Co-rotational 3D beam element for nonlinear dynamic analysis of risers manufactured with functionally graded materials (FGMs)

This paper considers a co-rotational beam formulation for beams, which is used for the finite element analysis of flexible risers and pipelines made of functionally graded materials. The influence of material gradation is addressed using an exponential variation of properties throughout the thickness of the pipe. Space discretization of the equilibrium equations is derived based on the Euler–Bernoulli assumptions considering two-node Hermitian beam elements which are referred to a co-rotation coordinate system attached to the element local frame of coordinates. The geometric non-linear effects of the beam are considered under large displacement and rotations, but under small-strain conditions. The deflections of the riser result from forces caused by self-weight, buoyancy, sea currents, waves, the action of floaters, seabed-structure interactions, and ship's motion. We provide numerical examples and compare our results with the ones available in the literature. In addition, applications related to practical offshore engineering situations are considered to highlight the behavior of functionally graded materials (FGMs) as compared to homogeneous risers.