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Using a FE static analysis instead of a FE transient analysis. Is it possible?

bxtsafe (Mechanical) (OP) 
15 May 12 14:08 
Dear friends,
Imagine that there is a component/structure that is subjected to one harmonic load with frequency W_{loading} and that I would like to make an assessment of fatigue life of it. Let's consider the load as F(t)= L_{max}*sin(W_{loading}*t). And imagine that the 1st natural frequency of this component/structure is W_{n,1st} in such a way that
W_{loading} = 0.25 * W_{n,1st}
I think the most accurate way to assess the fatigue life is to do a (linear) transient analysis using FEA (for example using the Superposition Method considering 4 or more modes). Then, use the stresses along the timehistory to assess the fatigue life, using rainflow counting, correction of mean stress and PalmgrenMiner.
Although, I would like to know if it is possible to do a static analysis instead of a transient one, because W_{loading} is relative lower than the W_{n,1st}. So, I thought that I could do a static analysis appling the load L_{max} in the component (in the same place and direction of the force F(t) ) and would obtain the displacements and stresses in the whole component. After that, I would calculate the Amplification Factor "AF" using the equation for 1 DOF system that is:
AF = 1/sqrt( (1(W_{loading}/W_{n,1st})^{2})^{2} + (2*zeta*W_{loading}/W_{n,1st})^{2} )
Where AF > 1 and let's consider zeta=0.03
So, I would multiply the component displacements and the component stresses by AF. So, will be these displacements and stresses (already amplified by AF), calculated by an static analysis, equal to the displacement/stresses of an FE transient analysis?


izax1 (Mechanical) 
16 May 12 9:42 
bxtguard
The fatigue life will not only depend on the first natural frequency of the system, but every frequency in the system (at least the lowest)How much the natural frequencies will contribute to the fatigue life is dependent on the load, load direction and mode shapes of the natural modes 

If the lowest natural frequency of your structure is at least twice the forcing frequency then a static analysis is acceptable. Actually even if this is not the case you can still do a static analysis using the amplification factor providing that your structure can be represented as a 1DOF system with reasonable accuracy.
I am a bit confused by your use of the term 'transient' What you describe as the forcing function is a harmonic load. When I think 'transient' I think of something like an impulse or a decaying sinusoidal function. However, if you are talking about a constant cyclic load (which I think of when I think fatigue) you don't need to do a transient analysis. You are not interested in what happens to your structure at every point in time. All you care about are the peak stresses. Compare the peak to your SN data and I think that is all you need. I am not familiar with rainflow counting and I have only used Miner with random vibration. 

We tend to use rainflow rather than anything else for fatigue, because our test fatigue loads are real world, not sinewave equivalents, the peak stresses are the killers (out of a 4 hour durability cycle there are maybe 30 impacts that actually crack things). Cheers
Greg Locock
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bxtsafe (Mechanical) (OP) 
17 May 12 11:26 
Thank for your answers guys!
In my question I tried to simplify the problem using an harmonic load as example. So, it's recommended to do an harmonic analysis instead of transient one, though it's also possible to do a transient analysis in harmonic loadings. I mentioned rainflow counting, correction of mean stress and PalmgrenMiner because, in fact, I'm thinking forward in a more general loading case, in which the loads have variable amplitude and mean different from zero.
Cheers! 



