Derivation of a new stiffness matrix for helically armoured cables considering tension and torsion

Abstract

SUMMARYA new element stiffness matrix is derived for straight cable elements subjected to tension and torsion. The cross-section of a cable, which may consist of many different structural components, is treated in the following as a single composite element. The derivation is quite general; consequently, the results can be used for a broad category of cable configurations. Individual helical armouring wires, for instance, may have unique geometric and material properties. In addition, no limit is placed on the number of wire layers. Furthermore, compressibility of the central core element can also be considered. The equations of equilibrium are first derived to include 'internal' geometric non-linearities produced by large deformations (axial elongation and rotation) of a straight cable element. These equations are then linearized in a consistent manner to give a linear stiffness matrix. Linear elasticity is assumed throughout. Excellent agreement with experimental results for two different cables validates the correctness of the analysis.

Analytical and finite element modelling of the elastic–plastic behaviour of metallic strands under axial–torsional loads

“…In fact, several authors (e.g. : [20], [23], [4]) have shown that, during the axial-torsional loading of the strand: (a) the core is subjected to the same elongation of the strand, and (b) the external wires undergo a transformation which preserves the geometrical shape of their centerline. Accordingly, the deformed centerline of the external wires is a circular helix, possibly characterized by different radius and pitch with respect to the reference configuration.…”

“…Within this context, analytical formulations (see e.g. [4]) have been developed to estimate both the stress state of 20 wires as well as global response parameters, such as the coupled axial-torsional cross sectional stiffness matrix. Only few works, instead, considered the evolution of plastic deformations under axial-torsional loads.…”

Proceedings of the 58th Conference on Simulation and Modelling (SIMS 58) Reykjavik, Iceland, September 25th – 27th, 2017

“…Mechanical cable analyses date back to at least half a century ago, with publications written in the 1960s and 1970s still being highly relevant today, such as Lutchansky (1969) and Knapp (1979). Over the later decades the field has matured through improved modeling and by including new considerations in the analyses.…”

Thermal Characteristics for Cross-sectional Design of the Integrated Production Umbilical

“…Finite element models (FEMs) based on macro-elements have been used for the cross-sectional analysis. Recently, finite element analysis (FEA) based on commercial software was introduced to the crosssectional analysis [4,5]. However, not much effort has been made on the design and analysis of the cross-sectional layout.…”