Coupled Analysis of a Spar Structure: Monte Carlo and Statistical Linearization Solutions

Abstract

The response of a combined dynamic system consisting of a Spar, a mooring line system, and top tension risers is presented. The top tension of a riser is provided by a buoyancy can that is laterally supported by a preloaded compliant guide. The overall system is nonlinear due to the mooring line restoring force, the friction between the buoyancy cans and the compliant guides, and the friction between the risers and the guides at the Spar keel. The friction between the Spar and the riser system is captured by a Coulomb model, whereas the stiffness of the mooring line system is accounted for by using a regression analysis of pertinent load versus displacement data. The combined model is numerically integrated using input time histories of force and moment that are compatible with a random representation (Jonswap spectrum) of a typical extreme environmental loading in the Gulf of Mexico. The input time histories of the force and the moment for the combined model are obtained at the center of gravity of the Spar by using a standard motion analysis program (MLTSIM). The numerical results of the time domain analysis of the combined model, in conjunction with ergodicity, are used for an associated Monte Carlo study. The Monte Carlo study provides useful information regarding the probability densities and the power spectra of various response components of the combined system. These results serve as a benchmark for additional analytical studies that use the technique of statistical linearization to derive equivalent linear stiffness and damping coefficients for the combined system.