A modification of the rigid finite element method and its application to the J-lay problem

This article presents the Rigid Finite Element Method (RFEM), which allows us to take into account the flexibility of a system. Beam-like structures are analyzed, in which large deformations occur. The RFEM has been developed many years ago and successfully applied to practical engineering problems. The main difference between this method and the classical Finite Element Method (FEM) is the element deformation during analysis. In RFEM, the finite elements generated in a discretization process are treated as nondeformable bodies, whilst in FEM the elements are deformable; in RFEM, flexible, mass-less elements with properly chosen coefficients are introduced. A modification of the stiffness coefficients used in RFEM is proposed and explained in the article. It is shown how these new coefficients applied in RFEM lead to the same energy of deformation as in the case when the system is discretized by the classical FEM. This means that the energy of deformation is identical to that obtained in FEM, which leads to identical deformations of the elements. It is of particular importance that the RFEM is a much simpler method, faster in calculations and easier to learn and interpret. Furthermore, the generation of the inertia and stiffness matrices is much faster than in FEM. Another advantage is relatively easy implementation for multicore processor architecture. The calculation examples investigated cover some practical problems related to the offshore pipe laying process. The J-lay method is simulated by the use of the author's own computer model based on a modified RFEM. The model takes into account wave and sea current loads, hydrodynamic forces and material nonlinearity (plastic strains can develop during large deformation). The simulation results are compared with those obtained from the commercial package ANSYS.