Central Notched Thin Aluminum Foil with Nonlinearity in Consideration

Metals ◽  
2020 ◽  
Vol 10 (5) ◽  
pp. 582 ◽  
Author(s):  
Mahdieh Shahmardani ◽  
Per Ståhle ◽  
Md Shafiqul Islam ◽  
Sharon Kao-Walter
Keyword(s):  
Mode Shape ◽  
Tensile Loading ◽  
Width Ratio ◽  
Plastic Behavior ◽  
Yield Limit ◽  
Buckling Mode ◽  
Buckling Stress ◽  
Buckling Behavior ◽  
Sheet Width ◽  
Post Buckling

In thin notched sheets under tensile loading, wrinkling appears on the sheet surface, specifically around the cracked area. This is due to local buckling and compression stresses near the crack surfaces. This study aims to numerically study the buckling behavior of a thin sheet with a central crack under tension. A numerical model of a notched sheet under tensile loading is developed using the finite element method, which considers both material and geometrical nonlinearity. To overcome the convergence problem caused by the small thickness-to-length/width ratio and to stimulate the buckling, an imperfection is defined as a small perturbation in the numerical model. Both elastic and elasto-plastic behavior are applied, and the influence of them is studied on the critical buckling stress and the post-buckling behavior of the notched sheet. Numerical results for both elastic and elasto-plastic behavior reflect that very small perturbations need more energy for the activation of buckling mode, and a higher buckling mode is predominant. The influences of different parameters, including Poisson’s ratio, yield limit, crack length-to-sheet-width ratio, and the sheet aspect ratio are also evaluated with a focus on the critical buckling stress and the buckling mode shape. With increase in Poisson’s ratio. First, the critical buckling stress reduces and then remains constant. A higher yield limit results in increases in the critical buckling stress, and no change in the buckling mode shape while adopting various crack length-to-sheet-width ratios, and the sheet aspect ratio changes the buckling mode shape.

Effects of symmetric imperfections on the behavior of bistable struts

2016 ◽  
Vol 22 (12) ◽  
pp. 2240-2252 ◽  
Author(s):  
Jianguo Cai ◽  
Xiaowei Deng ◽  
Jian Feng
Keyword(s):  
Virtual Work ◽  
Variable Geometry ◽  
Equilibrium Equations ◽  
Buckling Mode ◽  
Concentrated Load ◽  
Virtual Work Principle ◽  
Shallow Arches ◽  
Buckling Behavior ◽  
Nonlinear Equilibrium ◽  
Post Buckling

The behavior of a bistable strut for variable geometry structures was investigated in this paper. A three-hinged arch subjected to a central concentrated load was used to study the effect of symmetric imperfections on the behavior of the bistable strut. Based on a nonlinear strain–displacement relationship, the virtual work principle was adopted to establish both the pre-buckling and buckling nonlinear equilibrium equations for the symmetric snap-through buckling mode. Then the critical load for symmetric snap-through buckling was obtained. The results show that the axial force is in compression before the arch is buckled, but it becomes in tension after buckling. Thus, the previous formulas cannot be used for the analysis of post-buckling behavior of three-hinged shallow arches. Then, the principle of virtual work was also used to establish the post-buckling equilibrium equations of the arch in the horizontal and vertical directions as well as the static boundary conditions, which are very important for bistable struts.

Buckling Behavior of Elliptical Shells of Changing Thickness under Uniform Axial Compression

2013 ◽  
Vol 351-352 ◽  
pp. 492-496 ◽  
Author(s):  
Li Wan ◽  
Lei Chen
Keyword(s):  
Axial Compression ◽  
Cylindrical Shells ◽  
Imperfection Sensitivity ◽  
Buckling Mode ◽  
Buckling Strength ◽  
Shell Buckling ◽  
Buckling Behavior ◽  
Structural Applications ◽  
Post Buckling ◽  
Shell Geometry

Many elliptical shells are used in structural applications in which the dominant loading condition is axial compression. Due to the fact that the radius varies along the cross-section midline, the buckling behavior is more difficult to identify than those of cylindrical shells. The general concerned aspects in cylindrical shell buckling analyses such as the buckling mode, the pre-buckling deformation and post-buckling deformation are all quite different related to specific elliptical shell geometry. The buckling behavior of elliptical cylindrical shells with uniform thickness has been widely studied by many researchers. However, the thickness around the circumference may change for some specific structural forms, the femoral neck for example, which makes the buckling behavior more complex. It is known that the buckling strength of thin cylindrical shells is quite sensitive to imperfections, so it is natural to explore the imperfection sensitivity of elliptical shells. This paper explores the buckling behavior of imperfect elliptical shells under axial compression. It is hoped that the results will make a useful contribution in this field.

