Summary. This article presents a natural frequency analysis performed with JuliaFEM -an open-source finite element method program. The results are compared with the analysis results pruduced with a commercial software. The comparison shows that the calculation results between the two programs do not differ significantly.

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.

An optimization routine was applied to high pressure fuel pipes to avoid resonance in a heavily vibrating environment. The optimization process and also the natural frequency calculations in every iteration were completely performed with the high-level programming language Julia; the optimization process was performed with the JuMP optimization environment, and the frequencies where calculated with JuliaFEM finite element method solver platform. The benefit of this kind of embedded implementation is a quick response which yields a pleasant development environment to focus on the essential-the choice of the optimization strategy.

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