Bend stiffener linear viscoelastic thermo-mechanical analysis, Part II: Numerical solution and case study

• Published in: Marine structures Vol. 77; p. 102947
• Main Authors: Gomez, Aynor J. Ariza, Caire, Marcelo, Torres, Luis Carlos Absalon Rojas, Vaz, Murilo Augusto
• Format: Journal Article
• Language: English
• Published: Barking Elsevier Ltd 01-05-2021; Elsevier BV
• Subjects: Bend stiffener; Boundary value problems; Case studies; Computer applications; Coordinate systems; Coordinates; Cyclic loading; Cyclic loads; Differential equations; Distribution; Domains; Energy dissipation; Energy exchange; Finite difference method; Flexible riser; Heat transfer; Iterative methods; Partial differential equations; Polyurethane; Polyurethane resins; Runge-Kutta method; Self-heating; Steady state; Steady state models; Temperature distribution; Temperature fields; Thermal analysis; Thermo-viscoelasticity; Thermomechanical analysis; Three dimensional models; Viscoelasticity; Thermo-viscoelasticity; Flexible riser; Self-heating; Bend stiffener
• ISSN: 0951-8339; 1873-4170
• DOI: 10.1016/j.marstruc.2021.102947

The viscoelastic energy dissipated by the bend stiffener when subjected to cyclic loading increases the polyurethane temperature and may affect the system curvature distribution in a coupled manner. The steady-state thermo-mechanical mathematical formulation and material experimental characterization has been presented in a companion paper (Part I). In this work (Part II), the rate of viscoelastic mechanical energy dissipation is obtained from the steady-state mechanical formulation employing the shooting method combined with the Runge–Kutta method for the two-point boundary value problem numerical solution. The temperature field distribution within the bend stiffener volume is then estimated with the three-dimensional steady-state thermal model employing the finite difference technique with a boundary-fitted coordinate system that transforms the physical domain into a structured computational domain grid. The partial differential equations governing heat transfer are solved in the computational domain and transformed back into the physical domain by transformation relations. A detailed description of the iterative thermo-mechanical numerical solution procedure is presented and a case study carried out demonstrating the loading frequency and oscillation amplitude influence on the bend stiffener temperature field distribution. It is shown that the bend stiffener may be exposed to high internal temperatures for some loading conditions.
•Bend stiffener viscoelastic dissipation is obtained with the shooting method.•The steady-state temperature field is calculated with a finite difference technique.•A boundary-fitted method is employed to generate a regular computational grid.•An iterative thermo-mechanical numerical procedure is presented.•High internal temperatures are observed in the case study for some loading conditions.