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Time History Analysis Of 2D Frame Using MATLAB (El Centro)

Time History Analysis Of 2D Frame Using MATLAB (El Centro)

Time History Analysis Of 2D Frame Using MATLAB (El Centro)

(OP)
Hi,
Consider a 2D frame like below which excited by el Centro earthquake:



I'm Using Direct Time Integration To obtain response of structure. I verified my program with SAP200 when a Harmonic load applied in node2 and results are the same. but in this case, i.e. base excitation, i have a problem. Consistent Mass Matrix used here and following relation used in order to obtain nodal forces due to base excitation:
{fg}=-[M]*{Ag}*Ug
and We know that:
[M]{A}+[C]{V}+[K]{D}={fg}
in which [M]=Consistent Matrix (6x6 in this case), {Ag} = Influence Vector (6x1) which is zero except for horizontal degrees of freedom, i.e 4 & 7 that equals to 1. in other words {Ag}=[1,0,0,1,0,0].also Ug is a scalar number that equals to earthquake record data at time t. I wonder if this is Right or Wrong? i know somethings wrong with this because i can't get correct results. I really appreciate if you help me.
thanx...

RE: Time History Analysis Of 2D Frame Using MATLAB (El Centro)

(OP)
Ug in m/sec2 (earthquake acceleration)

RE: Time History Analysis Of 2D Frame Using MATLAB (El Centro)

(OP)
No...The Result differs from SAP.I know something's wrong with {fg}. I didn't find anything in Structural Dynamics books. most of them use modal analysis to this kind of analysis. sad

RE: Time History Analysis Of 2D Frame Using MATLAB (El Centro)

In that case your maths is wrong. in a linear system if you apply the accelerations to get the forces, then if you apply the forces you should get the accelerations.

Cheers

Greg Locock


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RE: Time History Analysis Of 2D Frame Using MATLAB (El Centro)

(OP)
thanx. Do you know a book,source or a computer program to find the right mathematical formulation?

RE: Time History Analysis Of 2D Frame Using MATLAB (El Centro)

It is not clear what is your mass matrix [M]; i.e. is it a global mass matrix, elemental mass matrix or just part attributed to the driven node?

One quick way to solve this (very crude) is to attach a large mass to your nodes 1 and 2, and then drive that mass with a force equal to "Large mass" * "ground acceleration".

RE: Time History Analysis Of 2D Frame Using MATLAB (El Centro)

I have the same probleme and i think that the problem is to use technique such static condensation méthod to resolve system

RE: Time History Analysis Of 2D Frame Using MATLAB (El Centro)

Quote:

Do you know a book, source or a computer program to find the right mathematical formulation?

It might take some finding, but it must be in Opensees somewhere.

http://opensees.berkeley.edu/


Doug Jenkins
Interactive Design Services
http://newtonexcelbach.wordpress.com/

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