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Reducing the number of degrees of freedom for dynamic anal
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kajal.chopra
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PostPosted: Tue Aug 30, 2011 7:46 am    Post subject: Reducing the number of degrees of freedom for dynamic anal Reply with quote

I have been reading the book by Prof Anil K Chopra on Structural Dynamics. You might all be aware that Prof Chopra is from University of California Berkeley.
I have been reading the chapter 14, wherein the author talk of reducing the dynamic degrees of freedom using Rayleigh Ritz method.My question is, in commercial FE software , is the reduction of dynamic degrees of freedom practised?
If yes, what are the methods used? IS Rayl;eigh Ritz approiach used?
Kajal
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anshugoel
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PostPosted: Tue Aug 30, 2011 4:43 pm    Post subject: Re: Reducing the number of degrees of freedom for dynamic an Reply with quote

kajal.chopra wrote:
I have been reading the book by Prof Anil K Chopra on Structural Dynamics. You might all be aware that Prof Chopra is from University of California Berkeley.
I have been reading the chapter 14, wherein the author talk of reducing the dynamic degrees of freedom using Rayleigh Ritz method.My question is, in commercial FE software , is the reduction of dynamic degrees of freedom practised?
If yes, what are the methods used? IS Rayl;eigh Ritz approiach used?
Kajal


I think that is a very good question. My input is that generally reduction of DOF to make it manageable was done (in recent past) when computing resources were limited and a whole lot of DOF were identified to be less important than others. But with recent explosion of computing resources, practicing this method would be like bringing back slide rule.
To answer the question - I have used quite a few advanced software - but did not find any literature for it. I don't think it has been done.

Further Rayleigh ritz method is dependent on identifying generalized coordinates and formulating equations of motion - which should require intuition (for which computers are not exactly known for). This is my understanding. I can participate in further discussion to improve it (i.e. my understanding).

Thanks for initiating the topic.
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kajal.chopra
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PostPosted: Tue Aug 30, 2011 9:56 pm    Post subject: Reply with quote

Dear Mr.Anshu Goel,

I guess when we are doing a time integration and the time step is very small as regards the basic requirement of time stepping procedures, reduction in degrees of freedom is very much called for even in commercial software (I guess)

Please can the experts put in their views?

Kajal
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rahul.leslie
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PostPosted: Wed Aug 31, 2011 11:15 am    Post subject: Reply with quote

I have seen this option in ANSYS - it's Guyan reduction, I guess. It should be there in other packages too.
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kajal.chopra
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PostPosted: Wed Aug 31, 2011 12:03 pm    Post subject: Reply with quote

Hi Rahul,

what si the basis of the erduction in degrees of freedom or Guyon reduction or Static condensation??

Do they do the Rayleigh Ritz approach as in Chopra's book?

Kajal
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anshugoel
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PostPosted: Wed Aug 31, 2011 9:54 pm    Post subject: Reply with quote

rahul.leslie wrote:
I have seen this option in ANSYS - it's Guyan reduction, I guess. It should be there in other packages too.


To my understanding, Guyon reduction would be a mathematical technique for reducing the number of equations to be solved.  I don't know if it can be used for Rayleigh Ritz method.
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anshugoel
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PostPosted: Wed Aug 31, 2011 10:12 pm    Post subject: Reply with quote

kajal.chopra wrote:
Dear Mr.Anshu Goel,

I guess when we are doing a time integration and the time step is very small as regards the basic requirement of time stepping procedures, reduction in degrees of freedom is very much called for even in commercial software (I guess)

Please can the experts put in their views?

Kajal


By time integration, what is meant ?
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kajal.chopra
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PostPosted: Thu Sep 01, 2011 12:29 am    Post subject: Reply with quote

Dear Mr.Anshu Goel,

Refer chapter 5 of Chopra for time integration.

IF the equation of moton cannot be anlytically solved, as being the case when the force causing excitation varies with time arbitrarily (may not be harmonic) we need to resort to numerical schemes like explicit (central difference) or implicit (Newmark/Wilson approach).

One requirement of explicit method is time step should be very small.

Kajal
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Abishek_Siingh
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PostPosted: Thu Sep 01, 2011 3:35 am    Post subject: Reply with quote

Dear Ms. Kajal,

Static condensation is done to make our lives easy. If we do not have some mass associated with a defined degree of freedom, we can reduce our computational effort by reducing the degrees of freedom and just playing with the quantities we are actually interested in.

Generally the rotational degree of freedoms are condensed. If vertical degrees of freedom are included in the dynamic analysis then they can also be removed because generally the ground motion is horizontal (with low fequency and high amplitude) and again to make our lives easier with pen, we assume that the ground motion will not have any component that will excite the vertical degree of freedom or in other words the inertial effect associated with the building's vertical degree of freedom will be small.

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anshugoel
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PostPosted: Thu Sep 01, 2011 1:58 pm    Post subject: Reply with quote

kajal.chopra wrote:
Dear Mr.Anshu Goel,

Refer chapter 5 of Chopra for time integration.

IF the equation of moton cannot be anlytically solved, as being the case when the force causing excitation varies with time arbitrarily (may not be harmonic) we need to resort to numerical schemes like explicit (central difference) or implicit (Newmark/Wilson approach).

One requirement of explicit method is time step should be very small.

Kajal


My understanding is that these two are different things.

Firstly DOF reduction is for the purpose of reducing the number of equations to solve. Here the aim is to determine the response (capture it to double digits of precision).  

The second is for defining the excitation force exactly using numerical techniques - because analytic functions do not exist.

Third 'time integration' is a really bad nomenclature.  

Lastly even if the time step is small - our aim is to get the maximum/envelope of response.
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