LiU Electronic Press

# Konferensartikel

## Derivation of Arc Length of Helical Cable Element at Cable Bending, with Emphasize on Taylor Series Expansion of the Non-Integrable Infinitesimal Arc Length

Magnus Komperød
Technological Analyses Centre, Nexans Norway AS, Norway

Linköping Electronic Conference Proceedings 119:36, s. 357-367

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ISBN: 978-91-7685-900-1

ISSN: 1650-3686 (tryckt), 1650-3740 (online)

### Abstract

Elements of subsea cables and umbilicals can be classified as helical and non-helical. These two element types behave very differently at cable bending. This paper focuses on helical cable elements during cable bending. The arc length of helical elements at cable bending is derived, which leads to an integral that can not be solved analytically. When establishing strains and stresses of helical elements, it is essential that this integral is calculated with very high accuracy. An integration error of 0.01% is unacceptable in many applications. Maclaurin series expansion is used to convert this integral into an integral that can be solved analytically. It is proved that arbitrary integration accuracy can be achieved by increasing the order of the Maclaurin polynomial. Expressions for upper and lower boundaries of the integration error are also provided. The main advantage of the integration approach derived in this paper is that it provides an analytical expression for the integral, which can be used in mechanical analyses of cables and umbilicals.

### Nyckelord

Analytical Integration; Cross Section Analysis; Helical Cable Element; Maclaurin Series Expansion; Offshore Technology; Subsea Cable; Taylor&#8217;s Theorem; Umbilical

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