# Analytical Investigation and Parametric study of Lateral Impact Behavior of Pressurized Pipelines and Influence of Internal Pressure

## Contents |

## Introduction

I have conducted a computational study to thoroughly investigate lateral impact behavior of pressurized pipelines and inspect effects of internal pressure and outside diameter of the pipelines on their impact responses. 72 impact simulations were carried out using 3D dynamic nonlinear finite element analysis (FEA) through LS-DYNA to predict the impact response of mild steel pipelines with different diameters and internal pressure levels, which subjected to lateral, struck at mid-span and one quarter span positions. The obtained computational results were verified by comparing with some published experimental results. Based on the results achieved from the preliminary analysis, one objective of this study is to employ numerical methods to establish analytical models to numerically show how the impact parameters (internal pressure and outside diameter) affect the impact response of the pipelines during low-speed lateral impact.

## Problem Description

In preliminary computer simulations, a rigid indenter impacted a number of pressurized pipelines at the mid-span position and the one quarter span position. The pressurized pipes were made from seamless cold drawn mild steel with outside diameters of 22, 42, 60, 80, 100, and 120 mm with a fixed ratio of 2L/D = 10, where 2L is the distance between the two supports and D is the outside diameter. The selected ratio of 2L/D = 10 is currently being used in most research laboratory and industry plant as the largest unsupported pipe length ratio ^{[1]}. The cold worked mild steel pipes have a 2mm wall thickness, and the mechanical properties in the axial direction of the pipe are: static uniaxial yield stress σy = 663 MPa, static ultimate tensile stress σu = 823 MPa, and static uniaxial rupture strain εr = 6 ~ 7%. In this study, the internal pressure p varies from 0 to 150 bar. Specifically, 6 different pressures, 0, 30, 60, 90, 120, 150 bar were applied on inner surface of the pipelines separately in order to achieve a complete understanding of how the internal pressure affects the lateral impact behavior of the pipelines.

In order to simulate those impact tests, 72 FEA models were created along with appropriate boundary, loading, and initial conditions. The generated FEA models include 1000 to more than 25,000 shell elements. Figs. 1 and 2 present two impact scenarios, where the indenter impacted a pipeline model with outside diameter of 60 mm and internal pressure of 60 bar at its center and one quarter span, respectively.

## Response Surface Method models and Assessment

As shown in Tables 1 and 2, six pressures and diameters were selected for modeling and simulation and totally 36 combinations were presented. Thus, the matrix Φ has 36 rows (m = 36), which corresponds to the 36 combinations of p and D (No. 1 to 36 in Tables 1 and 2). In this study, quartic polynomial is used as the basic function because it provides the best fitness to the real problems^{[2]}. Thus, the basic functions φi are terms in a full quartic form, which are 1, p, D, p*p, p*D, D*D, p*P*P, p*p*D, p*D*D, D*D*D, p*P*P*p, p*P*P*D, p*p*D*D, p*D*D*D, D*D*D*D. Substituting p and D values, a 36 × 15 matrix Φ then can be created.

## Parametric Studies

### Influence of Internal Pressure

In order to reveal the effects of internal pressure on the pipelines’ lateral impact response, as well as validate the accuracy of the developed response surface models, we substitute D = 22, 42, 60, 80, 100, and 120 into Eqns. (12-17) to obtain a series of simplified analytical models with the internal pressure p as the only variable. Curves are then plotted from those analytical models and compared with the results obtained from FEA simulations. (As displayed in Figs. 5 and 6)

### Influence of Outside Diameter

Similarly, in order to study the effects of outside diameter on the pipelines’ lateral impact response, p = 0, 30, 60, 90, 120, 150 are substituted into Eqns. (12-17) separately to create a series of analytical models with the outside diameter as the only variable. Those analytical models are then compared with the FEA results and the comparison results are shown in Figs. 8 and 9.

## References

- ↑ "[1]B.N. Leis, R.B. Francini, R. Mohan, D.L. Rudland and R.J. Olson, “Pressure-displacement behavior of transmission pipelines under outside forces towards a serviceability criterion for mechanical damage”, Proceedings of the 8th International Offshore and Polar Engineering Conference, Canada, 1998, 60-67. "
- ↑ "[9]S.-J. Hou, Q. Li, S.-Y. Long, X.-J. Yang and W. Li, “Design optimization of regular hexagonal thin-walled columns with crashworthiness criteria”, Finite Elements in Analysis and Design, 43, 2007, 555-565."