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How to consider gravity in a dynamic analysis?

This question may be a little simple. But it confuses me.....

In my case,the analysis is a time-history analysis of a structure under earthquake.

First, gravity analysis, and then, dynamic analysis with constant gravity load (stress and deformation obtained by dynamic analysis will superimpose on those obtained by gravity analysis). However, if the structure is damage, the superimposition is not rational.

1. the equilibrium equation is Mx''+Cx'+Kdx = -Ma - Mg -R or Mx''+Cx'+Kdx = -Ma -R ??

2. is [do one step dynamic analysis (t->t+dt) and do one gravity analysis at the same time, and then superimpose them] rational?

3. if the 2. is not ture, How to consider gravity in a dynamic analysis?

If you are using ABAQUS, you can perform a static analysis followed by a dynamic analysis. You can import your deformed geometry and stress state before you run your dynamic analysis. Not all elements are supported - check the documentation. Perhaps other software will be able to do the same.

It is interesting that these analyses should be separated. It has been some time since I have run eaerthquake damage simulations myself, but it is a simple matter to show (e.g, through free body diagrams) that the equilibrium equation is x" + 2zwx' + wwx = f/m, where the gravitational body force is folded into the RHS.

The functional form you show  suggests you are doing a lumped mass type dynamic analysis (perhaps with damage softening and perhaps with associated damping changes). This system of equations can be well-treated with an explicit algorithm (e.g., Newmark) without the need to divorce a static calculation from a dynamic one. If this is a full structural finite element treatment, the situation does not appreciably change in terms of being able to do both analyses concurrently with an explicit integration algorithm.

Scott,

The question is not whether one should or should not separate the analysis into static and dynamic parts. It is a question of efficiency. When one applies the gravitational body force through an explicit algorithm, one needs to ramp up the gravity load slowly to minimize the inertial effects. Depending on the natural time scale of the problem of interest, this ramping of gravity load can be inordinately long for large 3-d finite element models. One can sometimes use a mass scaling technique to speed things up but in most cases, it is simply faster to solve the problem statically.

Hi,

Dynamics analysis should be departed from "equilibrium conditions" either in gravitational environment or not. Therefore, you should solve dynamics analysis out of gravity analysis (self weight ??). How to combine them? Save all results from gravity analysis and use them in dynamics analysis by considering zero gravity load.

 

 

hi ..this quesion always confused me .. but i think this better ans. for it

In my case,the analysis is a time-history analysis of a structure
under earthquake.

First, gravity analysis, and then, dynamic analysis with constant
gravity load (stress and deformation obtained by dynamic analysis
will
superimpose on those obtained by gravity analysis). However, if the
structure is damage, the superimposition is not rational.

1. the equilibrium equation is Mx''+Cx'+kdx = -ma - mg -R or
Mx''+Cx'+kdx = -ma -R ??

2. is [do one step dynamic analysis (t->t+dt) and do one gravity
analysis at the same time, and then superimpose them] rational?

3. if the 2. is not ture, How to consider gravity in a dynamic
analysis?

i hope it will you.

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