Rigorous Joining of Asymptotic Beam Models to Three-Dimensional Finite Element Models

The present paper presents a rigorous approach that can accurately and efficiently capture the linear, static and free-vibration behaviors of a beam-like structure by the rigorous combination of a one-dimensional beam model with a three-dimensional continuum model. This study focuses on coupling these disparate finite element types, putting them both into a single finite element model while making use of the asymptotically exact information available as part of the beam model, which itself is obtained by asymptotic dimensional reduction. The coupling is undertaken by use of appropriate transformation matrices at the interface together with stress and displacement recovery relations that are part of the beam theory. Results obtained from the so-called joined model" are compared with those from a finely meshed model using three-dimensional brick elements. It is demonstrated that the present approach provides accurate solutions for effects previously available only from three-dimensional models. However, because the joined model uses far fewer elements than a full three-dimensional model, the joined model is more efficient.