A Three-Dimensional Curved Beam Element for Helical Components Modeling

The structural behavior of flexible pipes and umbilical cables is difficult to model due to their complex construction that includes components of different materials, shapes, and functions. Also, it is difficult to model due to the nonlinear interaction between those components, which includes contacts, gaps, and friction. To model a flexible pipe or umbilical cable, one can rely on analytical or numerical approaches. Analytical models need a large set of simplifying hypotheses. Numerical models, like classical finite elements models, require large meshes and have great difficulties to converge. But one can take profit of the particular characteristics of a specific component and develop a custom-made finite element that represents its structural behavior, a so-called finite macro-element. Adopting this approach, in a previous work, it was developed a cylindrical macro-element with orthotropic behavior, to model the plastic layers of a flexible pipe or umbilical cable. This paper presents a three-dimensional (3D) curved beam element, built to model a helical metallic component, which takes into account the effects of curvature and tortuosity of that kind of component. This is accomplished by using a strong coupling between displacements and assuming that the twist and shear strains vary linearly within the element, to avoid the shear lock phenomenon. The complete formulation of this element is presented. Results obtained with this formulation are also presented and compared to those obtained by a classical finite element modeling tool, with good agreement.