The need to reduce the size of large discrete models is a reoccurring theme in computational mechanics in recent years. One situation which calls for such a reduction is that where the solution in some region in a high-dimensional computational domain behaves in a low-dimensional way. Typically, this situation occurs when the LowD (Low-Dimensional) model is employed as an approximation to the HighD (High-Dimensional) model in a partial region of the spatial domain. Then, one has to couple the two models on the interface between them. Fields of application where the scenario of LowD-HighD coupling is of special interest include, among others, blood-flow analysis, hydrological and geophysical flow models and elastic structures, where slender members behave in a 1D way, while joints connecting these members possess a 3D behavior. The hybrid HighD-LowD model, if designed properly, is much more efficient than the standard HighD model taken for the entire problem.
This work focuses on the coupling of two-dimensional (2D) and one-dimensional (1D) models in time-harmonic elasticity. The 2D and 1D structural regions are discretized by using 2D and 1D Finite Element (FE) formulations. Two important issues related to such hybrid 2D-1D models are: (a) the design of the hybrid model and its validation (with respect to the original problem), and (b) the way the 2D-1D coupling is done, and the coupling error generated. This research focuses on the second issue.
Several methods are adapted to the 2D-1D coupling scenario, implemented and compared numerically through a specially designed benchmark problem , as well as some more advanced problems.
