Novel exact solution of elastic catenary and applications on floating wind turbine mooring systems

Abstract This research addresses the mathematical solution of the elastic catenary, a fundamental problem in offshore mooring engineering. A novel exact solution in a non-Lagrangian form is developed through rigorous mathematical derivation, distinguishing it from classical Lagrangian solutions. The procedure is described in detail, and the resulting expressions are applied to analyze the mooring system of a reference floating turbine. A general analytical approach is introduced to solve the transcendental equations associated with catenary mooring problems. The newly derived formulae exhibit greater applicability to geometry-to-force problems compared to existing Lagrangian expressions, making them particularly valuable for conceptual design and front-end engineering. In summary, this work provides valuable new insights into the exact solution of the elastic catenary, enhancing understanding and enabling practical applications in the field of floating wind turbines.