Extracting loads from measured strains

[vorwald]

I have a NASTRAN model, and will be recieving time histories of a number of strain gages for a number of tests. The objective is to calculate the fatigue life thoughout the part. Has anyone correlated their NASTRAN FEM with time history without having the applied load? Can you send me references / code.

For the time being, I am planning on calculating the frequency response of the measured strains. Then I'm going to write some code to optimize the force amplitudes and phases (at some interface nodes) and optimize the modal damping to get the NASTRAN output to match the strain gages at as many locations as possible. Once I have the "best" match, I will look for the peak stresses and use that for fatigue life. Does anyone have any opinions on the strenghts / weaknesses of this approach.

 

[freebody]

Correlating measured strain data to a finite element model can be extremely tricky, especially if the applied loads are unknown. Also, other influential factors include modeling details of your parts, measured strains in high gradient areas, mechancal attachment assumptions, etc...

I have been able to correlate detailed redundant support structure only to a limited degree. (Without precise known applied loads) What has helped to a certain extent is to determine stiffness "coefficients" near measured strain areas (based on unit loads applied to your finite element model) and performing a regression analysis to optimize your applied loads. This helped with strain correlation in some part areas but hurt in others.

I am interested in the details of the approach you mentioned as well as others experience.

-George

 

[jvorwald]

Now that I have recieved/reviewed the measured data, the situation is quite a bit worse than I had anticipated.

George, previously I have correlated against measured strains at discrete frequencies. I used an optimization routine because I was varying the modal damping in addition to addjusting the load input. Using influence coefficents as you described is a good idea. Also, the load path was well defined in my previous applications.

In the current problem, the response is broadband even though the load is applied at ~18 Hz. The load appears to be shock type (gun firing), so it is exicting the structure between 180 to 400 Hz. Also, several of the strain gauges are responding like a damped, single-dof-system. However, they are responding at different frequencies (167, 250, 310, 400) which are not all multiples of 18 Hz.

Things that I have done
a) Did cycle count and applied miner's rule to the measured strain. Strains are below the level that causes fatigue damage, so part has infinte life.
a) Calculated frequency response (doesn't help too much, shows the response is broadband)
b) Calculated coherence between gauges (may help, clearly identifies where the frequency ranges where the gauges have high coherence. Possibly this implies structural modes.
c) Used the nastran model to calculate mode shapes up to 400 Hz (37 modes). Divided the maximum stress in the mode shape by the stress at the gauge location, and plotted vs frequency. The values depend on the gauge, but the averages range from about 30 to 120.
d) Showed that a modal amplification factor (Maximum stress divided by gauge stress for a NASTRAN mode) of 10 results in an unacceptable fatigue life.
e) Fitted a single dof equation,
d2x/dt2+2*zeta*wn*dx/dt+wn^2*x = g(t), and calculated damping, natural frequency, and g(t) for one of the gauges.

Things I would like to do
a) 3 of the strain gauges are on primary load paths, but not in the direction of the primary load. Also, there is a 4th primary load path that is not gauged, and numerous secondary load paths. Use the 3 primary loads as inputs, and the large response strain gauges as outputs, and a routine like N4SID to calculate the linear function relating the inputs/output/states. If the predicted response matches the measured response, determine how much of the response is due to input vs natural frequencies.
b) Use coherence between the gauges to identify the strain mode shape. Compare back to NASTRAN modes to (hopefully) identify which modes are responding at that high frequency.
c) In NASTRAN, modify the frequencies of the modes from step b (I've done this before) to the estimated value from data. Apply shock time history loads to NASTRAN. Optimize the shape of the shock time history, and the modal damping to generate the measured strains.

Unresolved problems are
a) On the one hand, the simple cycle count/miner's rule shows large life. On the other hand, the response has clear, damped, cyclic response. Estimates of the maximum stress indicates that the part would have a very short life.
b) Currently, the data supports the hypothesis that structural modes are being excited. How to prove this definatively. An alternate explanation is that the load support structure modes are being excited, and the primary structure is just responding to inertia forcing.
c) Currently, the NASTRAN estimation of the amplification factors are quite a bit higher than allowed, resulting in a high oscillatory stress and a very low fatigue life. The system has been in field use for a few months, and there hasn't been a fatigue failure.

 

[jetmaker]

jvorwald,

The question of calculating loads is nearly impossible if the loading is multiaxial and you are recording strains in a region that is affected by the multiaxial loading. Look for regions where the strain is governed predominatly by axial loading. If you are using linear static analysis, simply apply a unit load, look at the reported strain, then compare against your actual strain. There ratio of the difference is how much you need to scale up the load to get the proper strain. This only works for linear elastic static analysis, in which the results are scalable.

Regards,

jetmaker

 

[vorwald]

I have the wrap up discussion of this problem under thread

"Damage from modal amplificaiton of stress"
thread 384-82721

in
Mechanical Acoustics/Vibration engineering Forum

Cheers
J. Vorwald