• Corpus ID: 244799408

On Vertex Conditions In Elastic Beam Frames: Analysis on Compact Graphs

@inproceedings{Bae2021OnVC,
  title={On Vertex Conditions In Elastic Beam Frames: Analysis on Compact Graphs},
  author={S. R. Bae and Mahmood Ettehad},
  year={2021}
}
We consider three-dimensional elastic frames constructed out of Euler-Bernoulli beams and describe extension of matching conditions by relaxing the vertex-rigidity assumption and the case in which concentrated mass may exists. 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. The corresponding differential operator is shown to be self-adjoint. Although for… 

Figures from this paper

On the Spectra of Periodic Elastic Beam Lattices: Single-Layer Graph

We present full description of spectra for a Hamiltonian defined on periodic hexagonal elastic lattices. These continua are constructed out of Euler-Bernoulli beams, each governed by a scalar-valued

References

SHOWING 1-10 OF 45 REFERENCES

Three‐dimensional elastic beam frames: Rigid joint conditions in variational and differential formulation

We consider three‐dimensional elastic frames constructed out of Euler–Bernoulli beams and describe a simple process of generating joint conditions out of the geometric description of the frame. The

On the Spectra of Periodic Elastic Beam Lattices: Single-Layer Graph

We present full description of spectra for a Hamiltonian defined on periodic hexagonal elastic lattices. These continua are constructed out of Euler-Bernoulli beams, each governed by a scalar-valued

Mechanics of Materials with Periodic Truss or Frame Micro-Structures

This paper describes the mechanics of materials with periodic skeletal micro-structures in infinite domains. The principal technical results consist of certain Korn-type inequalities that provide

A Hierarchy of Plate Models Derived from Nonlinear Elasticity by Gamma-Convergence

We derive a hierarchy of plate models from three-dimensional nonlinear elasticity by Γ-convergence. What distinguishes the different limit models is the scaling of the elastic energy per unit volume

Spectrum of a network of Euler–Bernoulli beams

A finite element method for quantum graphs

It is shown that a combination of Schur complement reduction and diagonally preconditioned conjugate gradients results in optimal complexity for model elliptic problems and a wide class of graphs.

Modelling of dynamic networks of thin thermoelastic beams

We derive a distributed-parameter model of a thin non-linear thermoelastic beam in three dimensions. The beam can also be initially curved and twisted. Our main task is to formulate the

Exact boundary controllability on a tree-like network of nonlinear planar Timoshenko beams

This paper concerns a system of equations describing the vibrations of a planar network of nonlinear Timoshenko beams. The authors derive the equations and appropriate nodal conditions, determine

Bloch principle for elliptic differential operators with periodic coefficients

Differential operators corresponding to elliptic equations of divergent type with 1-periodic coefficients are considered. The equations are put in Sobolev spaces with an arbitrary 1-periodic Borel