Talk by Mahmood Ettehad
On March 10th, 2021, Dr. Mahmood Ettehad (University of Minnesota) gave a talk about "Three Dimensional Elastic Frames: Rigid Joint Conditions in Variational and Differential Formulation" as part of the research seminar Analysis of the FernUniversität in Hagen.
We consider elastic frames constructed out of Euler-Bernoulli beams. Correct vertex conditions corresponding to rigid joints have been a subject of active interest in both mathematical and structural engineering literature, with consideration usually limited to planar frames. In this paper we will describe a simple process of generating joint conditions out of the geometric description of an arbitrary three-dimensional frame. The corresponding differential operator is shown to be self-adjoint. Furthermore, in the presence of symmetry, one can restrict the operator onto reducing subspaces corresponding to irreducible representations of the symmetry group. This decomposition is demonstrated in general planar frames and in a three dimensional example with rotational symmetry.
This is a joint work with G. Berkolaiko