Structural Behavior of Umbilicals: Part I—Mathematical Modeling

Umbilicals for offshore application are very complex, since they combine elements of different mechanical behavior, such as steel tubes, thermoplastic hoses and power cores in a single structure, not to mention helically laid-up armouring layers and polymeric sheathes. This motivates continuous research on their mechanical modeling. This paper presents research undertaken in the structural behavior of umbilicals and focus on the mathematical modeling of the elements, which are gathered into concentric layers. Interaction between layers is included as well as helical lay-up of elements. The model here presented will be compared to a set of experimental results in a separate paper (Part II). An analytical model was developed combining equilibrium equations, geometric compatibility and constitutive relations to obtain a set of equations that describe the umbilical behavior under external loads. This set of equations is numerically solved to obtain contact pressures (or gaps) among layers, radial variations and strains in the elements (used to calculate the stresses). The model was built to be general in order to be able to cope with complex cross-sections designs often encountered. It was then implemented in a tailor made local analysis software, called UTILFLEX®. Both modeling and software resulted from a development program partnership between Prysmian Cables & Systems and University of Sa˜o Paulo. The paper will present modeling hypotheses and structural models that were used for steel tubes, hoses (thermoplastic and reinforced) and power cables and how the interaction among them has been treated.