Definition of a beam-like reduced order model element by means of a mixed dimensional coupling

The use of Reduced Dimensional Models (RDM) discretized like beams, plates and shell elements drastically decreases the computational cost of solving a full 3D elastic problem with a Finite Element Method (FEM). However, its kinematic assumptions are only applicable to bodies with regular sections or continuous layouts. For the correct analysis of irregular regions, it is necessary to rely on bi-dimensional or solid models that fully reproduce the geometry of the body and its behavior but have a much higher computational cost. The Mixing Dimensional Coupling (MDC) technique allows linking models discretized with elements of different topologies, allowing the possibility of considering the most cost-effective model in each region. This coupling takes place at the interface that delimits both models and relies on the equilibrium of work and reactions on its two faces. In this paper, the formulation is presented for coupling beams with laminar sections and 2D Plane-Stress (PS) models demonstrating its proper behavior. Finally, this coupling is used for defining a new beam element, the Beam-Like Reduced Order Model (BLROM), which is obtained from a Plane-Stress model of their longitudinal section.