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Materials

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

[+] Author and Article Information
Ralf Peek

Shell International Exploration and Production, B. V. Rijswijk, The Netherlands 2288 GS

Heedo Yun

Shell International Exploration and Production, Inc., Houston, TX 77079

J. Offshore Mech. Arct. Eng 131(3), 031401 (May 28, 2009) (9 pages) doi:10.1115/1.3058689 History: Received July 11, 2007; Revised August 27, 2008; Published May 28, 2009

## Abstract

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.

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## Figures

Figure 7

Example results: lateral displacement v at the apex of the buckle

Figure 8

Example results: bending strain at the apex of the buckle

Figure 2

Normalized moment-curvature relationship for elastic-perfectly plastic pipe

Figure 3

Deformed shapes from FE reference solution of the laterally buckled pipe for [g]nd=0.252 (first yield), and [g]nd=0.771 (when maximum bending strain is ten times the yield strain)

Figure 5

Nondimensional moment [M]nd and curvature [K]nd at the apex of the lateral buckle

Figure 6

Nondimensional lateral displacement at the apex of a buckle [v]nd as a function of nondimensional geometric shortening [g]nd

Figure 4

Normalized axial compressive force [N]nd as a function of the normalized geometric shortening [g]nd

Figure 9

Example results from the scaling theory: geometric shortening g; g0 represents the amount of expansion that would need to be accommodated geometrically if the axial force in the buckle dropped to zero

Figure 1

Illustration of the combination of the solution for the axial slip region with lateral buckling region

## Errata

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