Distributed dynamic response of a catenary mooring cable over an uneven seabed

Dynamic interaction between catenary mooring lines and uneven seabeds involves repeated contact transitions and localized mechanical responses that cannot be characterized by global fairlead tension alone. This study develops a contact-consistent continuum framework for the static-dynamic analysis of an elastic mooring cable subjected to time-varying current and prescribed fairlead motion over an uneven seabed. The static equilibrium is obtained using a residual-controlled boundary-value formulation with iterative contact updating and is transferred directly to a fixed graded mesh for transient analysis. The dynamic response is solved using a mixed P 1 / P 0 finite-element discretization, generalized- α integration, and active-set treatment of unilateral seabed contact, enabling distributed strain, shear force, curvature, velocity, and contact evolution to be resolved without dynamic remeshing. The static solution agrees closely with the elastic-catenary reference, while spatial and temporal refinement studies show satisfactory convergence. A limited comparison with MoorDyn yields comparable axial-strain levels for the examined cases. Parametric results show that cable diameter and axial stiffness mainly reduce strain, and current intensity primarily governs velocity and strain responses. The framework therefore provides a mechanics-oriented tool for resolving local mooring responses.