FinEtoolsRapidEig.jl: Using Coherent Node Cluster model reduction to calculate free vibration frequencies and mode shapes.
Paper accepted for publication as NME-Jul-19-0522.R1 - Rapid Free-vibration analysis with Model Reduction based on Coherent Nodal Clusters, in the International Journal for Numerical Methods in Engineering, 03/03/2020. Authors: Krysl, Petr, and Sivapuram, Raghavendra; both of University of California, San Diego , Jacobs School of Engineering Department of Structural Engineering; and Abawi, Ahmad, of Heat, Light, and Sound Research, Inc.
Abstract: Modal expansion is a workhorse used in many engineering analysis algorithms. One example is the coupled boundary element-finite element computation of the backscattering target strength of underwater elastic objects. To obtain the modal basis, a free-vibration (generalized eigenvalue) problem needs to be solved, which tends to be expensive when there are many basis vectors to compute. In the above mentioned backscattering example it could be many hundreds or thousands. Excellent algorithms exist to solve the free-vibration problem, and most use some form of the Rayleigh-Ritz (RR) procedure. The key to an efficient RR application is a low-cost transformation into a reduced basis. In this work a novel, inexpensive a priori transformation is constructed for solid-mechanics finite element models based on the notion of coherent nodal clusters. The inexpensive RR procedure then leads to significant speedups of the computation of an approximate solution to the free vibration problem.
Use the Git
git clone https://gitlab.com/PetrKrysl/FinEtoolsRapidEig.git
to clone the repository into some suitable folder. This will create the folder FinEtoolsRapidEig.
The Julia environment needs to be initialized. This first part is best done by running Julia without starting up multiple workers. Change the current folder to be FinEtoolsRapidEig. Start Julia and run
using Pkg; Pkg.activate("."); Pkg.instantiate()
For instance for the aluminum cylinder example (folder alucyl) change the working folder to this directory
cd(".\\examples\\alucyl")
Unzip the meshes
unzip meshes.zip
Now run the file alu_cyl_full.jl
include("alu_cyl_full.jl")
and then the file alu_cyl_red.jl
include("alu_cyl_red.jl")