Finite element modeling of nonsymmetrical cable cross-sections considering nonuniform radial loadings

Abstract

A new two-dimensional finite element model, named the REMCC (ring element model with contact constraint), is proposed for the analysis of radial deformations in an umbilical cable. This model accounts for material orthotropy and unsymmetrical geometry and loads. Each component of the cable is assumed to possess a circular cross-section and is modeled as a REMCC element having nodal degrees-of-freedom at all contacting points with adjacent components. A new numerical scheme is developed for forming the stiffness matrices of the REMCC elements. Axisymmetric two-dimensional ring elements are used to form the geometrical configuration of the REMCC element. with the aid of the penalty method for imposing displacement constraints, the unit displacement theorem is applied numerically for obtaining the stiffness matrix of the REMCC element with respect to its contact nodal points. Once the stiffness matrices of all the REMCC elements are generated, the normal global coordinate transformations and assembly procedures of the finite element method are applied to form the system of equations for the entire cable cross-section. Loads are then applied and the system equations are solved for the unknown displacements of the contact nodal points. The model is verified by several examples involving exact classical solutions and the test results obtained for an as-built cable.