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

Ladda ner artikelhttp://dx.doi.org/10.3384/ecp15119357

Ingår i: Proceedings of the 56th Conference on Simulation and Modelling (SIMS 56), October, 7-9, 2015, Linköping University, Sweden

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

Visa mer +

Publicerad: 2015-11-25

ISBN: 978-91-7685-900-1

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


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.


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


C. H. Edwards and D. E. Penney. Calculus and analytic geometry - 2nd edition. Prentice-Hall International Ltd., 1986.

J. J. Féret and C. L. Bournazel. Calculation of stresses and slip in structural layers of unbonded flexible pipes. Journal of Offshore Mechanics and Arctic Engineering, 109:263 – 269, 1987.

E. Kebadze. Theoretical modelling of unbonded flexible pipe cross-sections. PhD thesis, South Bank University, 2000.

M. Komperød, B. Konradsen, and R. Slora. Theoretical and practical considerations of helical cable elements subject to end effects at cable bending. In Proceedings of the ASME 2015 34th International Conference on Ocean, Offshore and Arctic Engineering OMAE 2015, 2015.

M. Lutchansky. Axial stress in armor wires of bent submarine cables. Journal of Engineering Industry, 91(3):687 – 693, 1969.

ProofWiki. Binomial theorem/general binomial theorem, 2015. URL www.proofwiki.org/wiki/Binomial_Theorem/General_Binomial_Theorem.

N. Sødahl, G. Skeie, O. Steinkjær, and A. J. Kalleklev. Efficient fatigue analysis of helix elements in umbilicals and flexible risers. In Proceedings of the ASME 29th International Conference on Ocean, Offshore and Arctic Engineering OMAE 2010, 2010.

G. Skeie, N. Sødahl, and O. Steinkjer. Efficient fatigue analysis of helix elements in umbilicals and flexible risers: Theory and applications. Journal of Applied Mathematics, 2012.

S. Sævik. On Stresses and Fatigue in Flexible Pipes. PhD thesis, Norwegian Institute of Technology, 1992.

G. B. Thomas, M. D. Weir, and J. Hass. Thomas’ calculus - global edition - 12th edition. Pearson Education, Inc., 2010.

Citeringar i Crossref