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. This lecture is partially supported by the COST action Mathematical models for interacting dynamics on networks.


Show Abstract

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

Video of the talk

Liza Schonlau | 10.05.2024