Variable kinematic beam elements coupled via Arlequin method

In this work, beam elements based on different kinematic assumptions are combined through the Arlequin method. Computational costs are reduced assuming refined models only in those zones with a quasi-three-dimensional stress field. Variable kinematics beam elements are formulated on the basis of a unified formulation (UF). This formulation is extended to the Arlequin method to derive matrices related to the coupling zones between high- and low-order kinematic beam theories. According to 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. Part of the structure can be accurately modelled with computationally cheap low-order elements, part calls for computationally demanding high-order elements. Slender, moderately deep and deep beams are investigated. Square and I-shaped cross-sections are accounted for. A cross-ply laminated composite beam is considered as well. Results are assessed towards Navier-type analytical models and three-dimensional finite element solutions. The numerical investigation has shown that Arlequin method in the context of a hierarchical formulation effectively couples sub-domains having different order finite elements without loss of accuracy and reducing the computational cost.