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# Best Method for Recovering Results at FEM Center of Gravity

## Best Method for Recovering Results at FEM Center of Gravity

(OP)
I want to track the accelerations for the CG of my spacecraft from frequency response analysis runs. This is is obviously not a physical point in the FEM though. I'm thinking an MPC of some sort is the approach to use, but unsure of the most accurate way to implement it. The simplest (as far as setup) method seems to just have a node at the CG and use an RBE3 spider out to every node in the FEM.

My concern is that this won't truly capture the response of the center of gravity since all the weighting on every independent node will be the same by default. In reality the weighting should be based on the mass of each node, correct? Perhaps with a fine enough mesh the difference is negligible? Is there a different approach entirely that anyone would suggest?

### RE: Best Method for Recovering Results at FEM Center of Gravity

One option is to create mass point at CG and connect it to spacecraft using RBE3 with complete mass of spacecraft at the CG. This can capture the exact acceleration at CG. But how the behavior of this mass point for frequency response is unknown, since I not tried this before in frequency response.

I am not Nastran user, so it may happen that there may be better tools available in software itself.

But why there is need to track imaginary point? IMO and guess, the resultant acceleration location should be close to CG.

### RE: Best Method for Recovering Results at FEM Center of Gravity

(OP)
I don't need a concentrated mass because all the mass is accounted for in the FEM itself. I just want to track the response of the spacecraft CG for notching/force limiting purposes for vibration testing predictions. There are design load factors we do not want to exceed on the overall spacecraft. Using the acceleration of the spacecraft CG to compare to these g-load limits seems the most appropriate. Maybe there is another method of recovering overall resultant acceleration that I am overlooking though?

### RE: Best Method for Recovering Results at FEM Center of Gravity

In RBE3 may be you can change the weighing factors by using constraint coefficients if you want. You need to check how that's done in Nastran. For RBE3 the the motion of master is average of slave nodes.

But there will be unnecessary constraints introduced in model due to RBE3. You can anyway try this on simple problem like plate or cylinder analysis and then once you are satisfied with results on simple problem you can implement it on spacecraft.

### RE: Best Method for Recovering Results at FEM Center of Gravity

Take a look at the MONDSP1 entry. It won't give you accelerations directly, only displacements, but in a frequency response analysis this is only a factor of omega^2 away.
DG

### RE: Best Method for Recovering Results at FEM Center of Gravity

Mr Rogers, did you find a good way to do this? Im trying to do this exact same thing: CG acceleration, frequency response analysis. I have heard of the method of using RBE3 or MPC to connect to all the nodes in the system, and then weighing each individual node with the nodal mass.

What about this. Can you create and RBE3 with the center (dependent) node at the CG, and place the legs (independent) at the system's interface locations. Each leg will result in individual interface forces & moments, which will then be balanced by the single point force & moments at the CG. Do you think that would work? Ive not tried this myself.

### RE: Best Method for Recovering Results at FEM Center of Gravity

(OP)

#### Quote (leonardober)

Mr Rogers, did you find a good way to do this? Im trying to do this exact same thing: CG acceleration, frequency response analysis. I have heard of the method of using RBE3 or MPC to connect to all the nodes in the system, and then weighing each individual node with the nodal mass.

I was overthinking it. It really just boils down to F = m*a since you want the CG's response. So use a CBUSH to recover the input force, and divide that by the total mass to get your net acceleration.

The issue with doing the RBE3 route is you would need to make sure each independent node's contribution is weighted by the mass associated with that node, otherwise it will not be technically correct. For instance if you have an area with a very fine mesh and an area with a very coarse mesh, the fine mesh will drive the dependent node's response disproportionately.

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