This paper presents a 3-dimensional finite element formulation for predicting the behaviour of complex umbilical cross-sections exposed to loading from tension, torque, internal and external pressure including bending. Helically wound armours and tubes are treated as thin and slender beams formulated within the framework of small strains but large displacements, applying the principle of virtual displacements to obtain finite element equations. Interaction between structural elements is handled by 2- and 3-noded contact elements based on a penalty parameter formulation. The model takes into account a number of features, such as material nonlinearity, gap and friction between individual bodies, and contact with external structures and with a full 3-dimensional description. Numerical studies are presented to validate the model against another model as well as test data.
S. Sævik. J. K. Ø. Gjøsteen. "Strength Analysis Modelling of Flexible Umbilical Members for Marine Structures." J. Appl. Math. 2012 (SI09) 1 - 18, 2012. https://doi.org/10.1155/2012/985349