Abstract: Modeling elastic frames constructed out of beam elements is of natural interest to engineers working on structural analysis discipline. From a more theoretical angle, this problem may be viewed as an analysis of a differential operator (Hamiltonian) acting on a metric graph in which the question of describing correct matching conditions is of central importance. We start this talk by considering three-dimensional elastic frames constructed out of Euler–Bernoulli beams and describe the notion of rigidity at a joint, i.e., the case in which relative angles of participating beams remain constant throughout the motion. Next, we discuss extension of matching conditions by relaxing the vertex-rigidity assumption and the case in which concentrated mass may exist. This generalization is based on coupling an (elastic) energy functional in terms of field’s discontinuities at a vertex along with purely geometric terms derived out of first principles. 

This talk is based on joint works with Gregory Berkolaiko (Texas A&M University) and Soohee Bae (Northeastern University).