Efficient Fatigue Analysis of Helix Elements in Umbilicals and Flexible Risers: Theory and Applications

Table 1

Typical elements used in modeling and analysis of axis-symmetrical response.

Element type	Assumption
Thin cylindrical element	Constant through thickness radial displacements; axial, circumferential, and in-plane shear strains: 𝜀𝑥𝑥, 𝜀𝜃𝜃, and 𝜀𝑥𝜃.
Thick cylindrical element	Logarithmic through thickness radial displacements; radial, axial, circumferential, and in-plane shear strains: 𝜀𝑅𝑅, 𝜀𝑥𝑥, 𝜀𝜃𝜃, and 𝜀𝑥𝜃.
Core element	Generalized cylinder element where the effect is expressed through and element stiffness matrix: 𝑘𝑖𝑗.
Helix element	Helix element with axial strains only: 𝜀011.
Helix element	Helix element with axial strains, curvatures, and torsional shear strains: 𝜀011, 𝜅2, 𝜅3, and 𝛾𝑠.