MIXED-DIMENSIONAL MODELING FOR TIME-HARMONIC ELASTIC BENDING PROBLEMS

In a time-harmonic setting, coupling of a high-dimensional [HighD-two-dimensional (2D) or three-dimensional (3D)] sub-model and a low-dimensional (LowD, 1D) sub-model (reduced from the former when circumstances allow such a reduction) is considered, forming a hybrid mixed-dimensional model. In particular, the coupling of 2D or 3D elasticity with a Bernoulli-Euler beam is under investigation for time-harmonic bending problems. A finite element scheme is applied, where the HighD part is modeled via standard isoparametric elements, and the LowD part is provided with C<sup>1</sup> continuity by using Hermite-cubic elements. The paper proposes special procedures performed at the discrete level to couple the two sub-domains. Continuity of the displacements and bending rotations is partially enforced strongly and partially weakly. The performance of the method is illustrated by several numerical examples.