It is common to find aerospace structural parts which behave in a one- or two-dimensional manner. This behaviour allows us to simplify the analysis, in comparison to that which would be required for a fully three-dimensional analysis, by treating these parts as beams, plates or shells. However, in certain cases we may not be able to reduce the dimension of the entire structure, but only a portion of it.
For example, in truss and frame structures, that are commonly found in aircraft wings, most of the structure exhibits a beam-like behaviour. However, around the joints connecting the beams we may find a more intricate 3D stress field. If we wish to capture the behaviour at the joints accurately, we must model them as 3D objects. Yet modelling the entire structure in 3D is very costly. We would like to utilize the 1D aspect of the beam-like substructures to simplify the model. Other examples for the need for a mixed-dimensional model exist in other fields of application, like medicine.
Lately various hybrid methods have been proposed for solving a coupled high- and low-dimensional problem. These methods involve a mechanism for coupling high- and low-dimensional models. Most of these methods have been developed and applied to static or steady state problems. The current work extends two of these methods to time-dependent wave problems. We will present the derivation and numerical implementation of the Nitsche and Panasenko coupling methods, as well as results of numerical experiments used assess their performance.
