earthquake simulation with non-linearities and displacement spectrum? 1

[cbrn]

Hi everybody,
I'm new to the group and hope someone can help me find a way through this problem:
Earthquake simulation using transient analysis and ground displacements specified via a spectrum.

Objective: performing a transient analysis of a structure having intrinsic non-linearities, using earthquake-type prescribed displacements as given by a displacement spectrum.

Problem: no data is given for displacement as function of time. Normated data gives only acceleration as a function of frequency (=spectrum). With integration it is easy to write the displacement spectrum.

Question: is there a way to use the acceleration spectrum, or better displacement spectrum, to extract a s=s(t)?
I can not revert to Harmonic Response because of the structure's non-linearities.

Thanks in advance.

 

[Drej]

> Question: is there a way to use the acceleration spectrum, or better displacement spectrum, to extract a s=s(t)?
I can not revert to Harmonic Response because of the structure's non-linearities.

Are there two questions here?

1) If you want to use a time-history which is time-displacement, then you have no problem. I assume by s=s(t) you want secondary response spectra (SRS) from your model? You can use the displacement spectrum in a non-linear transient analysis (you can also use the acceleration, but it is messy). You will have to *VREAD your time history data into an ANSYS "table" (see *DIM command) from your raw text data (search the ANSYS archives here for *VREAD). Once you have this data in a table you can then apply this as a "D" command (D,node,label,value) by inputting the name of the table in % marks (e.g. D,1,UX,%table_name%) and run your transient analysis.

The structure is:

*DIM,.....,
*VREAD,...,
D,.....,


2) On the other hand, if you have an acceleration-frequency spectra, and you want to convert this to displacement-time, this is not easy in ANSYS (but it is possible with knowledge of the original data), and you may lose some of the data integrity in the transfer. Also, you cannot directly integrate acceleration wrt frequency, because this does not give you velocity or displacement. You need to integrate wrt time. If all you have is frequency-acceleration (response spectrum), then unfortunately your analysis is limited to the frequency domain, which means linear.


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[cbrn]

Thank you Drej.
I feared it would not be simple... I'll explain a little bit more clearly what I wanted to do, wrt to your answers:

1) this case is not appliable to my data because I don't have the D=D(t) functions for ground excitation wrt time (I previously wrote s=s(t) using the "math-world" notation for "displacement"). I have the D=D(f) ground spectra wrt frequency. No problem with handling tables, but the problem is that I haven't got a "time-history" ground excitation. So we come directly to your point number 2...:

2) The starting point is exactly a set of acceleration amplitude-versus-frequency spectra (one for vertical, one for horizontal). From this, I already calculated the corresponding set of displacement amplitude-versus-frequency spectra. For this, I used a formula given by the Norms to which I am refering for the rest of the analysis. Now, the core problem:
from these spectra, I should extract a discrete number of frequencies and give to them the corresponding amplitude and phase (then sum them altogether to get the displacement-versus-time waveform). The best way I know is using Inverse Fourier Transform, but what about the phase since I haven't information about it? Possibly I could reconstruct the "signal" with random phases, but I wonder if it's correct. The response of the structure should be influenced by it...

Btw, I made a mistake writing "can not revert to Harmonic Response", I wanted to say "... to Spectrum Analysis".

Bye, thanks!

 

[Drej]

Interesting problem.

> The best way I know is using Inverse Fourier Transform, but what about the phase since I haven't information about it? Possibly I could reconstruct the "signal" with random phases, but I wonder if it's correct. The response of the structure should be influenced by it...

Correct. You'll need to know the amplitude, phase and the length of the record and the sample rate. You can do the inverse FFT in ANSYS using the *MFOURI command and using the EVAL label.

! t_COEFF is the INPUT amplitude phase amplitude phase...
! mode is 0 1 1 2 2... number of frequencies
! ISYM 0 1 -1 1 -1... this tells ANSYS the form of t_COEFF i.e. 0 amplitude phase amplitude phase...
! THETA = 0 1 2... 360 degrees
! curve = OUTPUT (amplitude)
*MFOURI,EVAL,t_COEFF(1),mode(1),isym(1),theta(1),curve(1)

t_coeff, mode and ISYM are the same size column matrix, as are theta and curve. Once you've got the amplitudes, you'll need to do some more calculation to find the peak amplitudes from the above, and then you'll need the original time axis data to plot it against - which is a problem!

If you don't feel as though you can do it in ANSYS and you need some more theory on the FFT side of things, please post in forum384 where someone will help you specifically for this.

Cheers.


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[cbrn]

Drej,
I'll follow your suggestions about *MFOURI. I already had a look to this function in the help but I got completely confused as regards the contents of the matrices! Now it's clear.
As regards phase, I fear that the best I can do is to have Excel generate a random list. Then I'll try to estimate the uncertainty associated with the fact that the random-generated phases could lead to a waveform that is "less critical" for the structure.
On the other side, being the normated data for earthquake independent from any structure, probably I can get rid of this concern and simply rely on the security factor.

Btw, as the spectra are piecewise curves described by analytical formulas, and as I know the statistical time duration of the normated earthquake, I can choose my sampling rate just like I need.

I'll let you know if I come to something "interesting" (i.e. feasible!)

Many thanks, bye!