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

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

(OP)

Dear friends,

Imagine that there is a component/structure that is subjected to one harmonic load with frequency Wloading and that I would like to make an assessment of fatigue life of it. Let's consider the load as F(t)= Lmax*sin(Wloading*t).
And imagine that the 1st natural frequency of this component/structure is Wn,1st in such a way that

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 time-history to assess the fatigue life, using rainflow counting, correction of mean stress and Palmgren-Miner.

Although, I would like to know if it is possible to do a static analysis instead of a transient one, because Wloading is relative lower than the Wn,1st. So, I thought that I could do a static analysis appling the load Lmax 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:

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?

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

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

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

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 S-N 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.

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

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

(OP)

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 Palmgren-Miner 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!

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