The Effect of Flexible Pipe Non-Linear Bending Stiffness Behavior on Bend Stiffener Analysis Available to Purchase

Bend stiffeners are critical components for flexible risers and umbilical cables employed to ensure a safe transition at the riser-vessel interface, avoiding overbending and accumulation of high cyclic fatigue damage. The analysis and design of bend stiffeners usually consider the system as a unique beam, in which the pipe bending response is linear. However, the structural mechanics of these complex layered structures is governed by internal friction mechanisms that yield non-linear moment versus curvature relationship. In fact, the pipe structure exhibits an approximately bi-linear hysteretic bending moment against curvature relationship arising from the progressive activation of friction and consequential slipping between adjacent layers. The flexible pipe bending stiffness substantially reduces after a given critical curvature (i.e., after slip between adjacent layers) is reached. In this paper, the effect of this flexible pipe non-linear response on the bend stiffener design is evaluated. The mathematical formulation and the solution methodology are presented. A set of four non-linear ordinary differential equations is obtained from geometrical compatibility, equilibrium of forces and moments and constitutive equations and a numerical solution is obtained using the shooting method. A finite element analysis is developed to validate the analytical model and to assess the effect of the radial clearance between the structures on the bend stiffener response. A case study is presented for some static loading conditions and it is observed that the bending stiffness bi-linear behavior may not affect the bend stiffener extreme load design results, but it may significantly influence the fatigue analysis.