Implementing model reduction to the JuliaFEM platform

Abstract

JuliaFEM is an open source nite element method solver written in the Julia language. This paper presents an implementation of two common model reduction methods: the Guyan reduction and the Craig-Bampton method. The goal was to implement these algorithms to the JuliaFEM platform and demonstrate that the code works correctly. This paper rst describes the JuliaFEM concept briey after which it presents the theory of model reduction, and nally, it demonstrates the implemented functions in an example model. This paper includes instructions for using the implemented algorithms, and reference the code itself in GitHub. The reduced stiness and mass matrices give the same results in both static and dynamic analyses as the original matrices, which proves that the code works correctly. The code runs smoothly on relatively large model of 12.6 million degrees of freedom. In future, damping could be included in the dynamic condensation now that it has been shown to work.

The MFrontGenericInterfaceSupport project

“…JuliaFEM (Aho et al, 2019a(Aho et al, , 2019bRapo, Aho, & Frondelius, 2017;Rapo, Aho, Koivurova, & Frondelius, 2018;Rapo et al, 2019) is an open-source finite element solver written in the Julia programming language (Bezanson, Edelman, Karpinski, & Shah, 2017). JuliaFEM enables flexible simulation models, takes advantage of the scripting language interface, which is easy to learn and embrace.…”

Pipe route optimization to avoid undesired vibration by using JuliaFEM

“…The optimization procedure was completed with JuMP [2], an optimization environment written in the fast and high-level programming language Julia [3]. JuliaFEM, a Finite Element Method framework also written in the Julia language, was used to create the mesh with 3D structural beam elements and also to solve the natural frequencies of the pipe route alternatives during the optimization [4][5][6][7]. In other words, the chosen approach allows the whole optimization procedure to be performed within the Julia programming environment.…”

Introduction to JuliaFEM, an open source FEM solver

“…JuliaFEM [1][2][3] is a new finite element method solver programmed using Julia. It evolved from the research and development conducted by Wärtsilä.…”

“…In JuliaFEM, a concept called Analysis is defining the further operation which should be performed to the linear system. Currently, JuliaFEM supports quasistatic and dynamical analysis, natural frequency analysis and model reduction using Craig-Bampton method [2,3].…”

“…This kind of approach allows for an extremely modular program structure as the new features can be implemented on their own GitHub projects, see e.g. ModelReduction.jl [2], and finally, they can be imported to the meta-package JuliaFEM. jl with minimal changes to the old code, probably only having one import line like using ModelReduction.…”