Rakenteiden Mekaniikka (Journal of Structural Mechanics) Vol. 50, No 3, 2017, pp. 300 –303
https://rakenteidenmekaniikka.journal.fi/index https://doi.org/10.23998/rm.65040
The author(s) 2017.c
Open access under CC BY-SA 4.0 license.
Natural frequency calculations with JuliaFEM
Marja Rapo, Jukka Aho and Tero Frondelius1
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 re- sults pruduced with a commercial software. The comparison shows that the calculation results between the two programs do not differ significantly.
Key words: natural frequency analysis, JuliaFEM, finite element method
Received 21 June 2017. Accepted 14 August 2017. Published online 21 August 2017
Introduction
It is reasonable to survey free, fast and easy-to-use alternatives for FEM calculations [9].
JuliaFEM [3] is an open-source [2] finite element solver written in the Julia programming language [1] that offers a free alternative for commercial FEM programs. The JuliaFEM software library is a framework that allows for the distributed processing of large finite element models across clusters of computers using simple programming models.
This example demonstrates a JuliaFEM natural frequency [4, 6, 7] calculation for an example model.
The example model and results
The example model is a bracket that is attached from its bolt holes to two adapter plates via tie contacts [8]. The plates are constrained from one side as fixed. Figure 1 shows the model and the locations of the contacts and constraints. The material is linear and elastic in this calculation. The material parameters are E1 = 208 GPa, v1 = 0.3 and ρ1
= 7800 kg/m3 for the bracket and E2 = 165 GPa, v2 = 0.275 and ρ2 = 7100 kg/m3 for the adapter plates.
The calculated natural frequencies [5] in the first six eigenmodes are presented in Table 1 in two decimal places. Also the error when comparing the JuliaFEM results to the commercial software results is presented in Table 1. Figure 2 shows a picture of the first six eigenmodes of the bracket. The source code for the simulation is shown in listing 1.
1Corresponding author. tero.frondelius@wartsila.com
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Figure 1: The model and the locations of the contacts and constraints.
Figure 2: The first six Eigen modes of the Bracket.
Table 1: Natural frequencies of the modes 1-6 calculated with JuliaFEM and compared to the results of commercial software. The average of the absolute error is ∆¯f = 0.082, and the average relative error is ∆¯f/¯f= 0.026 %.
Mode f [Hz] JuliaFEM f [Hz] Commercial software ∆f ∆f / f
1 111.38 111.36 0.023 0.021 %
2 155.03 154.98 0.050 0.032 %
3 215.40 215.34 0.059 0.027 %
4 358.76 358.67 0.091 0.025 %
5 409.65 409.61 0.044 0.011 %
6 603.51 603.29 0.225 0.037 %
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Code Listing 1 JuliaFEM code 1 u s i n g J u l i a F E M
2 u s i n g J u l i a F E M . P r e p r o c e s s 3 u s i n g J u l i a F E M . P o s t p r o c e s s
4 u s i n g J u l i a F E M . A b a q u s : c r e a t e _ s u r f a c e _ e l e m e n t s 5
6 # read mesh
7 m e s h = a b a q u s _ r e a d _ m e s h (" L D U _ l d _ r 2 . inp ")
8 i n f o (" e l e m e n t s e t s = ", c o l l e c t ( k e y s ( m e s h . e l e m e n t _ s e t s ) ) ) 9 i n f o (" s u r f a c e s e t s = ", c o l l e c t ( k e y s ( m e s h . s u r f a c e _ s e t s ) ) ) 10
11 # create field problem with two different materials
12 b r a c k e t = P r o b l e m ( E l a s t i c i t y , " L D U _ B r a c k e t ", 3 ) 13 e l s 1 = c r e a t e _ e l e m e n t s ( mesh , " L D U B r a c k e t ")
