Umbilical is a critical equipment in subsea production system for extracting offshore hydrocarbon resources, providing electrical and hydraulic power, control signal transmission and chemical injection. A diversity of components such as electrical cables, optical cables, steel tubes and filler bodies compose the cross-section of an umbilical. Different components perform different physical properties, so different cross-sections will present different geometrical characteristic, carrying capacities, thermal distribution, the cost and the ease of manufacture. Therefore, the cross-sectional design of the umbilical is a typical multi-objective optimization problem. The methodology of pseudo mechanical mechanism is introduced in this paper. Pseudo forces are assumed based on geometrical characteristics, carrying capacities and thermal productivities of different electrical cables, optical cables, steel tube and filler bodies. Each component is analogized to a sphere with different diameters on a funnel surface. Moreover, potential energy and interaction force between different components are defined to avoid the overlap and congestion. Then, the pseudo mechanical model is established and mathematics description is presented corresponding to the cross-section of an umbilical. Iteration algorithm procedure is given to solve this problem. Finally, a case of an umbilical is studied and the optimal cross-section is obtained, which is compared with the result used in practical engineering. It is shown that the methodology of the pseudo mechanical mechanism is effective to obtain the optimal design of cross-section of an umbilical.

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