Hybrid 3D-1D finite element modeling for elastodynamic bending

Complex 3D geometries analyzed using the finite element (FE) method often require fine discretization and involve many degrees of freedom (DOF), demanding substantial computational resources. To mitigate this, dimensional reduction techniques are applied, such as asymptotic analysis or integration through the thickness, to transform high-dimensional (HighD) models into more manageable low-dimensional (LowD) representations.
For instance, in the bending analysis of a wing, where understanding maximal bending and stress distribution at the wing-fuselage connection is crucial, a 3D model can be simplified using a 1D Euler-Bernoulli beam theory for global bending estimation. However, detailed strain and stress distribution necessitates a comprehensive 3D model, especially for analyzing structural strength at fixed wing ends.
A mixed-dimensional FE model integrating HighD and LowD sub-models can effectively address such cases, employing coupling methods to maintain continuity and accurately reduce variables along the HighD-LowD interface.
This study introduces a novel application of this approach: a 3D-1D hybrid model for elastodynamic time-harmonic bending problems. The coupling of sub-models was implemented using two different methods: the Panasenko-based approach and a newly developed 3D transition element (TE).
The effectiveness of both methods was demonstrated through simulations of a model that exhibits high stresses and strains. Panasenko-based model shows promising agreement with a full 3D reference model while significantly reducing computational costs due to fewer DOFs. However, the TE method was found to be unstable due to a locking phenomenon. Despite this unexpected discovery, it highlights an intriguing potential direction for future research.

The work is towards M.Sc. degree under the supervision of Prof. Dan Givoli, , Aerospace Engineering faculty, Technion – Israel Institute of Technology.