14 e l s 2 = c r e a t e _ e l e m e n t s ( mesh , " A d a p t e r p l a t e 1 ", " A d a p t e r p l a t e 2 ") 15 u p d a t e !( els1 , " y o u n g s m o d u l u s ", 208 . 0E3 )
16 u p d a t e !( els1 , " p o i s s o n s r a t i o ", 0 . 30 ) 17 u p d a t e !( els1 , " d e n s i t y ", 7 . 80E - 9 )
18 u p d a t e !( els2 , " y o u n g s m o d u l u s ", 165 . 0E3 ) 19 u p d a t e !( els2 , " p o i s s o n s r a t i o ", 0 . 275 ) 20 u p d a t e !( els2 , " d e n s i t y ", 7 . 10E - 9 ) 21 b r a c k e t . e l e m e n t s = [ e l s 1 ; e l s 2 ] 22
23 # create boundary condition from node set
24 f i x e d = P r o b l e m ( D i r i c h l e t , " f i x e d ", 3 , " d i s p l a c e m e n t ") 25 f i x e d _ n o d e s = m e s h . n o d e _ s e t s [: F a c e _ C o n s t r a i n t _ 1 ]
26 f i x e d . e l e m e n t s = [ E l e m e n t ( Poi1 , [ nid ]) for nid in f i x e d _ n o d e s ] 27 u p d a t e !( f i x e d . e l e m e n t s , " d i s p l a c e m e n t 1 ", 0 . 0 )
28 u p d a t e !( f i x e d . e l e m e n t s , " d i s p l a c e m e n t 2 ", 0 . 0 ) 29 u p d a t e !( f i x e d . e l e m e n t s , " d i s p l a c e m e n t 3 ", 0 . 0 ) 30
31 " " " A h e l p e r f u n c t i o n to c r e a t e tie c o n t a c t . " " "
32 f u n c t i o n c r e a t e _ i n t e r f a c e ( m e s h :: Mesh , s l a v e :: String , m a s t e r :: S t r i n g ) 33 i n t e r f a c e = P r o b l e m ( Mortar , " tie c o n t a c t ", 3 , " d i s p l a c e m e n t ") 34 i n t e r f a c e . p r o p e r t i e s . d u a l _ b a s i s = f a l s e
35 s l a v e _ e l e m e n t s = c r e a t e _ s u r f a c e _ e l e m e n t s ( mesh , s l a v e ) 36 m a s t e r _ e l e m e n t s = c r e a t e _ s u r f a c e _ e l e m e n t s ( mesh , m a s t e r ) 37 n s l a v e s = l e n g t h ( s l a v e _ e l e m e n t s )
38 n m a s t e r s = l e n g t h ( m a s t e r _ e l e m e n t s )
39 u p d a t e !( s l a v e _ e l e m e n t s , " m a s t e r e l e m e n t s ", m a s t e r _ e l e m e n t s ) 40 i n t e r f a c e . e l e m e n t s = [ s l a v e _ e l e m e n t s ; m a s t e r _ e l e m e n t s ] 41 r e t u r n i n t e r f a c e
42 end 43
44 # call helper function to create tie contacts 45 t i e 1 = c r e a t e _ i n t e r f a c e ( mesh , 46 " L D U B r a c k e t T o A d a p t e r p l a t e 1 ", 47 " A d a p t e r p l a t e 1 T o L D U B r a c k e t ") 48 t i e 2 = c r e a t e _ i n t e r f a c e ( mesh , 49 " L D U B r a c k e t T o A d a p t e r p l a t e 2 ", 50 " A d a p t e r p l a t e 2 T o L D U B r a c k e t ") 51
52 # add field and boundary problems to solver
53 s o l v e r = S o l v e r ( Modal , bracket , fixed , tie1 , t i e 2 ) 54 # save results to Xdmf data format ready for ParaView visualization 55 s o l v e r . x d m f = X d m f (" r e s u l t s ")
56 # solve 6 smallest eigenvalues 57 s o l v e r . p r o p e r t i e s . nev = 6 58 s o l v e r . p r o p e r t i e s . w h i c h = : SM 59 s o l v e r ()
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Conclusion
The calculation results between the two programs do not differ significantly. On the basis of this example, it can be concluded that FEM calculations can be calculated with an open-source code instead of a commercial FEM software.
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Marja Rapo and Tero Frondelius W¨artsil¨a
J¨arvikatu 2-4 65100 Vaasa
marja.rapo@wartsila.com, tero.frondelius@wartsila.com
Jukka Aho
Global Boiler Works Oy Lumijoentie 8
90400 Oulu
jukka.aho@gbw.fi
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