scholarly journals The Influence of the Layer Arrangement on the Distortional Post-Buckling Behavior of Open Section Beams

Materials ◽  
2020 ◽  
Vol 13 (13) ◽  
pp. 3002
Author(s):  
Tomasz Kubiak ◽  
Mariusz Urbaniak ◽  
Filip Kazmierczyk
Keyword(s):  
Cross Sections ◽  
Numerical Models ◽  
Experimental Tests ◽  
Distortional Buckling ◽  
Buckling Mode ◽  
Layer Arrangement ◽  
Reinforced Polymer ◽  
Glass Fiber Reinforced ◽  
Buckling Behavior ◽  
Post Buckling

The paper deals with the design of the stacking sequence of layers in the laminate beams with open-cross sections in order to create the desired behavior in the post-buckling range. Laminate beams with channel and lipped channel cross-sections made of glass fiber reinforced polymer (GFRP) laminate with different layer arrangements (symmetrical and nonsymmetrical) have been considered. In case of the nonsymmetrical stacking sequences, hygro-thermally curvature stable (HTCS) laminates have been taken into account. Pure bending was assumed as the type of load. In the case of beams with open cross-sections, this load type can cause the lateral-distortional buckling mode. A parametric study was performed to analyze the influence of layer arrangement on post-buckling behavior. The finite element method was used to developed numerical models and conduct simulations. Additionally, the experimental tests of the channel section beams were performed in order to validate the developed numerical models.

Combined Effects of Wellbore Curvature, Connector, and Friction Force on Tubular Buckling Behaviors

SPE Journal ◽  
2019 ◽  
Vol 24 (05) ◽  
pp. 2083-2096 ◽  
Author(s):  
Wenjun Huang ◽  
Deli Gao
Keyword(s):  
Potential Energy ◽  
Friction Force ◽  
Energy Method ◽  
Combined Effects ◽  
Mechanical Behaviors ◽  
Buckling Loads ◽  
New Model ◽  
Column Model ◽  
Helical Buckling ◽  
Relevant Factors

Summary A tubular buckling model is built, while considering the combined effects of wellbore curvature, tubular connector, and friction force. On the basis of certain assumptions, the expressions of critical helical–buckling loads are deduced with the equivalent beam–column model and energy method and the amendment factors of critical buckling loads because of relevant factors are obtained. The results from the new model are compared with those from previous models and experiments. The roles of relevant factors in tubular mechanical behaviors are discussed. It is indicated that wellbore curvature affects equivalent tubular–string weight, the connectors affect potential energy, and friction force leads to dissipative energy in the buckling–initiation process. Critical helical–buckling loads are most likely underestimated if the combined effects are not considered.

scholarly journals Stress, Strain-Rate Analysis of Sub-Surface Driveway Plants

2017 ◽  
Vol 6 (2) ◽  
pp. 55 ◽  
Author(s):  
Peter R. Greene ◽  
Virginia A. Greene
Keyword(s):  
Turgor Pressure ◽  
Maxwell Model ◽  
Taraxacum Officinale ◽  
Time Data ◽  
Buckling Mode ◽  
Rate Analysis ◽  
Buckling Behavior ◽  
Post Buckling ◽  
Surface Deflection ◽  
Plant Stem

Sub-surface driveway plants are strong enough to penetrate a macadam surface of thickness 7 – 9 cm. The mechanics of how the Taraxacum officinale accomplishes this feat remain a mystery. Using the Maxwell model for pavement yielding over time, data are presented which may shed some light on this phenomenon. The post-buckling behavior of the plant stalk is quantified. Euler bending and buckling theory enables calculation of the cellular stress field, compared to turgor pressure, indicating impending cell buckling. Post-buckling plastic strain of the plant stem is 19%. At the cell wall, the stress concentration factor is 3-times greater than the applied external field, so the cell’s internal turgor pressure is overwhelmed by imposed external stress. An Impulse Integral is developed for the surface whereby the product of applied FORCE times TIME is CONSTANT, in order to produce a given amount of surface deflection. Taraxacum officinale stems and leaf stalks are strong enough, in buckling mode, to lift and push apart the fractured macadam crater through which they erupt, but not strong enough to initially crack the surface. The purpose of this work is to determine the mechanisms underlying this unusual plant survival phenomenon, backed by quantified data.

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