Hierarchical Beam Models coupling via the Arlequin Method

The Arlequin method is employed to combine beam elements based on different kinematic assumptions. Refined models are assumed only in those zones with a quasi-three-dimensional stress field reducing the computational costs. Variable kinematics beam elements are formulated on the basis of a Unified Formulation (UF). A N-order polynomials approximation is assumed on the beam cross-section for the unknown displacements, being N a free parameter of the formulation. Several hierarchical finite elements can be formulated. This formulation is extended to the Arlequin method to derive matrices related to the coupling zones between high and low order kinematic beam theories. Results are assessed towards Navier-type analytical models and three-dimensional finite element solutions. Numerical investigation have proved that Arlequin method in the context of a hierarchical formulation effectively couples subdomains having different order finite elements without loss of accuracy and reducing the computational cost.